Daily Papers

Reconstructing dynamic objects from monocular videos is a severely underconstrained and challenging problem, and recent work has approached it in various directions. However, owing to the ill-posed nature of this problem, there has been no solution that can provide consistent, high-quality novel views from camera positions that are significantly different from the training views. In this work, we introduce Neural Parametric Gaussians (NPGs) to take on this challenge by imposing a two-stage approach: first, we fit a low-rank neural deformation model, which then is used as regularization for non-rigid reconstruction in the second stage. The first stage learns the object's deformations such that it preserves consistency in novel views. The second stage obtains high reconstruction quality by optimizing 3D Gaussians that are driven by the coarse model. To this end, we introduce a local 3D Gaussian representation, where temporally shared Gaussians are anchored in and deformed by local oriented volumes. The resulting combined model can be rendered as radiance fields, resulting in high-quality photo-realistic reconstructions of the non-rigidly deforming objects, maintaining 3D consistency across novel views. We demonstrate that NPGs achieve superior results compared to previous works, especially in challenging scenarios with few multi-view cues.

We present a novel appearance model that simultaneously realizes explicit high-quality 3D surface mesh recovery and photorealistic novel view synthesis from sparse view samples. Our key idea is to model the underlying scene geometry Mesh as an Atlas of Charts which we render with 2D Gaussian surfels (MAtCha Gaussians). MAtCha distills high-frequency scene surface details from an off-the-shelf monocular depth estimator and refines it through Gaussian surfel rendering. The Gaussian surfels are attached to the charts on the fly, satisfying photorealism of neural volumetric rendering and crisp geometry of a mesh model, i.e., two seemingly contradicting goals in a single model. At the core of MAtCha lies a novel neural deformation model and a structure loss that preserve the fine surface details distilled from learned monocular depths while addressing their fundamental scale ambiguities. Results of extensive experimental validation demonstrate MAtCha's state-of-the-art quality of surface reconstruction and photorealism on-par with top contenders but with dramatic reduction in the number of input views and computational time. We believe MAtCha will serve as a foundational tool for any visual application in vision, graphics, and robotics that require explicit geometry in addition to photorealism. Our project page is the following: https://anttwo.github.io/matcha/

In this paper we present a high fidelity and articulated 3D human foot model. The model is parameterised by a disentangled latent code in terms of shape, texture and articulated pose. While high fidelity models are typically created with strong supervision such as 3D keypoint correspondences or pre-registration, we focus on the difficult case of little to no annotation. To this end, we make the following contributions: (i) we develop a Foot Implicit Neural Deformation field model, named FIND, capable of tailoring explicit meshes at any resolution i.e. for low or high powered devices; (ii) an approach for training our model in various modes of weak supervision with progressively better disentanglement as more labels, such as pose categories, are provided; (iii) a novel unsupervised part-based loss for fitting our model to 2D images which is better than traditional photometric or silhouette losses; (iv) finally, we release a new dataset of high resolution 3D human foot scans, Foot3D. On this dataset, we show our model outperforms a strong PCA implementation trained on the same data in terms of shape quality and part correspondences, and that our novel unsupervised part-based loss improves inference on images.

We propose a novel 3D morphable model for complete human heads based on hybrid neural fields. At the core of our model lies a neural parametric representation that disentangles identity and expressions in disjoint latent spaces. To this end, we capture a person's identity in a canonical space as a signed distance field (SDF), and model facial expressions with a neural deformation field. In addition, our representation achieves high-fidelity local detail by introducing an ensemble of local fields centered around facial anchor points. To facilitate generalization, we train our model on a newly-captured dataset of over 5200 head scans from 255 different identities using a custom high-end 3D scanning setup. Our dataset significantly exceeds comparable existing datasets, both with respect to quality and completeness of geometry, averaging around 3.5M mesh faces per scan. Finally, we demonstrate that our approach outperforms state-of-the-art methods in terms of fitting error and reconstruction quality.

High-fidelity human 3D models can now be learned directly from videos, typically by combining a template-based surface model with neural representations. However, obtaining a template surface requires expensive multi-view capture systems, laser scans, or strictly controlled conditions. Previous methods avoid using a template but rely on a costly or ill-posed mapping from observation to canonical space. We propose a hybrid point-based representation for reconstructing animatable characters that does not require an explicit surface model, while being generalizable to novel poses. For a given video, our method automatically produces an explicit set of 3D points representing approximate canonical geometry, and learns an articulated deformation model that produces pose-dependent point transformations. The points serve both as a scaffold for high-frequency neural features and an anchor for efficiently mapping between observation and canonical space. We demonstrate on established benchmarks that our representation overcomes limitations of prior work operating in either canonical or in observation space. Moreover, our automatic point extraction approach enables learning models of human and animal characters alike, matching the performance of the methods using rigged surface templates despite being more general. Project website: https://lemonatsu.github.io/npc/

We present Articulated Kinematics Distillation (AKD), a framework for generating high-fidelity character animations by merging the strengths of skeleton-based animation and modern generative models. AKD uses a skeleton-based representation for rigged 3D assets, drastically reducing the Degrees of Freedom (DoFs) by focusing on joint-level control, which allows for efficient, consistent motion synthesis. Through Score Distillation Sampling (SDS) with pre-trained video diffusion models, AKD distills complex, articulated motions while maintaining structural integrity, overcoming challenges faced by 4D neural deformation fields in preserving shape consistency. This approach is naturally compatible with physics-based simulation, ensuring physically plausible interactions. Experiments show that AKD achieves superior 3D consistency and motion quality compared with existing works on text-to-4D generation. Project page: https://research.nvidia.com/labs/dir/akd/

Animating a newly designed character using motion capture (mocap) data is a long standing problem in computer animation. A key consideration is the skeletal structure that should correspond to the available mocap data, and the shape deformation in the joint regions, which often requires a tailored, pose-specific refinement. In this work, we develop a neural technique for articulating 3D characters using enveloping with a pre-defined skeletal structure which produces high quality pose dependent deformations. Our framework learns to rig and skin characters with the same articulation structure (e.g., bipeds or quadrupeds), and builds the desired skeleton hierarchy into the network architecture. Furthermore, we propose neural blend shapes--a set of corrective pose-dependent shapes which improve the deformation quality in the joint regions in order to address the notorious artifacts resulting from standard rigging and skinning. Our system estimates neural blend shapes for input meshes with arbitrary connectivity, as well as weighting coefficients which are conditioned on the input joint rotations. Unlike recent deep learning techniques which supervise the network with ground-truth rigging and skinning parameters, our approach does not assume that the training data has a specific underlying deformation model. Instead, during training, the network observes deformed shapes and learns to infer the corresponding rig, skin and blend shapes using indirect supervision. During inference, we demonstrate that our network generalizes to unseen characters with arbitrary mesh connectivity, including unrigged characters built by 3D artists. Conforming to standard skeletal animation models enables direct plug-and-play in standard animation software, as well as game engines.

In this paper, we address the challenge of reconstructing general articulated 3D objects from a single video. Existing works employing dynamic neural radiance fields have advanced the modeling of articulated objects like humans and animals from videos, but face challenges with piece-wise rigid general articulated objects due to limitations in their deformation models. To tackle this, we propose Quasi-Rigid Blend Skinning, a novel deformation model that enhances the rigidity of each part while maintaining flexible deformation of the joints. Our primary insight combines three distinct approaches: 1) an enhanced bone rigging system for improved component modeling, 2) the use of quasi-sparse skinning weights to boost part rigidity and reconstruction fidelity, and 3) the application of geodesic point assignment for precise motion and seamless deformation. Our method outperforms previous works in producing higher-fidelity 3D reconstructions of general articulated objects, as demonstrated on both real and synthetic datasets. Project page: https://chaoyuesong.github.io/REACTO.

Recent techniques for text-to-4D generation synthesize dynamic 3D scenes using supervision from pre-trained text-to-video models. However, existing representations for motion, such as deformation models or time-dependent neural representations, are limited in the amount of motion they can generate-they cannot synthesize motion extending far beyond the bounding box used for volume rendering. The lack of a more flexible motion model contributes to the gap in realism between 4D generation methods and recent, near-photorealistic video generation models. Here, we propose TC4D: trajectory-conditioned text-to-4D generation, which factors motion into global and local components. We represent the global motion of a scene's bounding box using rigid transformation along a trajectory parameterized by a spline. We learn local deformations that conform to the global trajectory using supervision from a text-to-video model. Our approach enables the synthesis of scenes animated along arbitrary trajectories, compositional scene generation, and significant improvements to the realism and amount of generated motion, which we evaluate qualitatively and through a user study. Video results can be viewed on our website: https://sherwinbahmani.github.io/tc4d.

Dynamic garment reconstruction from monocular video is an important yet challenging task due to the complex dynamics and unconstrained nature of the garments. Recent advancements in neural rendering have enabled high-quality geometric reconstruction with image/video supervision. However, implicit representation methods that use volume rendering often provide smooth geometry and fail to model high-frequency details. While template reconstruction methods model explicit geometry, they use vertex displacement for deformation, which results in artifacts. Addressing these limitations, we propose NGD, a Neural Gradient-based Deformation method to reconstruct dynamically evolving textured garments from monocular videos. Additionally, we propose a novel adaptive remeshing strategy for modelling dynamically evolving surfaces like wrinkles and pleats of the skirt, leading to high-quality reconstruction. Finally, we learn dynamic texture maps to capture per-frame lighting and shadow effects. We provide extensive qualitative and quantitative evaluations to demonstrate significant improvements over existing SOTA methods and provide high-quality garment reconstructions.

Animating virtual avatars with free-view control is crucial for various applications like virtual reality and digital entertainment. Previous studies have attempted to utilize the representation power of the neural radiance field (NeRF) to reconstruct the human body from monocular videos. Recent works propose to graft a deformation network into the NeRF to further model the dynamics of the human neural field for animating vivid human motions. However, such pipelines either rely on pose-dependent representations or fall short of motion coherency due to frame-independent optimization, making it difficult to generalize to unseen pose sequences realistically. In this paper, we propose a novel framework MonoHuman, which robustly renders view-consistent and high-fidelity avatars under arbitrary novel poses. Our key insight is to model the deformation field with bi-directional constraints and explicitly leverage the off-the-peg keyframe information to reason the feature correlations for coherent results. Specifically, we first propose a Shared Bidirectional Deformation module, which creates a pose-independent generalizable deformation field by disentangling backward and forward deformation correspondences into shared skeletal motion weight and separate non-rigid motions. Then, we devise a Forward Correspondence Search module, which queries the correspondence feature of keyframes to guide the rendering network. The rendered results are thus multi-view consistent with high fidelity, even under challenging novel pose settings. Extensive experiments demonstrate the superiority of our proposed MonoHuman over state-of-the-art methods.

Reconstructing 3D human heads in low-view settings presents technical challenges, mainly due to the pronounced risk of overfitting with limited views and high-frequency signals. To address this, we propose geometry decomposition and adopt a two-stage, coarse-to-fine training strategy, allowing for progressively capturing high-frequency geometric details. We represent 3D human heads using the zero level-set of a combined signed distance field, comprising a smooth template, a non-rigid deformation, and a high-frequency displacement field. The template captures features that are independent of both identity and expression and is co-trained with the deformation network across multiple individuals with sparse and randomly selected views. The displacement field, capturing individual-specific details, undergoes separate training for each person. Our network training does not require 3D supervision or object masks. Experimental results demonstrate the effectiveness and robustness of our geometry decomposition and two-stage training strategy. Our method outperforms existing neural rendering approaches in terms of reconstruction accuracy and novel view synthesis under low-view settings. Moreover, the pre-trained template serves a good initialization for our model when encountering unseen individuals.

