Daily Papers

We introduce a framework for learning continuous neural representations of formal specifications by distilling the geometry of their semantics into a latent space. Existing approaches rely either on symbolic kernels -- which preserve behavioural semantics but are computationally prohibitive, anchor-dependent, and non-invertible -- or on syntax-based neural embeddings that fail to capture underlying structures. Our method bridges this gap: using a teacher-student setup, we distill a symbolic robustness kernel into a Transformer encoder. Unlike standard contrastive methods, we supervise the model with a continuous, kernel-weighted geometric alignment objective that penalizes errors in proportion to their semantic discrepancies. Once trained, the encoder produces embeddings in a single forward pass, effectively mimicking the kernel's logic at a fraction of its computational cost. We apply our framework to Signal Temporal Logic (STL), demonstrating that the resulting neural representations faithfully preserve the semantic similarity of STL formulae, accurately predict robustness and constraint satisfaction, and remain intrinsically invertible. Our proposed approach enables highly efficient, scalable neuro-symbolic reasoning and formula reconstruction without repeated kernel computation at runtime.

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals with a small number of parameters. However, existing INR models often fail to capture important frequency components specific to each task. To address this issue, in this paper, we propose a Fourier Kolmogorov Arnold network (FKAN) for INRs. The proposed FKAN utilizes learnable activation functions modeled as Fourier series in the first layer to effectively control and learn the task-specific frequency components. In addition, the activation functions with learnable Fourier coefficients improve the ability of the network to capture complex patterns and details, which is beneficial for high-resolution and high-dimensional data. Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes, and improves the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) for the image representation task and intersection over union (IoU) for the 3D occupancy volume representation task, respectively.

Self-supervised learning methods like masked autoencoders (MAE) have shown significant promise in learning robust feature representations, particularly in image reconstruction-based pretraining task. However, their performance is often strongly dependent on the masking strategies used during training and can degrade when applied to out-of-distribution data. To address these limitations, we introduce the masked implicit neural representations (MINR) framework that synergizes implicit neural representations with masked image modeling. MINR learns a continuous function to represent images, enabling more robust and generalizable reconstructions irrespective of masking strategies. Our experiments demonstrate that MINR not only outperforms MAE in in-domain scenarios but also in out-of-distribution settings, while reducing model complexity. The versatility of MINR extends to various self-supervised learning applications, confirming its utility as a robust and efficient alternative to existing frameworks.

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state-of-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields.

Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signal's spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. We propose to leverage periodic activation functions for implicit neural representations and demonstrate that these networks, dubbed sinusoidal representation networks or Sirens, are ideally suited for representing complex natural signals and their derivatives. We analyze Siren activation statistics to propose a principled initialization scheme and demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how Sirens can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. Lastly, we combine Sirens with hypernetworks to learn priors over the space of Siren functions.

Implicit Neural Representations (INRs) have revolutionized signal processing and computer vision by modeling signals as continuous, differentiable functions parameterized by neural networks. However, their inherent formulation as a regression problem makes them prone to regression to the mean, limiting their ability to capture fine details, retain high-frequency information, and handle noise effectively. To address these challenges, we propose Iterative Implicit Neural Representations (I-INRs) a novel plug-and-play framework that enhances signal reconstruction through an iterative refinement process. I-INRs effectively recover high-frequency details, improve robustness to noise, and achieve superior reconstruction quality. Our framework seamlessly integrates with existing INR architectures, delivering substantial performance gains across various tasks. Extensive experiments show that I-INRs outperform baseline methods, including WIRE, SIREN, and Gauss, in diverse computer vision applications such as image restoration, image denoising, and object occupancy prediction.

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

Implicit Neural Representation (INR) has emerged as a powerful tool for encoding discrete signals into continuous, differentiable functions using neural networks. However, these models often have an unfortunate reliance on monolithic architectures to represent high-dimensional data, leading to prohibitive computational costs as dimensionality grows. We propose F-INR, a framework that reformulates INR learning through functional tensor decomposition, breaking down high-dimensional tasks into lightweight, axis-specific sub-networks. Each sub-network learns a low-dimensional data component (e.g., spatial or temporal). Then, we combine these components via tensor operations, reducing forward pass complexity while improving accuracy through specialized learning. F-INR is modular and, therefore, architecture-agnostic, compatible with MLPs, SIREN, WIRE, or other state-of-the-art INR architecture. It is also decomposition-agnostic, supporting CP, TT, and Tucker modes with user-defined rank for speed-accuracy control. In our experiments, F-INR trains 100times faster than existing approaches on video tasks while achieving higher fidelity (+3.4 dB PSNR). Similar gains hold for image compression, physics simulations, and 3D geometry reconstruction. Through this, F-INR offers a new scalable, flexible solution for high-dimensional signal modeling.