Respiratory motion complicates accurate irradiation of thoraco-abdominal tumors during radiotherapy, as treatment-system latency entails target-location uncertainties. This work addresses frame forecasting in chest and liver cine MRI to compensate for such delays. We investigate RNNs trained with online learning algorithms, enabling adaptation to changing respiratory patterns via on-the-fly parameter updates, and transformers, increasingly common in time-series forecasting for their ability to capture long-term dependencies. Experiments used 12 sagittal thoracic and upper-abdominal cine-MRI sequences from ETH Zürich and OvGU; the OvGU data exhibited higher motion variability, noise, and lower contrast. PCA decomposes the Lucas-Kanade optical-flow field into static deformation modes and low-dimensional, time-dependent weights. We compare various methods for forecasting these weights: linear filters, population and sequence-specific transformer encoders, and RNNs trained with real-time recurrent learning (RTRL), unbiased online recurrent optimization, decoupled neural interfaces, and sparse one-step approximation (SnAp-1). Predicted displacements were used to warp the reference frame and generate future images. Prediction accuracy decreased with the horizon h. Linear regression performed best at short horizons (1.3mm geometrical error at h=0.32s, ETH Zürich dataset), while RTRL and SnAp-1 outperformed the other algorithms at medium-to-long horizons, with geometrical errors below 1.4mm and 2.8mm on the sequences from ETH Zürich and OvGU, respectively. The sequence-specific transformer was competitive for low-to-medium horizons, but transformers remained overall limited by data scarcity and domain shift between datasets. Predicted frames visually resembled the ground truth, with notable errors occurring near the diaphragm at end-inspiration and regions affected by out-of-plane motion.

Recent advances in diffusion models such as ControlNet have enabled geometrically controllable, high-fidelity text-to-image generation. However, none of them addresses the question of adding such controllability to text-to-3D generation. In response, we propose Text2Control3D, a controllable text-to-3D avatar generation method whose facial expression is controllable given a monocular video casually captured with hand-held camera. Our main strategy is to construct the 3D avatar in Neural Radiance Fields (NeRF) optimized with a set of controlled viewpoint-aware images that we generate from ControlNet, whose condition input is the depth map extracted from the input video. When generating the viewpoint-aware images, we utilize cross-reference attention to inject well-controlled, referential facial expression and appearance via cross attention. We also conduct low-pass filtering of Gaussian latent of the diffusion model in order to ameliorate the viewpoint-agnostic texture problem we observed from our empirical analysis, where the viewpoint-aware images contain identical textures on identical pixel positions that are incomprehensible in 3D. Finally, to train NeRF with the images that are viewpoint-aware yet are not strictly consistent in geometry, our approach considers per-image geometric variation as a view of deformation from a shared 3D canonical space. Consequently, we construct the 3D avatar in a canonical space of deformable NeRF by learning a set of per-image deformation via deformation field table. We demonstrate the empirical results and discuss the effectiveness of our method.

Volumetric neural rendering methods, such as neural radiance fields (NeRFs), have enabled photo-realistic novel view synthesis. However, in their standard form, NeRFs do not support the editing of objects, such as a human head, within a scene. In this work, we propose RigNeRF, a system that goes beyond just novel view synthesis and enables full control of head pose and facial expressions learned from a single portrait video. We model changes in head pose and facial expressions using a deformation field that is guided by a 3D morphable face model (3DMM). The 3DMM effectively acts as a prior for RigNeRF that learns to predict only residuals to the 3DMM deformations and allows us to render novel (rigid) poses and (non-rigid) expressions that were not present in the input sequence. Using only a smartphone-captured short video of a subject for training, we demonstrate the effectiveness of our method on free view synthesis of a portrait scene with explicit head pose and expression controls. The project page can be found here: http://shahrukhathar.github.io/2022/06/06/RigNeRF.html

Lightweight creation of 3D digital avatars is a highly desirable but challenging task. With only sparse videos of a person under unknown illumination, we propose a method to create relightable and animatable neural avatars, which can be used to synthesize photorealistic images of humans under novel viewpoints, body poses, and lighting. The key challenge here is to disentangle the geometry, material of the clothed body, and lighting, which becomes more difficult due to the complex geometry and shadow changes caused by body motions. To solve this ill-posed problem, we propose novel techniques to better model the geometry and shadow changes. For geometry change modeling, we propose an invertible deformation field, which helps to solve the inverse skinning problem and leads to better geometry quality. To model the spatial and temporal varying shading cues, we propose a pose-aware part-wise light visibility network to estimate light occlusion. Extensive experiments on synthetic and real datasets show that our approach reconstructs high-quality geometry and generates realistic shadows under different body poses. Code and data are available at https://wenbin-lin.github.io/RelightableAvatar-page/.

We present the first method capable of photorealistically reconstructing deformable scenes using photos/videos captured casually from mobile phones. Our approach augments neural radiance fields (NeRF) by optimizing an additional continuous volumetric deformation field that warps each observed point into a canonical 5D NeRF. We observe that these NeRF-like deformation fields are prone to local minima, and propose a coarse-to-fine optimization method for coordinate-based models that allows for more robust optimization. By adapting principles from geometry processing and physical simulation to NeRF-like models, we propose an elastic regularization of the deformation field that further improves robustness. We show that our method can turn casually captured selfie photos/videos into deformable NeRF models that allow for photorealistic renderings of the subject from arbitrary viewpoints, which we dub "nerfies." We evaluate our method by collecting time-synchronized data using a rig with two mobile phones, yielding train/validation images of the same pose at different viewpoints. We show that our method faithfully reconstructs non-rigidly deforming scenes and reproduces unseen views with high fidelity.

Dynamic scene reconstruction from multi-view videos remains a fundamental challenge in computer vision. While recent neural surface reconstruction methods have achieved remarkable results in static 3D reconstruction, extending these approaches with comparable quality for dynamic scenes introduces significant computational and representational challenges. Existing dynamic methods focus on novel-view synthesis, therefore, their extracted meshes tend to be noisy. Even approaches aiming for geometric fidelity often result in too smooth meshes due to the ill-posedness of the problem. We present a novel framework for highly detailed dynamic reconstruction that extends the static 3D reconstruction method NeuralAngelo to work in dynamic settings. To that end, we start with a high-quality template scene reconstruction from the initial frame using NeuralAngelo, and then jointly optimize deformation fields that track the template and refine it based on the temporal sequence. This flexible template allows updating the geometry to include changes that cannot be modeled with the deformation field, for instance occluded parts or the changes in the topology. We show superior reconstruction accuracy in comparison to previous state-of-the-art methods on the ActorsHQ dataset.

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent approach in current deep learning is the set-based approach which measures the discrepancy between two surfaces by comparing two randomly sampled point-clouds from the two meshes with Chamfer pseudo-distance. Nevertheless, the set-based approach still has limitations such as lacking a theoretical guarantee for choosing the number of points in sampled point-clouds, and the pseudo-metricity and the quadratic complexity of the Chamfer divergence. To address these issues, we propose a novel metric for learning mesh deformation. The metric is defined by sliced Wasserstein distance on meshes represented as probability measures that generalize the set-based approach. By leveraging probability measure space, we gain flexibility in encoding meshes using diverse forms of probability measures, such as continuous, empirical, and discrete measures via varifold representation. After having encoded probability measures, we can compare meshes by using the sliced Wasserstein distance which is an effective optimal transport distance with linear computational complexity and can provide a fast statistical rate for approximating the surface of meshes. To the end, we employ a neural ordinary differential equation (ODE) to deform the input surface into the target shape by modeling the trajectories of the points on the surface. Our experiments on cortical surface reconstruction demonstrate that our approach surpasses other competing methods in multiple datasets and metrics.

Building on the success of 3D Gaussian Splatting (3DGS) in static 3D scene representation, its extension to dynamic scenes, commonly referred to as 4DGS or dynamic 3DGS, has attracted increasing attention. However, designing more compact and efficient deformation schemes together with rate-distortion-optimized compression strategies for dynamic 3DGS representations remains an underexplored area. Prior methods either rely on space-time 4DGS with overspecified, short-lived Gaussian primitives or on canonical 3DGS with deformation that lacks explicit temporal control. To address this, we present TED-4DGS, a temporally activated and embedding-based deformation scheme for rate-distortion-optimized 4DGS compression that unifies the strengths of both families. TED-4DGS is built on a sparse anchor-based 3DGS representation. Each canonical anchor is assigned learnable temporal-activation parameters to specify its appearance and disappearance transitions over time, while a lightweight per-anchor temporal embedding queries a shared deformation bank to produce anchor-specific deformation. For rate-distortion compression, we incorporate an implicit neural representation (INR)-based hyperprior to model anchor attribute distributions, along with a channel-wise autoregressive model to capture intra-anchor correlations. With these novel elements, our scheme achieves state-of-the-art rate-distortion performance on several real-world datasets. To the best of our knowledge, this work represents one of the first attempts to pursue a rate-distortion-optimized compression framework for dynamic 3DGS representations.

This paper tackles the challenge of creating relightable and animatable neural avatars from sparse-view (or even monocular) videos of dynamic humans under unknown illumination. Compared to studio environments, this setting is more practical and accessible but poses an extremely challenging ill-posed problem. Previous neural human reconstruction methods are able to reconstruct animatable avatars from sparse views using deformed Signed Distance Fields (SDF) but cannot recover material parameters for relighting. While differentiable inverse rendering-based methods have succeeded in material recovery of static objects, it is not straightforward to extend them to dynamic humans as it is computationally intensive to compute pixel-surface intersection and light visibility on deformed SDFs for inverse rendering. To solve this challenge, we propose a Hierarchical Distance Query (HDQ) algorithm to approximate the world space distances under arbitrary human poses. Specifically, we estimate coarse distances based on a parametric human model and compute fine distances by exploiting the local deformation invariance of SDF. Based on the HDQ algorithm, we leverage sphere tracing to efficiently estimate the surface intersection and light visibility. This allows us to develop the first system to recover animatable and relightable neural avatars from sparse view (or monocular) inputs. Experiments demonstrate that our approach is able to produce superior results compared to state-of-the-art methods. Our code will be released for reproducibility.

Despite much progress, achieving real-time high-fidelity head avatar animation is still difficult and existing methods have to trade-off between speed and quality. 3DMM based methods often fail to model non-facial structures such as eyeglasses and hairstyles, while neural implicit models suffer from deformation inflexibility and rendering inefficiency. Although 3D Gaussian has been demonstrated to possess promising capability for geometry representation and radiance field reconstruction, applying 3D Gaussian in head avatar creation remains a major challenge since it is difficult for 3D Gaussian to model the head shape variations caused by changing poses and expressions. In this paper, we introduce PSAvatar, a novel framework for animatable head avatar creation that utilizes discrete geometric primitive to create a parametric morphable shape model and employs 3D Gaussian for fine detail representation and high fidelity rendering. The parametric morphable shape model is a Point-based Morphable Shape Model (PMSM) which uses points instead of meshes for 3D representation to achieve enhanced representation flexibility. The PMSM first converts the FLAME mesh to points by sampling on the surfaces as well as off the meshes to enable the reconstruction of not only surface-like structures but also complex geometries such as eyeglasses and hairstyles. By aligning these points with the head shape in an analysis-by-synthesis manner, the PMSM makes it possible to utilize 3D Gaussian for fine detail representation and appearance modeling, thus enabling the creation of high-fidelity avatars. We show that PSAvatar can reconstruct high-fidelity head avatars of a variety of subjects and the avatars can be animated in real-time (ge 25 fps at a resolution of 512 times 512 ).

Face animation, one of the hottest topics in computer vision, has achieved a promising performance with the help of generative models. However, it remains a critical challenge to generate identity preserving and photo-realistic images due to the sophisticated motion deformation and complex facial detail modeling. To address these problems, we propose a Face Neural Volume Rendering (FNeVR) network to fully explore the potential of 2D motion warping and 3D volume rendering in a unified framework. In FNeVR, we design a 3D Face Volume Rendering (FVR) module to enhance the facial details for image rendering. Specifically, we first extract 3D information with a well-designed architecture, and then introduce an orthogonal adaptive ray-sampling module for efficient rendering. We also design a lightweight pose editor, enabling FNeVR to edit the facial pose in a simple yet effective way. Extensive experiments show that our FNeVR obtains the best overall quality and performance on widely used talking-head benchmarks.