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs excel especially in low-data regimes, where it outperforms existing methods by an order of magnitude in mean squared error for imputation task.

Multi-layer perceptrons (MLP) have proven to be effective scene encoders when combined with higher-dimensional projections of the input, commonly referred to as positional encoding. However, scenes with a wide frequency spectrum remain a challenge: choosing high frequencies for positional encoding introduces noise in low structure areas, while low frequencies result in poor fitting of detailed regions. To address this, we propose a progressive positional encoding, exposing a hierarchical MLP structure to incremental sets of frequency encodings. Our model accurately reconstructs scenes with wide frequency bands and learns a scene representation at progressive level of detail without explicit per-level supervision. The architecture is modular: each level encodes a continuous implicit representation that can be leveraged separately for its respective resolution, meaning a smaller network for coarser reconstructions. Experiments on several 2D and 3D datasets show improvements in reconstruction accuracy, representational capacity and training speed compared to baselines.

Reconfigurable intelligent surfaces (RISs) have become one of the key technologies in 6G wireless communications. By configuring the reflection beamforming codebooks, RIS focuses signals on target receivers. In this paper, we investigate the codebook configuration for 1-bit RIS-aided systems. We propose a novel learning-based method built upon the advanced methodology of implicit neural representations. The proposed model learns a continuous and differentiable coordinate-to-codebook representation from samplings. Our method only requires the information of the user's coordinate and avoids the assumption of channel models. Moreover, we propose an encoding-decoding strategy to reduce the dimension of codebooks, and thus improve the learning efficiency of the proposed method. Experimental results on simulation and measured data demonstrated the remarkable advantages of the proposed method.

Recent studies have introduced a new class of generative models for synthesizing implicit neural representations (INRs) that capture arbitrary continuous signals in various domains. These models opened the door for domain-agnostic generative models, but they often fail to achieve high-quality generation. We observed that the existing methods generate the weights of neural networks to parameterize INRs and evaluate the network with fixed positional embeddings (PEs). Arguably, this architecture limits the expressive power of generative models and results in low-quality INR generation. To address this limitation, we propose Domain-agnostic Latent Diffusion Model for INRs (DDMI) that generates adaptive positional embeddings instead of neural networks' weights. Specifically, we develop a Discrete-to-continuous space Variational AutoEncoder (D2C-VAE), which seamlessly connects discrete data and the continuous signal functions in the shared latent space. Additionally, we introduce a novel conditioning mechanism for evaluating INRs with the hierarchically decomposed PEs to further enhance expressive power. Extensive experiments across four modalities, e.g., 2D images, 3D shapes, Neural Radiance Fields, and videos, with seven benchmark datasets, demonstrate the versatility of DDMI and its superior performance compared to the existing INR generative models.

Clinical routine and retrospective cohorts commonly include multi-parametric Magnetic Resonance Imaging; however, they are mostly acquired in different anisotropic 2D views due to signal-to-noise-ratio and scan-time constraints. Thus acquired views suffer from poor out-of-plane resolution and affect downstream volumetric image analysis that typically requires isotropic 3D scans. Combining different views of multi-contrast scans into high-resolution isotropic 3D scans is challenging due to the lack of a large training cohort, which calls for a subject-specific framework. This work proposes a novel solution to this problem leveraging Implicit Neural Representations (INR). Our proposed INR jointly learns two different contrasts of complementary views in a continuous spatial function and benefits from exchanging anatomical information between them. Trained within minutes on a single commodity GPU, our model provides realistic super-resolution across different pairs of contrasts in our experiments with three datasets. Using Mutual Information (MI) as a metric, we find that our model converges to an optimum MI amongst sequences, achieving anatomically faithful reconstruction. Code is available at: https://github.com/jqmcginnis/multi_contrast_inr/

Natural images are continuous, yet most generative models synthesize them on discrete grids, limiting resolution-flexible generation. Continuous neural fields enable resolution-free rendering, but prior methods introduce continuity only at the decoding stage as an interpolation module, leaving the generative latent space discretized and reconstruction-oriented. We propose RaPD (Resolution-agnostic Pixel Diffusion), which performs diffusion in a continuous Neural Image Field (NIF) latent space. RaPD bridges this reconstruction-generation gap with Semantic Representation Guidance for generation-aware latent learning and a Coordinate-Queried Attention Renderer for coordinate-conditioned, scale-aware rendering. A single denoised latent can be rendered at arbitrary resolutions by changing only the query coordinates, keeping diffusion cost fixed. Experiments demonstrate superior generation quality and resolution scalability.