While previous years have seen great progress in the 3D reconstruction of humans from monocular videos, few of the state-of-the-art methods are able to handle loose garments that exhibit large non-rigid surface deformations during articulation. This limits the application of such methods to humans that are dressed in standard pants or T-shirts. Our method, ReLoo, overcomes this limitation and reconstructs high-quality 3D models of humans dressed in loose garments from monocular in-the-wild videos. To tackle this problem, we first establish a layered neural human representation that decomposes clothed humans into a neural inner body and outer clothing. On top of the layered neural representation, we further introduce a non-hierarchical virtual bone deformation module for the clothing layer that can freely move, which allows the accurate recovery of non-rigidly deforming loose clothing. A global optimization jointly optimizes the shape, appearance, and deformations of the human body and clothing via multi-layer differentiable volume rendering. To evaluate ReLoo, we record subjects with dynamically deforming garments in a multi-view capture studio. This evaluation, both on existing and our novel dataset, demonstrates ReLoo's clear superiority over prior art on both indoor datasets and in-the-wild videos.

It is now possible to reconstruct dynamic human motion and shape from a sparse set of cameras using Neural Radiance Fields (NeRF) driven by an underlying skeleton. However, a challenge remains to model the deformation of cloth and skin in relation to skeleton pose. Unlike existing avatar models that are learned implicitly or rely on a proxy surface, our approach is motivated by the observation that different poses necessitate unique frequency assignments. Neglecting this distinction yields noisy artifacts in smooth areas or blurs fine-grained texture and shape details in sharp regions. We develop a two-branch neural network that is adaptive and explicit in the frequency domain. The first branch is a graph neural network that models correlations among body parts locally, taking skeleton pose as input. The second branch combines these correlation features to a set of global frequencies and then modulates the feature encoding. Our experiments demonstrate that our network outperforms state-of-the-art methods in terms of preserving details and generalization capabilities.

In this paper, we present TailorNet, a neural model which predicts clothing deformation in 3D as a function of three factors: pose, shape and style (garment geometry), while retaining wrinkle detail. This goes beyond prior models, which are either specific to one style and shape, or generalize to different shapes producing smooth results, despite being style specific. Our hypothesis is that (even non-linear) combinations of examples smooth out high frequency components such as fine-wrinkles, which makes learning the three factors jointly hard. At the heart of our technique is a decomposition of deformation into a high frequency and a low frequency component. While the low-frequency component is predicted from pose, shape and style parameters with an MLP, the high-frequency component is predicted with a mixture of shape-style specific pose models. The weights of the mixture are computed with a narrow bandwidth kernel to guarantee that only predictions with similar high-frequency patterns are combined. The style variation is obtained by computing, in a canonical pose, a subspace of deformation, which satisfies physical constraints such as inter-penetration, and draping on the body. TailorNet delivers 3D garments which retain the wrinkles from the physics based simulations (PBS) it is learned from, while running more than 1000 times faster. In contrast to PBS, TailorNet is easy to use and fully differentiable, which is crucial for computer vision algorithms. Several experiments demonstrate TailorNet produces more realistic results than prior work, and even generates temporally coherent deformations on sequences of the AMASS dataset, despite being trained on static poses from a different dataset. To stimulate further research in this direction, we will make a dataset consisting of 55800 frames, as well as our model publicly available at https://virtualhumans.mpi-inf.mpg.de/tailornet.

Animating stylized characters to match a reference motion sequence is a highly demanded task in film and gaming industries. Existing methods mostly focus on rigid deformations of characters' body, neglecting local deformations on the apparel driven by physical dynamics. They deform apparel the same way as the body, leading to results with limited details and unrealistic artifacts, e.g. body-apparel penetration. In contrast, we present a novel method aiming for high-quality motion transfer with realistic apparel animation. As existing datasets lack annotations necessary for generating realistic apparel animations, we build a new dataset named MMDMC, which combines stylized characters from the MikuMikuDance community with real-world Motion Capture data. We then propose a data-driven pipeline that learns to disentangle body and apparel deformations via two neural deformation modules. For body parts, we propose a geodesic attention block to effectively incorporate semantic priors into skeletal body deformation to tackle complex body shapes for stylized characters. Since apparel motion can significantly deviate from respective body joints, we propose to model apparel deformation in a non-linear vertex displacement field conditioned on its historic states. Extensive experiments show that our method produces results with superior quality for various types of apparel. Our dataset is released in https://github.com/rongakowang/MMDMC.

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Image registration is an essential step in many medical image analysis tasks. Traditional methods for image registration are primarily optimization-driven, finding the optimal deformations that maximize the similarity between two images. Recent learning-based methods, trained to directly predict transformations between two images, run much faster, but suffer from performance deficiencies due to model generalization and the inefficiency in handling individual image specific deformations. Here we present a new neural net based image registration framework, called NIR (Neural Image Registration), which is based on optimization but utilizes deep neural nets to model deformations between image pairs. NIR represents the transformation between two images with a continuous function implemented via neural fields, receiving a 3D coordinate as input and outputting the corresponding deformation vector. NIR provides two ways of generating deformation field: directly output a displacement vector field for general deformable registration, or output a velocity vector field and integrate the velocity field to derive the deformation field for diffeomorphic image registration. The optimal registration is discovered by updating the parameters of the neural field via stochastic gradient descent. We describe several design choices that facilitate model optimization, including coordinate encoding, sinusoidal activation, coordinate sampling, and intensity sampling. Experiments on two 3D MR brain scan datasets demonstrate that NIR yields state-of-the-art performance in terms of both registration accuracy and regularity, while running significantly faster than traditional optimization-based methods.

We introduce MIGS (Multi-Identity Gaussian Splatting), a novel method that learns a single neural representation for multiple identities, using only monocular videos. Recent 3D Gaussian Splatting (3DGS) approaches for human avatars require per-identity optimization. However, learning a multi-identity representation presents advantages in robustly animating humans under arbitrary poses. We propose to construct a high-order tensor that combines all the learnable 3DGS parameters for all the training identities. By assuming a low-rank structure and factorizing the tensor, we model the complex rigid and non-rigid deformations of multiple subjects in a unified network, significantly reducing the total number of parameters. Our proposed approach leverages information from all the training identities, enabling robust animation under challenging unseen poses, outperforming existing approaches. We also demonstrate how it can be extended to learn unseen identities.

Recent years have witnessed significant progress in the field of neural surface reconstruction. While the extensive focus was put on volumetric and implicit approaches, a number of works have shown that explicit graphics primitives such as point clouds can significantly reduce computational complexity, without sacrificing the reconstructed surface quality. However, less emphasis has been put on modeling dynamic surfaces with point primitives. In this work, we present a dynamic point field model that combines the representational benefits of explicit point-based graphics with implicit deformation networks to allow efficient modeling of non-rigid 3D surfaces. Using explicit surface primitives also allows us to easily incorporate well-established constraints such as-isometric-as-possible regularisation. While learning this deformation model is prone to local optima when trained in a fully unsupervised manner, we propose to additionally leverage semantic information such as keypoint dynamics to guide the deformation learning. We demonstrate our model with an example application of creating an expressive animatable human avatar from a collection of 3D scans. Here, previous methods mostly rely on variants of the linear blend skinning paradigm, which fundamentally limits the expressivity of such models when dealing with complex cloth appearances such as long skirts. We show the advantages of our dynamic point field framework in terms of its representational power, learning efficiency, and robustness to out-of-distribution novel poses.

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive fields. In this paper, we investigate such neural fields in a multilayer architecture to investigate the supervised learning of the fields. We empirically compare the performances of our field model with those of randomly connected deep networks. The behavior of a randomly connected network is investigated on the basis of the key idea of the neural tangent kernel regime, a recent development in the machine learning theory of over-parameterized networks; for most randomly connected neural networks, it is shown that global minima always exist in their small neighborhoods. We numerically show that this claim also holds for our neural fields. In more detail, our model has two structures: i) each neuron in a field has a continuously distributed receptive field, and ii) the initial connection weights are random but not independent, having correlations when the positions of neurons are close in each layer. We show that such a multilayer neural field is more robust than conventional models when input patterns are deformed by noise disturbances. Moreover, its generalization ability can be slightly superior to that of conventional models.

The superior performance of Deformable Convolutional Networks arises from its ability to adapt to the geometric variations of objects. Through an examination of its adaptive behavior, we observe that while the spatial support for its neural features conforms more closely than regular ConvNets to object structure, this support may nevertheless extend well beyond the region of interest, causing features to be influenced by irrelevant image content. To address this problem, we present a reformulation of Deformable ConvNets that improves its ability to focus on pertinent image regions, through increased modeling power and stronger training. The modeling power is enhanced through a more comprehensive integration of deformable convolution within the network, and by introducing a modulation mechanism that expands the scope of deformation modeling. To effectively harness this enriched modeling capability, we guide network training via a proposed feature mimicking scheme that helps the network to learn features that reflect the object focus and classification power of R-CNN features. With the proposed contributions, this new version of Deformable ConvNets yields significant performance gains over the original model and produces leading results on the COCO benchmark for object detection and instance segmentation.

Existing methods for the 4D reconstruction of general, non-rigidly deforming objects focus on novel-view synthesis and neglect correspondences. However, time consistency enables advanced downstream tasks like 3D editing, motion analysis, or virtual-asset creation. We propose SceNeRFlow to reconstruct a general, non-rigid scene in a time-consistent manner. Our dynamic-NeRF method takes multi-view RGB videos and background images from static cameras with known camera parameters as input. It then reconstructs the deformations of an estimated canonical model of the geometry and appearance in an online fashion. Since this canonical model is time-invariant, we obtain correspondences even for long-term, long-range motions. We employ neural scene representations to parametrize the components of our method. Like prior dynamic-NeRF methods, we use a backwards deformation model. We find non-trivial adaptations of this model necessary to handle larger motions: We decompose the deformations into a strongly regularized coarse component and a weakly regularized fine component, where the coarse component also extends the deformation field into the space surrounding the object, which enables tracking over time. We show experimentally that, unlike prior work that only handles small motion, our method enables the reconstruction of studio-scale motions.

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos.

Learning 3D shape representation with dense correspondence for deformable objects is a fundamental problem in computer vision. Existing approaches often need additional annotations of specific semantic domain, e.g., skeleton poses for human bodies or animals, which require extra annotation effort and suffer from error accumulation, and they are limited to specific domain. In this paper, we propose a novel self-supervised approach to learn neural implicit shape representation for deformable objects, which can represent shapes with a template shape and dense correspondence in 3D. Our method does not require the priors of skeleton and skinning weight, and only requires a collection of shapes represented in signed distance fields. To handle the large deformation, we constrain the learned template shape in the same latent space with the training shapes, design a new formulation of local rigid constraint that enforces rigid transformation in local region and addresses local reflection issue, and present a new hierarchical rigid constraint to reduce the ambiguity due to the joint learning of template shape and correspondences. Extensive experiments show that our model can represent shapes with large deformations. We also show that our shape representation can support two typical applications, such as texture transfer and shape editing, with competitive performance. The code and models are available at https://iscas3dv.github.io/deformshape

In medical imaging, the diffusion models have shown great potential in synthetic image generation tasks. However, these models often struggle with the interpretable connections between the generated and existing images and could create illusions. To address these challenges, our research proposes a novel diffusion-based generative model based on deformation diffusion and recovery. This model, named Deformation-Recovery Diffusion Model (DRDM), diverges from traditional score/intensity and latent feature-based approaches, emphasizing morphological changes through deformation fields rather than direct image synthesis. This is achieved by introducing a topological-preserving deformation field generation method, which randomly samples and integrates a set of multi-scale Deformation Vector Fields (DVF). DRDM is trained to learn to recover unreasonable deformation components, thereby restoring each randomly deformed image to a realistic distribution. These innovations facilitate the generation of diverse and anatomically plausible deformations, enhancing data augmentation and synthesis for further analysis in downstream tasks, such as few-shot learning and image registration. Experimental results in cardiac MRI and pulmonary CT show DRDM is capable of creating diverse, large (over 10\% image size deformation scale), and high-quality (negative rate of the Jacobian matrix's determinant is lower than 1\%) deformation fields. The further experimental results in downstream tasks, 2D image segmentation and 3D image registration, indicate significant improvements resulting from DRDM, showcasing the potential of our model to advance image manipulation and synthesis in medical imaging and beyond. Project page: https://jianqingzheng.github.io/def_diff_rec/

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

Many patterns in nature exhibit self-similarity: they can be compactly described via self-referential transformations. Said patterns commonly appear in natural and artificial objects, such as molecules, shorelines, galaxies and even images. In this work, we investigate the role of learning in the automated discovery of self-similarity and in its utilization for downstream tasks. To this end, we design a novel class of implicit operators, Neural Collages, which (1) represent data as the parameters of a self-referential, structured transformation, and (2) employ hypernetworks to amortize the cost of finding these parameters to a single forward pass. We investigate how to leverage the representations produced by Neural Collages in various tasks, including data compression and generation. Neural Collages image compressors are orders of magnitude faster than other self-similarity-based algorithms during encoding and offer compression rates competitive with implicit methods. Finally, we showcase applications of Neural Collages for fractal art and as deep generative models.

This paper introduces a network for volumetric segmentation that learns from sparsely annotated volumetric images. We outline two attractive use cases of this method: (1) In a semi-automated setup, the user annotates some slices in the volume to be segmented. The network learns from these sparse annotations and provides a dense 3D segmentation. (2) In a fully-automated setup, we assume that a representative, sparsely annotated training set exists. Trained on this data set, the network densely segments new volumetric images. The proposed network extends the previous u-net architecture from Ronneberger et al. by replacing all 2D operations with their 3D counterparts. The implementation performs on-the-fly elastic deformations for efficient data augmentation during training. It is trained end-to-end from scratch, i.e., no pre-trained network is required. We test the performance of the proposed method on a complex, highly variable 3D structure, the Xenopus kidney, and achieve good results for both use cases.

Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a scene. Nevertheless, it is challenging for users to directly deform or manipulate these implicit representations with large deformations in the real-time fashion. Gaussian Splatting(GS) has recently become a promising method with explicit geometry for representing static scenes and facilitating high-quality and real-time synthesis of novel views. However,it cannot be easily deformed due to the use of discrete Gaussians and lack of explicit topology. To address this, we develop a novel GS-based method that enables interactive deformation. Our key idea is to design an innovative mesh-based GS representation, which is integrated into Gaussian learning and manipulation. 3D Gaussians are defined over an explicit mesh, and they are bound with each other: the rendering of 3D Gaussians guides the mesh face split for adaptive refinement, and the mesh face split directs the splitting of 3D Gaussians. Moreover, the explicit mesh constraints help regularize the Gaussian distribution, suppressing poor-quality Gaussians(e.g. misaligned Gaussians,long-narrow shaped Gaussians), thus enhancing visual quality and avoiding artifacts during deformation. Based on this representation, we further introduce a large-scale Gaussian deformation technique to enable deformable GS, which alters the parameters of 3D Gaussians according to the manipulation of the associated mesh. Our method benefits from existing mesh deformation datasets for more realistic data-driven Gaussian deformation. Extensive experiments show that our approach achieves high-quality reconstruction and effective deformation, while maintaining the promising rendering results at a high frame rate(65 FPS on average).

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

Obtaining personalized 3D animatable avatars from a monocular camera has several real world applications in gaming, virtual try-on, animation, and VR/XR, etc. However, it is very challenging to model dynamic and fine-grained clothing deformations from such sparse data. Existing methods for modeling 3D humans from depth data have limitations in terms of computational efficiency, mesh coherency, and flexibility in resolution and topology. For instance, reconstructing shapes using implicit functions and extracting explicit meshes per frame is computationally expensive and cannot ensure coherent meshes across frames. Moreover, predicting per-vertex deformations on a pre-designed human template with a discrete surface lacks flexibility in resolution and topology. To overcome these limitations, we propose a novel method `\keyfeature: Neural Surface Fields' for modeling 3D clothed humans from monocular depth. NSF defines a neural field solely on the base surface which models a continuous and flexible displacement field. NSF can be adapted to the base surface with different resolution and topology without retraining at inference time. Compared to existing approaches, our method eliminates the expensive per-frame surface extraction while maintaining mesh coherency, and is capable of reconstructing meshes with arbitrary resolution without retraining. To foster research in this direction, we release our code in project page at: https://yuxuan-xue.com/nsf.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

Implicit Neural Representations (INRs) and Neural Fields are a novel paradigm for signal representation, from images and audio to 3D scenes and videos. The fundamental idea is to represent a signal as a continuous and differentiable neural network. This idea offers unprecedented benefits such as continuous resolution and memory efficiency, enabling new compression techniques. However, representing data as neural networks poses new challenges. For instance, given a 2D image as a neural network, how can we further compress such a neural image?. In this work, we present a novel analysis on compressing neural fields, with the focus on images. We also introduce Adaptive Neural Images (ANI), an efficient neural representation that enables adaptation to different inference or transmission requirements. Our proposed method allows to reduce the bits-per-pixel (bpp) of the neural image by 4x, without losing sensitive details or harming fidelity. We achieve this thanks to our successful implementation of 4-bit neural representations. Our work offers a new framework for developing compressed neural fields.

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the Fast Fourier transform (FFT), which is limited to rectangular domains with uniform grids. In this work, we propose a new framework, viz., geo-FNO, to solve PDEs on arbitrary geometries. Geo-FNO learns to deform the input (physical) domain, which may be irregular, into a latent space with a uniform grid. The FNO model with the FFT is applied in the latent space. The resulting geo-FNO model has both the computation efficiency of FFT and the flexibility of handling arbitrary geometries. Our geo-FNO is also flexible in terms of its input formats, viz., point clouds, meshes, and design parameters are all valid inputs. We consider a variety of PDEs such as the Elasticity, Plasticity, Euler's, and Navier-Stokes equations, and both forward modeling and inverse design problems. Geo-FNO is 10^5 times faster than the standard numerical solvers and twice more accurate compared to direct interpolation on existing ML-based PDE solvers such as the standard FNO.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time R^3times R, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually R^3 times {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

Large language model (LLM)-based agentic frameworks increasingly adopt the paradigm of dynamically generating task-specific agents. We suggest that not only agents but also specialized software modules for scientific and engineering tasks can be generated on demand. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models are required to describe the relationship between mechanical stress and body deformation. Constitutive models are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete code generation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy comparable to or greater than manually engineered counterparts, while also exhibiting reliable generalization to unseen loading scenarios and extrapolation to large deformations. These findings indicate that LLM-based generation of physics-constrained neural networks can substantially reduce the expertise required for constitutive modeling and represent a step toward practical end-to-end automation.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

Reconstructing dynamic 3D scenes from 2D images and generating diverse views over time is challenging due to scene complexity and temporal dynamics. Despite advancements in neural implicit models, limitations persist: (i) Inadequate Scene Structure: Existing methods struggle to reveal the spatial and temporal structure of dynamic scenes from directly learning the complex 6D plenoptic function. (ii) Scaling Deformation Modeling: Explicitly modeling scene element deformation becomes impractical for complex dynamics. To address these issues, we consider the spacetime as an entirety and propose to approximate the underlying spatio-temporal 4D volume of a dynamic scene by optimizing a collection of 4D primitives, with explicit geometry and appearance modeling. Learning to optimize the 4D primitives enables us to synthesize novel views at any desired time with our tailored rendering routine. Our model is conceptually simple, consisting of a 4D Gaussian parameterized by anisotropic ellipses that can rotate arbitrarily in space and time, as well as view-dependent and time-evolved appearance represented by the coefficient of 4D spherindrical harmonics. This approach offers simplicity, flexibility for variable-length video and end-to-end training, and efficient real-time rendering, making it suitable for capturing complex dynamic scene motions. Experiments across various benchmarks, including monocular and multi-view scenarios, demonstrate our 4DGS model's superior visual quality and efficiency.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

This paper addresses the challenge of novel view synthesis for a human performer from a very sparse set of camera views. Some recent works have shown that learning implicit neural representations of 3D scenes achieves remarkable view synthesis quality given dense input views. However, the representation learning will be ill-posed if the views are highly sparse. To solve this ill-posed problem, our key idea is to integrate observations over video frames. To this end, we propose Neural Body, a new human body representation which assumes that the learned neural representations at different frames share the same set of latent codes anchored to a deformable mesh, so that the observations across frames can be naturally integrated. The deformable mesh also provides geometric guidance for the network to learn 3D representations more efficiently. To evaluate our approach, we create a multi-view dataset named ZJU-MoCap that captures performers with complex motions. Experiments on ZJU-MoCap show that our approach outperforms prior works by a large margin in terms of novel view synthesis quality. We also demonstrate the capability of our approach to reconstruct a moving person from a monocular video on the People-Snapshot dataset. The code and dataset are available at https://zju3dv.github.io/neuralbody/.

Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic foundation and an easy implementation in current deep learning frameworks. While neural fields have been applied to signals on manifolds, e.g., for texture reconstruction, their representation has been limited to extrinsically embedding the shape into Euclidean space. The extrinsic embedding ignores known intrinsic manifold properties and is inflexible wrt. transfer of the learned function. To overcome these limitations, this work introduces intrinsic neural fields, a novel and versatile representation for neural fields on manifolds. Intrinsic neural fields combine the advantages of neural fields with the spectral properties of the Laplace-Beltrami operator. We show theoretically that intrinsic neural fields inherit many desirable properties of the extrinsic neural field framework but exhibit additional intrinsic qualities, like isometry invariance. In experiments, we show intrinsic neural fields can reconstruct high-fidelity textures from images with state-of-the-art quality and are robust to the discretization of the underlying manifold. We demonstrate the versatility of intrinsic neural fields by tackling various applications: texture transfer between deformed shapes & different shapes, texture reconstruction from real-world images with view dependence, and discretization-agnostic learning on meshes and point clouds.

Seam carving is an image editing method that enable content-aware resizing, including operations like removing objects. However, the seam-finding strategy based on dynamic programming or graph-cut limits its applications to broader visual data formats and degrees of freedom for editing. Our observation is that describing the editing and retargeting of images more generally by a displacement field yields a generalisation of content-aware deformations. We propose to learn a deformation with a neural network that keeps the output plausible while trying to deform it only in places with low information content. This technique applies to different kinds of visual data, including images, 3D scenes given as neural radiance fields, or even polygon meshes. Experiments conducted on different visual data show that our method achieves better content-aware retargeting compared to previous methods.

Existing methods for 3D tracking from monocular RGB videos predominantly consider articulated and rigid objects. Modelling dense non-rigid object deformations in this setting remained largely unaddressed so far, although such effects can improve the realism of the downstream applications such as AR/VR and avatar communications. This is due to the severe ill-posedness of the monocular view setting and the associated challenges. While it is possible to naively track multiple non-rigid objects independently using 3D templates or parametric 3D models, such an approach would suffer from multiple artefacts in the resulting 3D estimates such as depth ambiguity, unnatural intra-object collisions and missing or implausible deformations. Hence, this paper introduces the first method that addresses the fundamental challenges depicted above and that allows tracking human hands interacting with human faces in 3D from single monocular RGB videos. We model hands as articulated objects inducing non-rigid face deformations during an active interaction. Our method relies on a new hand-face motion and interaction capture dataset with realistic face deformations acquired with a markerless multi-view camera system. As a pivotal step in its creation, we process the reconstructed raw 3D shapes with position-based dynamics and an approach for non-uniform stiffness estimation of the head tissues, which results in plausible annotations of the surface deformations, hand-face contact regions and head-hand positions. At the core of our neural approach are a variational auto-encoder supplying the hand-face depth prior and modules that guide the 3D tracking by estimating the contacts and the deformations. Our final 3D hand and face reconstructions are realistic and more plausible compared to several baselines applicable in our setting, both quantitatively and qualitatively. https://vcai.mpi-inf.mpg.de/projects/Decaf

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction and then feed the results thereof into a trainable classifier. The mathematical analysis of deep convolutional neural networks for feature extraction was initiated by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on a wavelet transform followed by the modulus non-linearity in each network layer, and proved translation invariance (asymptotically in the wavelet scale parameter) and deformation stability of the corresponding feature extractor. This paper complements Mallat's results by developing a theory that encompasses general convolutional transforms, or in more technical parlance, general semi-discrete frames (including Weyl-Heisenberg filters, curvelets, shearlets, ridgelets, wavelets, and learned filters), general Lipschitz-continuous non-linearities (e.g., rectified linear units, shifted logistic sigmoids, hyperbolic tangents, and modulus functions), and general Lipschitz-continuous pooling operators emulating, e.g., sub-sampling and averaging. In addition, all of these elements can be different in different network layers. For the resulting feature extractor we prove a translation invariance result of vertical nature in the sense of the features becoming progressively more translation-invariant with increasing network depth, and we establish deformation sensitivity bounds that apply to signal classes such as, e.g., band-limited functions, cartoon functions, and Lipschitz functions.

We introduce HOSNeRF, a novel 360{\deg} free-viewpoint rendering method that reconstructs neural radiance fields for dynamic human-object-scene from a single monocular in-the-wild video. Our method enables pausing the video at any frame and rendering all scene details (dynamic humans, objects, and backgrounds) from arbitrary viewpoints. The first challenge in this task is the complex object motions in human-object interactions, which we tackle by introducing the new object bones into the conventional human skeleton hierarchy to effectively estimate large object deformations in our dynamic human-object model. The second challenge is that humans interact with different objects at different times, for which we introduce two new learnable object state embeddings that can be used as conditions for learning our human-object representation and scene representation, respectively. Extensive experiments show that HOSNeRF significantly outperforms SOTA approaches on two challenging datasets by a large margin of 40% ~ 50% in terms of LPIPS. The code, data, and compelling examples of 360{\deg} free-viewpoint renderings from single videos will be released in https://showlab.github.io/HOSNeRF.

The creation of high-fidelity, digital versions of human heads is an important stepping stone in the process of further integrating virtual components into our everyday lives. Constructing such avatars is a challenging research problem, due to a high demand for photo-realism and real-time rendering performance. In this work, we propose Neural Parametric Gaussian Avatars (NPGA), a data-driven approach to create high-fidelity, controllable avatars from multi-view video recordings. We build our method around 3D Gaussian Splatting for its highly efficient rendering and to inherit the topological flexibility of point clouds. In contrast to previous work, we condition our avatars' dynamics on the rich expression space of neural parametric head models (NPHM), instead of mesh-based 3DMMs. To this end, we distill the backward deformation field of our underlying NPHM into forward deformations which are compatible with rasterization-based rendering. All remaining fine-scale, expression-dependent details are learned from the multi-view videos. To increase the representational capacity of our avatars, we augment the canonical Gaussian point cloud using per-primitive latent features which govern its dynamic behavior. To regularize this increased dynamic expressivity, we propose Laplacian terms on the latent features and predicted dynamics. We evaluate our method on the public NeRSemble dataset, demonstrating that NPGA significantly outperforms the previous state-of-the-art avatars on the self-reenactment task by 2.6 PSNR. Furthermore, we demonstrate accurate animation capabilities from real-world monocular videos.

Accurate 3D shape abstraction from a single 2D image is a long-standing problem in computer vision and graphics. By leveraging a set of primitives to represent the target shape, recent methods have achieved promising results. However, these methods either use a relatively large number of primitives or lack geometric flexibility due to the limited expressibility of the primitives. In this paper, we propose a novel bi-channel Transformer architecture, integrated with parameterized deformable models, termed DeFormer, to simultaneously estimate the global and local deformations of primitives. In this way, DeFormer can abstract complex object shapes while using a small number of primitives which offer a broader geometry coverage and finer details. Then, we introduce a force-driven dynamic fitting and a cycle-consistent re-projection loss to optimize the primitive parameters. Extensive experiments on ShapeNet across various settings show that DeFormer achieves better reconstruction accuracy over the state-of-the-art, and visualizes with consistent semantic correspondences for improved interpretability.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can exhibit the "catapult phase" [Lewkowycz et al. 2020] that arises when training such models with large learning rates. We then empirically show that the behaviour of neural quadratic models parallels that of neural networks in generalization, especially in the catapult phase regime. Our analysis further demonstrates that quadratic models can be an effective tool for analysis of neural networks.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

Recurrent Neural Networks (RNNs) are popular models of brain function. The typical training strategy is to adjust their input-output behavior so that it matches that of the biological circuit of interest. Even though this strategy ensures that the biological and artificial networks perform the same computational task, it does not guarantee that their internal activity dynamics match. This suggests that the trained RNNs might end up performing the task employing a different internal computational mechanism, which would make them a suboptimal model of the biological circuit. In this work, we introduce a novel training strategy that allows learning not only the input-output behavior of an RNN but also its internal network dynamics, based on sparse neural recordings. We test the proposed method by training an RNN to simultaneously reproduce internal dynamics and output signals of a physiologically-inspired neural model. Specifically, this model generates the multiphasic muscle-like activity patterns typically observed during the execution of reaching movements, based on the oscillatory activation patterns concurrently observed in the motor cortex. Remarkably, we show that the reproduction of the internal dynamics is successful even when the training algorithm relies on the activities of a small subset of neurons sampled from the biological network. Furthermore, we show that training the RNNs with this method significantly improves their generalization performance. Overall, our results suggest that the proposed method is suitable for building powerful functional RNN models, which automatically capture important computational properties of the biological circuit of interest from sparse neural recordings.

Learning implicit templates as neural fields has recently shown impressive performance in unsupervised shape correspondence. Despite the success, we observe current approaches, which solely rely on geometric information, often learn suboptimal deformation across generic object shapes, which have high structural variability. In this paper, we highlight the importance of part deformation consistency and propose a semantic-aware implicit template learning framework to enable semantically plausible deformation. By leveraging semantic prior from a self-supervised feature extractor, we suggest local conditioning with novel semantic-aware deformation code and deformation consistency regularizations regarding part deformation, global deformation, and global scaling. Our extensive experiments demonstrate the superiority of the proposed method over baselines in various tasks: keypoint transfer, part label transfer, and texture transfer. More interestingly, our framework shows a larger performance gain under more challenging settings. We also provide qualitative analyses to validate the effectiveness of semantic-aware deformation. The code is available at https://github.com/mlvlab/PDC.

We propose a neural physics system for real-time, interactive fluid simulations. Traditional physics-based methods, while accurate, are computationally intensive and suffer from latency issues. Recent machine-learning methods reduce computational costs while preserving fidelity; yet most still fail to satisfy the latency constraints for real-time use and lack support for interactive applications. To bridge this gap, we introduce a novel hybrid method that integrates numerical simulation, neural physics, and generative control. Our neural physics jointly pursues low-latency simulation and high physical fidelity by employing a fallback safeguard to classical numerical solvers. Furthermore, we develop a diffusion-based controller that is trained using a reverse modeling strategy to generate external dynamic force fields for fluid manipulation. Our system demonstrates robust performance across diverse 2D/3D scenarios, material types, and obstacle interactions, achieving real-time simulations at high frame rates (11~29% latency) while enabling fluid control guided by user-friendly freehand sketches. We present a significant step towards practical, controllable, and physically plausible fluid simulations for real-time interactive applications. We promise to release both models and data upon acceptance.

We present a method to reconstruct time-consistent human body models from monocular videos, focusing on extremely loose clothing or handheld object interactions. Prior work in human reconstruction is either limited to tight clothing with no object interactions, or requires calibrated multi-view captures or personalized template scans which are costly to collect at scale. Our key insight for high-quality yet flexible reconstruction is the careful combination of generic human priors about articulated body shape (learned from large-scale training data) with video-specific articulated "bag-of-bones" deformation (fit to a single video via test-time optimization). We accomplish this by learning a neural implicit model that disentangles body versus clothing deformations as separate motion model layers. To capture subtle geometry of clothing, we leverage image-based priors such as human body pose, surface normals, and optical flow during optimization. The resulting neural fields can be extracted into time-consistent meshes, or further optimized as explicit 3D Gaussians for high-fidelity interactive rendering. On datasets with highly challenging clothing deformations and object interactions, DressRecon yields higher-fidelity 3D reconstructions than prior art. Project page: https://jefftan969.github.io/dressrecon/

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

We introduce Gaussian-Flow, a novel point-based approach for fast dynamic scene reconstruction and real-time rendering from both multi-view and monocular videos. In contrast to the prevalent NeRF-based approaches hampered by slow training and rendering speeds, our approach harnesses recent advancements in point-based 3D Gaussian Splatting (3DGS). Specifically, a novel Dual-Domain Deformation Model (DDDM) is proposed to explicitly model attribute deformations of each Gaussian point, where the time-dependent residual of each attribute is captured by a polynomial fitting in the time domain, and a Fourier series fitting in the frequency domain. The proposed DDDM is capable of modeling complex scene deformations across long video footage, eliminating the need for training separate 3DGS for each frame or introducing an additional implicit neural field to model 3D dynamics. Moreover, the explicit deformation modeling for discretized Gaussian points ensures ultra-fast training and rendering of a 4D scene, which is comparable to the original 3DGS designed for static 3D reconstruction. Our proposed approach showcases a substantial efficiency improvement, achieving a 5times faster training speed compared to the per-frame 3DGS modeling. In addition, quantitative results demonstrate that the proposed Gaussian-Flow significantly outperforms previous leading methods in novel view rendering quality. Project page: https://nju-3dv.github.io/projects/Gaussian-Flow

Implicit neural fields, typically encoded by a multilayer perceptron (MLP) that maps from coordinates (e.g., xyz) to signals (e.g., signed distances), have shown remarkable promise as a high-fidelity and compact representation. However, the lack of a regular and explicit grid structure also makes it challenging to apply generative modeling directly on implicit neural fields in order to synthesize new data. To this end, we propose HyperDiffusion, a novel approach for unconditional generative modeling of implicit neural fields. HyperDiffusion operates directly on MLP weights and generates new neural implicit fields encoded by synthesized MLP parameters. Specifically, a collection of MLPs is first optimized to faithfully represent individual data samples. Subsequently, a diffusion process is trained in this MLP weight space to model the underlying distribution of neural implicit fields. HyperDiffusion enables diffusion modeling over a implicit, compact, and yet high-fidelity representation of complex signals across 3D shapes and 4D mesh animations within one single unified framework.

Understanding the inner workings of neural networks is essential for enhancing model performance and interpretability. Current research predominantly focuses on examining the connection between individual neurons and the model's final predictions. Which suffers from challenges in interpreting the internal workings of the model, particularly when neurons encode multiple unrelated features. In this paper, we propose a novel framework that transitions the focus from analyzing individual neurons to investigating groups of neurons, shifting the emphasis from neuron-output relationships to functional interaction between neurons. Our automated framework, NeurFlow, first identifies core neurons and clusters them into groups based on shared functional relationships, enabling a more coherent and interpretable view of the network's internal processes. This approach facilitates the construction of a hierarchical circuit representing neuron interactions across layers, thus improving interpretability while reducing computational costs. Our extensive empirical studies validate the fidelity of our proposed NeurFlow. Additionally, we showcase its utility in practical applications such as image debugging and automatic concept labeling, thereby highlighting its potential to advance the field of neural network explainability.

State-of-the-art systems neuroscience experiments yield large-scale multimodal data, and these data sets require new tools for analysis. Inspired by the success of large pretrained models in vision and language domains, we reframe the analysis of large-scale, cellular-resolution neuronal spiking data into an autoregressive spatiotemporal generation problem. Neuroformer is a multimodal, multitask generative pretrained transformer (GPT) model that is specifically designed to handle the intricacies of data in systems neuroscience. It scales linearly with feature size, can process an arbitrary number of modalities, and is adaptable to downstream tasks, such as predicting behavior. We first trained Neuroformer on simulated datasets, and found that it both accurately predicted simulated neuronal circuit activity, and also intrinsically inferred the underlying neural circuit connectivity, including direction. When pretrained to decode neural responses, the model predicted the behavior of a mouse with only few-shot fine-tuning, suggesting that the model begins learning how to do so directly from the neural representations themselves, without any explicit supervision. We used an ablation study to show that joint training on neuronal responses and behavior boosted performance, highlighting the model's ability to associate behavioral and neural representations in an unsupervised manner. These findings show that Neuroformer can analyze neural datasets and their emergent properties, informing the development of models and hypotheses associated with the brain.

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

We develop a learning framework for building deformable templates, which play a fundamental role in many image analysis and computational anatomy tasks. Conventional methods for template creation and image alignment to the template have undergone decades of rich technical development. In these frameworks, templates are constructed using an iterative process of template estimation and alignment, which is often computationally very expensive. Due in part to this shortcoming, most methods compute a single template for the entire population of images, or a few templates for specific sub-groups of the data. In this work, we present a probabilistic model and efficient learning strategy that yields either universal or conditional templates, jointly with a neural network that provides efficient alignment of the images to these templates. We demonstrate the usefulness of this method on a variety of domains, with a special focus on neuroimaging. This is particularly useful for clinical applications where a pre-existing template does not exist, or creating a new one with traditional methods can be prohibitively expensive. Our code and atlases are available online as part of the VoxelMorph library at http://voxelmorph.csail.mit.edu.

Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a generic density function. Furthermore, the geometry itself was extracted using an arbitrary level set of the density function leading to a noisy, often low fidelity reconstruction. The goal of this paper is to improve geometry representation and reconstruction in neural volume rendering. We achieve that by modeling the volume density as a function of the geometry. This is in contrast to previous work modeling the geometry as a function of the volume density. In more detail, we define the volume density function as Laplace's cumulative distribution function (CDF) applied to a signed distance function (SDF) representation. This simple density representation has three benefits: (i) it provides a useful inductive bias to the geometry learned in the neural volume rendering process; (ii) it facilitates a bound on the opacity approximation error, leading to an accurate sampling of the viewing ray. Accurate sampling is important to provide a precise coupling of geometry and radiance; and (iii) it allows efficient unsupervised disentanglement of shape and appearance in volume rendering. Applying this new density representation to challenging scene multiview datasets produced high quality geometry reconstructions, outperforming relevant baselines. Furthermore, switching shape and appearance between scenes is possible due to the disentanglement of the two.

This paper introduces a new learning paradigm termed Neural Metamorphosis (NeuMeta), which aims to build self-morphable neural networks. Contrary to crafting separate models for different architectures or sizes, NeuMeta directly learns the continuous weight manifold of neural networks. Once trained, we can sample weights for any-sized network directly from the manifold, even for previously unseen configurations, without retraining. To achieve this ambitious goal, NeuMeta trains neural implicit functions as hypernetworks. They accept coordinates within the model space as input, and generate corresponding weight values on the manifold. In other words, the implicit function is learned in a way, that the predicted weights is well-performed across various models sizes. In training those models, we notice that, the final performance closely relates on smoothness of the learned manifold. In pursuit of enhancing this smoothness, we employ two strategies. First, we permute weight matrices to achieve intra-model smoothness, by solving the Shortest Hamiltonian Path problem. Besides, we add a noise on the input coordinates when training the implicit function, ensuring models with various sizes shows consistent outputs. As such, NeuMeta shows promising results in synthesizing parameters for various network configurations. Our extensive tests in image classification, semantic segmentation, and image generation reveal that NeuMeta sustains full-size performance even at a 75% compression rate.

Cortical visual prostheses aim to restore sight by electrically stimulating neurons in early visual cortex (V1). With the emergence of high-density and flexible neural interfaces, electrode placement within three-dimensional cortex has become a critical surgical planning problem. Existing strategies emphasize visual field coverage and anatomical heuristics but do not directly optimize predicted perceptual outcomes under safety constraints. We present a percept-aware framework for surgical planning of cortical visual prostheses that formulates electrode placement as a constrained optimization problem in anatomical space. Electrode coordinates are treated as learnable parameters and optimized end-to-end using a differentiable forward model of prosthetic vision. The objective minimizes task-level perceptual error while incorporating vascular avoidance and gray matter feasibility constraints. Evaluated on simulated reading and natural image tasks using realistic folded cortical geometry (FreeSurfer fsaverage), percept-aware optimization consistently improves reconstruction fidelity relative to coverage-based placement strategies. Importantly, vascular safety constraints eliminate margin violations while preserving perceptual performance. The framework further enables co-optimization of multi-electrode thread configurations under fixed insertion budgets. These results demonstrate how differentiable percept models can inform anatomically grounded, safety-aware computer-assisted planning for cortical neural interfaces and provide a foundation for optimizing next-generation visual prostheses.

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

In this study, we examine the potential of one of the ``superexpressive'' networks in the context of learning neural functions for representing complex signals and performing machine learning downstream tasks. Our focus is on evaluating their performance on computer vision and scientific machine learning tasks including signal representation/inverse problems and solutions of partial differential equations. Through an empirical investigation in various benchmark tasks, we demonstrate that superexpressive networks, as proposed by [Zhang et al. NeurIPS, 2022], which employ a specialized network structure characterized by having an additional dimension, namely width, depth, and ``height'', can surpass recent implicit neural representations that use highly-specialized nonlinear activation functions.

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural representations. This mismatch leaves no suitable method to solve surface PDEs directly within the neural domain, forcing explicit mesh extraction or per-instance residual training, preventing end-to-end workflows. We present a novel, mesh-free formulation that learns a local update operator conditioned on neural (local) shape attributes, enabling surface PDEs to be solved directly where the (neural) data lives. The operator integrates naturally with prevalent neural surface representations, is trained once on a single representative shape, and generalizes across shape and topology variations, enabling accurate, fast inference without explicit meshing or per-instance optimization while preserving differentiability. Across analytic benchmarks (heat equation and Poisson solve on sphere) and real neural assets across different representations, our method slightly outperforms CPM while remaining reasonably close to FEM, and, to our knowledge, delivers the first end-to-end pipeline that solves surface PDEs on both neural and classical surface representations. Code will be released on acceptance.

Aligning a template to 3D human point clouds is a long-standing problem crucial for tasks like animation, reconstruction, and enabling supervised learning pipelines. Recent data-driven methods leverage predicted surface correspondences. However, they are not robust to varied poses, identities, or noise. In contrast, industrial solutions often rely on expensive manual annotations or multi-view capturing systems. Recently, neural fields have shown promising results. Still, their purely data-driven and extrinsic nature does not incorporate any guidance toward the target surface, often resulting in a trivial misalignment of the template registration. Currently, no method can be considered the standard for 3D Human registration, limiting the scalability of downstream applications. In this work, we propose a neural scalable registration method, NSR, a pipeline that, for the first time, generalizes and scales across thousands of shapes and more than ten different data sources. Our essential contribution is NICP, an ICP-style self-supervised task tailored to neural fields. NSR takes a few seconds, is self-supervised, and works out of the box on pre-trained neural fields. NSR combines NICP with a localized neural field trained on a large MoCap dataset, achieving the state of the art over public benchmarks. The release of our code and checkpoints provides a powerful tool useful for many downstream tasks like dataset alignments, cleaning, or asset animation.

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

Deep implicit functions (DIFs) have emerged as a powerful paradigm for many computer vision tasks such as 3D shape reconstruction, generation, registration, completion, editing, and understanding. However, given a set of 3D shapes with associated covariates there is at present no shape representation method which allows to precisely represent the shapes while capturing the individual dependencies on each covariate. Such a method would be of high utility to researchers to discover knowledge hidden in a population of shapes. For scientific shape discovery, we propose a 3D Neural Additive Model for Interpretable Shape Representation (NAISR) which describes individual shapes by deforming a shape atlas in accordance to the effect of disentangled covariates. Our approach captures shape population trends and allows for patient-specific predictions through shape transfer. NAISR is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. We evaluate NAISR with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer on three datasets: 1) Starman, a simulated 2D shape dataset; 2) the ADNI hippocampus 3D shape dataset; and 3) a pediatric airway 3D shape dataset. Our experiments demonstrate that Starman achieves excellent shape reconstruction performance while retaining interpretability. Our code is available at https://github.com/uncbiag/NAISR{https://github.com/uncbiag/NAISR}.

We present animatable neural radiance fields (animatable NeRF) for detailed human avatar creation from monocular videos. Our approach extends neural radiance fields (NeRF) to the dynamic scenes with human movements via introducing explicit pose-guided deformation while learning the scene representation network. In particular, we estimate the human pose for each frame and learn a constant canonical space for the detailed human template, which enables natural shape deformation from the observation space to the canonical space under the explicit control of the pose parameters. To compensate for inaccurate pose estimation, we introduce the pose refinement strategy that updates the initial pose during the learning process, which not only helps to learn more accurate human reconstruction but also accelerates the convergence. In experiments we show that the proposed approach achieves 1) implicit human geometry and appearance reconstruction with high-quality details, 2) photo-realistic rendering of the human from novel views, and 3) animation of the human with novel poses.

We introduce PICA, a novel representation for high-fidelity animatable clothed human avatars with physics-accurate dynamics, even for loose clothing. Previous neural rendering-based representations of animatable clothed humans typically employ a single model to represent both the clothing and the underlying body. While efficient, these approaches often fail to accurately represent complex garment dynamics, leading to incorrect deformations and noticeable rendering artifacts, especially for sliding or loose garments. Furthermore, previous works represent garment dynamics as pose-dependent deformations and facilitate novel pose animations in a data-driven manner. This often results in outcomes that do not faithfully represent the mechanics of motion and are prone to generating artifacts in out-of-distribution poses. To address these issues, we adopt two individual 3D Gaussian Splatting (3DGS) models with different deformation characteristics, modeling the human body and clothing separately. This distinction allows for better handling of their respective motion characteristics. With this representation, we integrate a graph neural network (GNN)-based clothed body physics simulation module to ensure an accurate representation of clothing dynamics. Our method, through its carefully designed features, achieves high-fidelity rendering of clothed human bodies in complex and novel driving poses, significantly outperforming previous methods under the same settings.

Adversarial examples are often cited by neuroscientists and machine learning researchers as an example of how computational models diverge from biological sensory systems. Recent work has proposed adding biologically-inspired components to visual neural networks as a way to improve their adversarial robustness. One surprisingly effective component for reducing adversarial vulnerability is response stochasticity, like that exhibited by biological neurons. Here, using recently developed geometrical techniques from computational neuroscience, we investigate how adversarial perturbations influence the internal representations of standard, adversarially trained, and biologically-inspired stochastic networks. We find distinct geometric signatures for each type of network, revealing different mechanisms for achieving robust representations. Next, we generalize these results to the auditory domain, showing that neural stochasticity also makes auditory models more robust to adversarial perturbations. Geometric analysis of the stochastic networks reveals overlap between representations of clean and adversarially perturbed stimuli, and quantitatively demonstrates that competing geometric effects of stochasticity mediate a tradeoff between adversarial and clean performance. Our results shed light on the strategies of robust perception utilized by adversarially trained and stochastic networks, and help explain how stochasticity may be beneficial to machine and biological computation.

Humans possess an exceptional ability to imagine 4D scenes, encompassing both motion and 3D geometry, from a single still image. This ability is rooted in our accumulated observations of similar scenes and an intuitive understanding of physics. In this paper, we aim to replicate this capacity in neural networks, specifically focusing on natural fluid imagery. Existing methods for this task typically employ simplistic 2D motion estimators to animate the image, leading to motion predictions that often defy physical principles, resulting in unrealistic animations. Our approach introduces a novel method for generating 4D scenes with physics-consistent animation from a single image. We propose the use of a physics-informed neural network that predicts motion for each surface point, guided by a loss term derived from fundamental physical principles, including the Navier-Stokes equations. To capture appearance, we predict feature-based 3D Gaussians from the input image and its estimated depth, which are then animated using the predicted motions and rendered from any desired camera perspective. Experimental results highlight the effectiveness of our method in producing physically plausible animations, showcasing significant performance improvements over existing methods. Our project page is https://physfluid.github.io/ .

Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that leverage small MLPs and explicit representations, these models train quickly and can fit large scenes. Yet in many applications like rendering and simulation, hybrid neural fields can cause noticeable and unreasonable artifacts. This is because they do not yield accurate spatial derivatives needed for these downstream applications. In this work, we propose two ways to circumvent these challenges. Our first approach is a post hoc operator that uses local polynomial fitting to obtain more accurate derivatives from pre-trained hybrid neural fields. Additionally, we also propose a self-supervised fine-tuning approach that refines the hybrid neural field to yield accurate derivatives directly while preserving the initial signal. We show applications of our method to rendering, collision simulation, and solving PDEs. We observe that using our approach yields more accurate derivatives, reducing artifacts and leading to more accurate simulations in downstream applications.

Current advances in human head modeling allow to generate plausible-looking 3D head models via neural representations. Nevertheless, constructing complete high-fidelity head models with explicitly controlled animation remains an issue. Furthermore, completing the head geometry based on a partial observation, e.g. coming from a depth sensor, while preserving details is often problematic for the existing methods. We introduce a generative model for detailed 3D head meshes on top of an articulated 3DMM which allows explicit animation and high-detail preservation at the same time. Our method is trained in two stages. First, we register a parametric head model with vertex displacements to each mesh of the recently introduced NPHM dataset of accurate 3D head scans. The estimated displacements are baked into a hand-crafted UV layout. Second, we train a StyleGAN model in order to generalize over the UV maps of displacements. The decomposition of the parametric model and high-quality vertex displacements allows us to animate the model and modify it semantically. We demonstrate the results of unconditional generation and fitting to the full or partial observation. The project page is available at https://seva100.github.io/headcraft.

Recent findings suggest that the consecutive layers of ReLU neural networks can be understood geometrically as space folding transformations of the input space, revealing patterns of self-similarity. In this paper, we present the first quantitative analysis of this space folding phenomenon in ReLU neural networks. Our approach focuses on examining how straight paths in the Euclidean input space are mapped to their counterparts in the Hamming activation space. In this process, the convexity of straight lines is generally lost, giving rise to non-convex folding behavior. To quantify this effect, we introduce a novel measure based on range metrics, similar to those used in the study of random walks, and provide the proof for the equivalence of convexity notions between the input and activation spaces. Furthermore, we provide empirical analysis on a geometrical analysis benchmark (CantorNet) as well as an image classification benchmark (MNIST). Our work advances the understanding of the activation space in ReLU neural networks by leveraging the phenomena of geometric folding, providing valuable insights on how these models process input information.

Neural material representations are becoming a popular way to represent materials for rendering. They are more expressive than analytic models and occupy less memory than tabulated BTFs. However, existing neural materials are immutable, meaning that their output for a certain query of UVs, camera, and light vector is fixed once they are trained. While this is practical when there is no need to edit the material, it can become very limiting when the fragment of the material used for training is too small or not tileable, which frequently happens when the material has been captured with a gonioreflectometer. In this paper, we propose a novel neural material representation which jointly tackles the problems of BTF compression, tiling, and extrapolation. At test time, our method uses a guidance image as input to condition the neural BTF to the structural features of this input image. Then, the neural BTF can be queried as a regular BTF using UVs, camera, and light vectors. Every component in our framework is purposefully designed to maximize BTF encoding quality at minimal parameter count and computational complexity, achieving competitive compression rates compared with previous work. We demonstrate the results of our method on a variety of synthetic and captured materials, showing its generality and capacity to learn to represent many optical properties.

Image registration is the process of bringing different images into a common coordinate system - a technique widely used in various applications of computer vision, such as remote sensing, image retrieval, and, most commonly, medical imaging. Deep learning based techniques have been applied successfully to tackle various complex medical image processing problems, including medical image registration. Over the years, several image registration techniques have been proposed using deep learning. Deformable image registration techniques such as Voxelmorph have been successful in capturing finer changes and providing smoother deformations. However, Voxelmorph, as well as ICNet and FIRE, do not explicitly encode global dependencies (i.e. the overall anatomical view of the supplied image) and, therefore, cannot track large deformations. In order to tackle the aforementioned problems, this paper extends the Voxelmorph approach in three different ways. To improve the performance in case of small as well as large deformations, supervision of the model at different resolutions has been integrated using a multi-scale UNet. To support the network to learn and encode the minute structural co-relations of the given image-pairs, a self-constructing graph network (SCGNet) has been used as the latent of the multi-scale UNet - which can improve the learning process of the model and help the model to generalise better. And finally, to make the deformations inverse-consistent, cycle consistency loss has been employed. On the task of registration of brain MRIs, the proposed method achieved significant improvements over ANTs and VoxelMorph, obtaining a Dice score of 0.8013 \pm 0.0243 for intramodal and 0.6211 \pm 0.0309 for intermodal, while VoxelMorph achieved 0.7747 \pm 0.0260 and 0.6071 \pm 0.0510, respectively

Intra-fraction motion in radiotherapy is commonly modeled using deformable image registration (DIR). However, existing methods often struggle to balance speed and accuracy, limiting their applicability in clinical scenarios. This study introduces a novel approach that harnesses Neural Graphics Primitives (NGP) to optimize the displacement vector field (DVF). Our method leverages learned primitives, processed as splats, and interpolates within space using a shallow neural network. Uniquely, it enables self-supervised optimization at an ultra-fast speed, negating the need for pre-training on extensive datasets and allowing seamless adaptation to new cases. We validated this approach on the 4D-CT lung dataset DIR-lab, achieving a target registration error (TRE) of 1.15\pm1.15 mm within a remarkable time of 1.77 seconds. Notably, our method also addresses the sliding boundary problem, a common challenge in conventional DIR methods.

Efficiently digitizing high-fidelity animatable human avatars from videos is a challenging and active research topic. Recent volume rendering-based neural representations open a new way for human digitization with their friendly usability and photo-realistic reconstruction quality. However, they are inefficient for long optimization times and slow inference speed; their implicit nature results in entangled geometry, materials, and dynamics of humans, which are hard to edit afterward. Such drawbacks prevent their direct applicability to downstream applications, especially the prominent rasterization-based graphic ones. We present EMA, a method that Efficiently learns Meshy neural fields to reconstruct animatable human Avatars. It jointly optimizes explicit triangular canonical mesh, spatial-varying material, and motion dynamics, via inverse rendering in an end-to-end fashion. Each above component is derived from separate neural fields, relaxing the requirement of a template, or rigging. The mesh representation is highly compatible with the efficient rasterization-based renderer, thus our method only takes about an hour of training and can render in real-time. Moreover, only minutes of optimization is enough for plausible reconstruction results. The disentanglement of meshes enables direct downstream applications. Extensive experiments illustrate the very competitive performance and significant speed boost against previous methods. We also showcase applications including novel pose synthesis, material editing, and relighting. The project page: https://xk-huang.github.io/ema/.

We interpret the function of individual neurons in CLIP by automatically describing them using text. Analyzing the direct effects (i.e. the flow from a neuron through the residual stream to the output) or the indirect effects (overall contribution) fails to capture the neurons' function in CLIP. Therefore, we present the "second-order lens", analyzing the effect flowing from a neuron through the later attention heads, directly to the output. We find that these effects are highly selective: for each neuron, the effect is significant for <2% of the images. Moreover, each effect can be approximated by a single direction in the text-image space of CLIP. We describe neurons by decomposing these directions into sparse sets of text representations. The sets reveal polysemantic behavior - each neuron corresponds to multiple, often unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we mass-produce "semantic" adversarial examples by generating images with concepts spuriously correlated to the incorrect class. Additionally, we use the second-order effects for zero-shot segmentation and attribute discovery in images. Our results indicate that a scalable understanding of neurons can be used for model deception and for introducing new model capabilities.

Understanding the hidden mechanisms behind human's visual perception is a fundamental question in neuroscience. To that end, investigating into the neural responses of human mind activities, such as functional Magnetic Resonance Imaging (fMRI), has been a significant research vehicle. However, analyzing fMRI signals is challenging, costly, daunting, and demanding for professional training. Despite remarkable progress in fMRI analysis, existing approaches are limited to generating 2D images and far away from being biologically meaningful and practically useful. Under this insight, we propose to generate visually plausible and functionally more comprehensive 3D outputs decoded from brain signals, enabling more sophisticated modeling of fMRI data. Conceptually, we reformulate this task as a {\em fMRI conditioned 3D object generation} problem. We design a novel 3D object representation learning method, Brain3D, that takes as input the fMRI data of a subject who was presented with a 2D image, and yields as output the corresponding 3D object images. The key capabilities of this model include tackling the noises with high-level semantic signals and a two-stage architecture design for progressive high-level information integration. Extensive experiments validate the superior capability of our model over previous state-of-the-art 3D object generation methods. Importantly, we show that our model captures the distinct functionalities of each region of human vision system as well as their intricate interplay relationships, aligning remarkably with the established discoveries in neuroscience. Further, preliminary evaluations indicate that Brain3D can successfully identify the disordered brain regions in simulated scenarios, such as V1, V2, V3, V4, and the medial temporal lobe (MTL) within the human visual system. Our data and code will be available at https://brain-3d.github.io/.

Recent findings suggest that consecutive layers of neural networks with the ReLU activation function fold the input space during the learning process. While many works hint at this phenomenon, an approach to quantify the folding was only recently proposed by means of a space folding measure based on Hamming distance in the ReLU activation space. We generalize this measure to a wider class of activation functions through introduction of equivalence classes of input data, analyse its mathematical and computational properties and come up with an efficient sampling strategy for its implementation. Moreover, it has been observed that space folding values increase with network depth when the generalization error is low, but decrease when the error increases. This underpins that learned symmetries in the data manifold (e.g., invariance under reflection) become visible in terms of space folds, contributing to the network's generalization capacity. Inspired by these findings, we outline a novel regularization scheme that encourages the network to seek solutions characterized by higher folding values.

This article addresses the challenge of modeling the amplitude of spatially indexed low frequency fluctuations (ALFF) in resting state functional MRI as a function of cortical structural features and a multi-task coactivation network in the Adolescent Brain Cognitive Development (ABCD) Study. It proposes a generative model that integrates effects of spatially-varying inputs and a network-valued input using deep neural networks to capture complex non-linear and spatial associations with the output. The method models spatial smoothness, accounts for subject heterogeneity and complex associations between network and spatial images at different scales, enables accurate inference of each images effect on the output image, and allows prediction with uncertainty quantification via Monte Carlo dropout, contributing to one of the first Explainable AI (XAI) frameworks for heterogeneous imaging data. The model is highly scalable to high-resolution data without the heavy pre-processing or summarization often required by Bayesian methods. Empirical results demonstrate its strong performance compared to existing statistical and deep learning methods. We applied the XAI model to the ABCD data which revealed associations between cortical features and ALFF throughout the entire brain. Our model performed comparably to existing methods in predictive accuracy but provided superior uncertainty quantification and faster computation, demonstrating its effectiveness for large-scale neuroimaging analysis. Open-source software in Python for XAI is available.

Over the past decade, predictive modeling of neural responses in the primate visual system has advanced significantly, largely driven by various DNN approaches. These include models optimized directly for visual recognition, cross-modal alignment through contrastive objectives, neural response prediction from scratch, and large language model embeddings.Likewise, different readout mechanisms, ranging from fully linear to spatial-feature factorized methods have been explored for mapping network activations to neural responses. Despite the diversity of these approaches, it remains unclear which method performs best across different visual regions. In this study, we systematically compare these approaches for modeling the human visual system and investigate alternative strategies to improve response predictions. Our findings reveal that for early to mid-level visual areas, response-optimized models with visual inputs offer superior prediction accuracy, while for higher visual regions, embeddings from LLMs based on detailed contextual descriptions of images and task-optimized models pretrained on large vision datasets provide the best fit. Through comparative analysis of these modeling approaches, we identified three distinct regions in the visual cortex: one sensitive primarily to perceptual features of the input that are not captured by linguistic descriptions, another attuned to fine-grained visual details representing semantic information, and a third responsive to abstract, global meanings aligned with linguistic content. We also highlight the critical role of readout mechanisms, proposing a novel scheme that modulates receptive fields and feature maps based on semantic content, resulting in an accuracy boost of 3-23% over existing SOTAs for all models and brain regions. Together, these findings offer key insights into building more precise models of the visual system.

Implicit neural representations (INR) have gained significant popularity for signal and image representation for many end-tasks, such as superresolution, 3D modeling, and more. Most INR architectures rely on sinusoidal positional encoding, which accounts for high-frequency information in data. However, the finite encoding size restricts the model's representational power. Higher representational power is needed to go from representing a single given image to representing large and diverse datasets. Our approach addresses this gap by representing an image with a polynomial function and eliminates the need for positional encodings. Therefore, to achieve a progressively higher degree of polynomial representation, we use element-wise multiplications between features and affine-transformed coordinate locations after every ReLU layer. The proposed method is evaluated qualitatively and quantitatively on large datasets like ImageNet. The proposed Poly-INR model performs comparably to state-of-the-art generative models without any convolution, normalization, or self-attention layers, and with far fewer trainable parameters. With much fewer training parameters and higher representative power, our approach paves the way for broader adoption of INR models for generative modeling tasks in complex domains. The code is available at https://github.com/Rajhans0/Poly_INR

Many AI models trained on natural images develop representations that resemble those of the human brain. However, the factors that drive this brain-model similarity remain poorly understood. To disentangle how the model, training and data independently lead a neural network to develop brain-like representations, we trained a family of self-supervised vision transformers (DINOv3) that systematically varied these different factors. We compare their representations of images to those of the human brain recorded with both fMRI and MEG, providing high resolution in spatial and temporal analyses. We assess the brain-model similarity with three complementary metrics focusing on overall representational similarity, topographical organization, and temporal dynamics. We show that all three factors - model size, training amount, and image type - independently and interactively impact each of these brain similarity metrics. In particular, the largest DINOv3 models trained with the most human-centric images reach the highest brain-similarity. This emergence of brain-like representations in AI models follows a specific chronology during training: models first align with the early representations of the sensory cortices, and only align with the late and prefrontal representations of the brain with considerably more training. Finally, this developmental trajectory is indexed by both structural and functional properties of the human cortex: the representations that are acquired last by the models specifically align with the cortical areas with the largest developmental expansion, thickness, least myelination, and slowest timescales. Overall, these findings disentangle the interplay between architecture and experience in shaping how artificial neural networks come to see the world as humans do, thus offering a promising framework to understand how the human brain comes to represent its visual world.

Neural Radiance Fields (NeRFs) have achieved great success in the past few years. However, most current methods still require intensive resources due to ray marching-based rendering. To construct urban-level radiance fields efficiently, we design Deformable Neural Mesh Primitive~(DNMP), and propose to parameterize the entire scene with such primitives. The DNMP is a flexible and compact neural variant of classic mesh representation, which enjoys both the efficiency of rasterization-based rendering and the powerful neural representation capability for photo-realistic image synthesis. Specifically, a DNMP consists of a set of connected deformable mesh vertices with paired vertex features to parameterize the geometry and radiance information of a local area. To constrain the degree of freedom for optimization and lower the storage budgets, we enforce the shape of each primitive to be decoded from a relatively low-dimensional latent space. The rendering colors are decoded from the vertex features (interpolated with rasterization) by a view-dependent MLP. The DNMP provides a new paradigm for urban-level scene representation with appealing properties: (1) High-quality rendering. Our method achieves leading performance for novel view synthesis in urban scenarios. (2) Low computational costs. Our representation enables fast rendering (2.07ms/1k pixels) and low peak memory usage (110MB/1k pixels). We also present a lightweight version that can run 33times faster than vanilla NeRFs, and comparable to the highly-optimized Instant-NGP (0.61 vs 0.71ms/1k pixels). Project page: https://dnmp.github.io/{https://dnmp.github.io/}.

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.

Despite their success, modern convolutional neural networks (CNNs) exhibit fundamental limitations, including data inefficiency, poor out-of-distribution generalization, and vulnerability to adversarial perturbations. These shortcomings can be traced to a lack of inductive biases that reflect the inherent geometric structure of the visual world. The primate visual system, in contrast, demonstrates superior efficiency and robustness, suggesting that its architectural and computational principles,which evolved to internalize these structures,may offer a blueprint for more capable artificial vision. This paper introduces Visual Cortex Network (VCNet), a novel neural network architecture whose design is informed by the macro-scale organization of the primate visual cortex. VCNet is framed as a geometric framework that emulates key biological mechanisms, including hierarchical processing across distinct cortical areas, dual-stream information segregation for learning disentangled representations, and top-down predictive feedback for representation refinement. We interpret these mechanisms through the lens of geometry and dynamical systems, positing that they guide the learning of structured, low-dimensional neural manifolds. We evaluate VCNet on two specialized benchmarks: the Spots-10 animal pattern dataset, which probes sensitivity to natural textures, and a light field image classification task, which requires processing higher-dimensional visual data. Our results show that VCNet achieves state-of-the-art accuracy of 92.1\% on Spots-10 and 74.4\% on the light field dataset, surpassing contemporary models of comparable size. This work demonstrates that integrating high-level neuroscientific principles, viewed through a geometric lens, can lead to more efficient and robust models, providing a promising direction for addressing long-standing challenges in machine learning.

Meaningful and simplified representations of neural activity can yield insights into how and what information is being processed within a neural circuit. However, without labels, finding representations that reveal the link between the brain and behavior can be challenging. Here, we introduce a novel unsupervised approach for learning disentangled representations of neural activity called Swap-VAE. Our approach combines a generative modeling framework with an instance-specific alignment loss that tries to maximize the representational similarity between transformed views of the input (brain state). These transformed (or augmented) views are created by dropping out neurons and jittering samples in time, which intuitively should lead the network to a representation that maintains both temporal consistency and invariance to the specific neurons used to represent the neural state. Through evaluations on both synthetic data and neural recordings from hundreds of neurons in different primate brains, we show that it is possible to build representations that disentangle neural datasets along relevant latent dimensions linked to behavior.

We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion model trained on a novel benchmark dataset comprising 1,000 synthetically simulated volumetric density fields. The neural diffusion model is trained on the latent codes of a novel, diffusion-friendly, monoplanar representation. The generative model is used to incorporate a tailored parametric diffusion posterior sampling technique into different reconstruction tasks. A physically-based differentiable volume renderer is employed to provide gradients with respect to light transport in the latent space. This stands in contrast to classic NeRF approaches and makes the reconstructions better aligned with observed data. Through various experiments, we demonstrate single-view reconstruction of volumetric clouds at a previously unattainable quality.

Current volumetric biomedical foundation models struggle to generalize as public 3D datasets are small and do not cover the broad diversity of medical procedures, conditions, anatomical regions, and imaging protocols. We address this by creating a representation learning method that instead anticipates strong domain shifts at training time itself. We first propose a data engine that synthesizes highly variable training samples that would enable generalization to new biomedical contexts. To then train a single 3D network for any voxel-level task, we develop a contrastive learning method that pretrains the network to be stable against nuisance imaging variation simulated by the data engine, a key inductive bias for generalization. This network's features can be used as robust representations of input images for downstream tasks and its weights provide a strong, dataset-agnostic initialization for finetuning on new datasets. As a result, we set new standards across both multimodality registration and few-shot segmentation, a first for any 3D biomedical vision model, all without (pre-)training on any existing dataset of real images.

A primary bottleneck in large-scale text-to-video generation today is physical consistency and controllability. Despite recent advances, state-of-the-art models often produce unrealistic motions, such as objects falling upward, or abrupt changes in velocity and direction. Moreover, these models lack precise parameter control, struggling to generate physically consistent dynamics under different initial conditions. We argue that this fundamental limitation stems from current models learning motion distributions solely from appearance, while lacking an understanding of the underlying dynamics. In this work, we propose NewtonGen, a framework that integrates data-driven synthesis with learnable physical principles. At its core lies trainable Neural Newtonian Dynamics (NND), which can model and predict a variety of Newtonian motions, thereby injecting latent dynamical constraints into the video generation process. By jointly leveraging data priors and dynamical guidance, NewtonGen enables physically consistent video synthesis with precise parameter control.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

Rendering moving human bodies at free viewpoints only from a monocular video is quite a challenging problem. The information is too sparse to model complicated human body structures and motions from both view and pose dimensions. Neural radiance fields (NeRF) have shown great power in novel view synthesis and have been applied to human body rendering. However, most current NeRF-based methods bear huge costs for both training and rendering, which impedes the wide applications in real-life scenarios. In this paper, we propose a rendering framework that can learn moving human body structures extremely quickly from a monocular video. The framework is built by integrating both neural fields and neural voxels. Especially, a set of generalizable neural voxels are constructed. With pretrained on various human bodies, these general voxels represent a basic skeleton and can provide strong geometric priors. For the fine-tuning process, individual voxels are constructed for learning differential textures, complementary to general voxels. Thus learning a novel body can be further accelerated, taking only a few minutes. Our method shows significantly higher training efficiency compared with previous methods, while maintaining similar rendering quality. The project page is at https://taoranyi.com/gneuvox .

Task-trained recurrent neural networks (RNNs) are widely used in neuroscience and machine learning to model dynamical computations. To gain mechanistic insight into how neural systems solve tasks, prior work often reverse-engineers individual trained networks. However, different RNNs trained on the same task and achieving similar performance can exhibit strikingly different internal solutions, a phenomenon known as solution degeneracy. Here, we develop a unified framework to systematically quantify and control solution degeneracy across three levels: behavior, neural dynamics, and weight space. We apply this framework to 3,400 RNNs trained on four neuroscience-relevant tasks: flip-flop memory, sine wave generation, delayed discrimination, and path integration, while systematically varying task complexity, learning regime, network size, and regularization. We find that higher task complexity and stronger feature learning reduce degeneracy in neural dynamics but increase it in weight space, with mixed effects on behavior. In contrast, larger networks and structural regularization reduce degeneracy at all three levels. These findings empirically validate the Contravariance Principle and provide practical guidance for researchers seeking to tune the variability of RNN solutions, either to uncover shared neural mechanisms or to model the individual variability observed in biological systems. This work provides a principled framework for quantifying and controlling solution degeneracy in task-trained RNNs, offering new tools for building more interpretable and biologically grounded models of neural computation.

High-quality material synthesis is essential for replicating complex surface properties to create realistic digital scenes. However, existing methods often suffer from inefficiencies in time and memory, require domain expertise, or demand extensive training data, with high-dimensional material data further constraining performance. Additionally, most approaches lack multi-modal guidance capabilities and standardized evaluation metrics, limiting control and comparability in synthesis tasks. To address these limitations, we propose NeuMaDiff, a novel neural material synthesis framework utilizing hyperdiffusion. Our method employs neural fields as a low-dimensional representation and incorporates a multi-modal conditional hyperdiffusion model to learn the distribution over material weights. This enables flexible guidance through inputs such as material type, text descriptions, or reference images, providing greater control over synthesis. To support future research, we contribute two new material datasets and introduce two BRDF distributional metrics for more rigorous evaluation. We demonstrate the effectiveness of NeuMaDiff through extensive experiments, including a novel statistics-based constrained synthesis approach, which enables the generation of materials of desired categories.

The neurons of artificial neural networks were originally invented when much less was known about biological neurons than is known today. Our work explores a modification to the core neuron unit to make it more parallel to a biological neuron. The modification is made with the knowledge that biological dendrites are not simply passive activation funnels, but also compute complex non-linear functions as they transmit activation to the cell body. The paper explores a novel system of "Perforated" backpropagation empowering the artificial neurons of deep neural networks to achieve better performance coding for the same features they coded for in the original architecture. After an initial network training phase, additional "Dendrite Nodes" are added to the network and separately trained with a different objective: to correlate their output with the remaining error of the original neurons. The trained Dendrite Nodes are then frozen, and the original neurons are further trained, now taking into account the additional error signals provided by the Dendrite Nodes. The cycle of training the original neurons and then adding and training Dendrite Nodes can be repeated several times until satisfactory performance is achieved. Our algorithm was successfully added to modern state-of-the-art PyTorch networks across multiple domains, improving upon original accuracies and allowing for significant model compression without a loss in accuracy.