Multispectral satellite images play a vital role in agriculture, fisheries, and environmental monitoring. However, their high dimensionality, large data volumes, and diverse spatial resolutions across multiple channels pose significant challenges for data compression and analysis. This paper presents ImpliSat, a unified framework specifically designed to address these challenges through efficient compression and reconstruction of multispectral satellite data. ImpliSat leverages Implicit Neural Representations (INR) to model satellite images as continuous functions over coordinate space, capturing fine spatial details across varying spatial resolutions. Furthermore, we introduce a Fourier modulation algorithm that dynamically adjusts to the spectral and spatial characteristics of each band, ensuring optimal compression while preserving critical image details.

Recent advances in implicit neural representations (INRs) have shown significant promise in modeling visual signals for various low-vision tasks including image super-resolution (ISR). INR-based ISR methods typically learn continuous representations, providing flexibility for generating high-resolution images at any desired scale from their low-resolution counterparts. However, existing INR-based ISR methods utilize multi-layer perceptrons for parameterization in the network; this does not take account of the hierarchical structure existing in local sampling points and hence constrains the representation capability. In this paper, we propose a new Hierarchical encoding based Implicit Image Function for continuous image super-resolution, HIIF, which leverages a novel hierarchical positional encoding that enhances the local implicit representation, enabling it to capture fine details at multiple scales. Our approach also embeds a multi-head linear attention mechanism within the implicit attention network by taking additional non-local information into account. Our experiments show that, when integrated with different backbone encoders, HIIF outperforms the state-of-the-art continuous image super-resolution methods by up to 0.17dB in PSNR. The source code of HIIF will be made publicly available at www.github.com.

Continuous space-time video super-resolution (C-STVSR) aims to simultaneously enhance video resolution and frame rate at an arbitrary scale. Recently, implicit neural representation (INR) has been applied to video restoration, representing videos as implicit fields that can be decoded at an arbitrary scale. However, the highly ill-posed nature of C-STVSR limits the effectiveness of current INR-based methods: they assume linear motion between frames and use interpolation or feature warping to generate features at arbitrary spatiotemporal positions with two consecutive frames. This restrains C-STVSR from capturing rapid and nonlinear motion and long-term dependencies (involving more than two frames) in complex dynamic scenes. In this paper, we propose a novel C-STVSR framework, called HR-INR, which captures both holistic dependencies and regional motions based on INR. It is assisted by an event camera, a novel sensor renowned for its high temporal resolution and low latency. To fully utilize the rich temporal information from events, we design a feature extraction consisting of (1) a regional event feature extractor - taking events as inputs via the proposed event temporal pyramid representation to capture the regional nonlinear motion and (2) a holistic event-frame feature extractor for long-term dependence and continuity motion. We then propose a novel INR-based decoder with spatiotemporal embeddings to capture long-term dependencies with a larger temporal perception field. We validate the effectiveness and generalization of our method on four datasets (both simulated and real data), showing the superiority of our method.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

Neural Fields have emerged as a transformative approach for 3D scene representation in computer vision and robotics, enabling accurate inference of geometry, 3D semantics, and dynamics from posed 2D data. Leveraging differentiable rendering, Neural Fields encompass both continuous implicit and explicit neural representations enabling high-fidelity 3D reconstruction, integration of multi-modal sensor data, and generation of novel viewpoints. This survey explores their applications in robotics, emphasizing their potential to enhance perception, planning, and control. Their compactness, memory efficiency, and differentiability, along with seamless integration with foundation and generative models, make them ideal for real-time applications, improving robot adaptability and decision-making. This paper provides a thorough review of Neural Fields in robotics, categorizing applications across various domains and evaluating their strengths and limitations, based on over 200 papers. First, we present four key Neural Fields frameworks: Occupancy Networks, Signed Distance Fields, Neural Radiance Fields, and Gaussian Splatting. Second, we detail Neural Fields' applications in five major robotics domains: pose estimation, manipulation, navigation, physics, and autonomous driving, highlighting key works and discussing takeaways and open challenges. Finally, we outline the current limitations of Neural Fields in robotics and propose promising directions for future research. Project page: https://robonerf.github.io

Neural fields, also known as implicit neural representations (INRs), have shown a remarkable capability of representing, generating, and manipulating various data types, allowing for continuous data reconstruction at a low memory footprint. Though promising, INRs applied to video compression still need to improve their rate-distortion performance by a large margin, and require a huge number of parameters and long training iterations to capture high-frequency details, limiting their wider applicability. Resolving this problem remains a quite challenging task, which would make INRs more accessible in compression tasks. We take a step towards resolving these shortcomings by introducing neural representations for videos NeRV++, an enhanced implicit neural video representation, as more straightforward yet effective enhancement over the original NeRV decoder architecture, featuring separable conv2d residual blocks (SCRBs) that sandwiches the upsampling block (UB), and a bilinear interpolation skip layer for improved feature representation. NeRV++ allows videos to be directly represented as a function approximated by a neural network, and significantly enhance the representation capacity beyond current INR-based video codecs. We evaluate our method on UVG, MCL JVC, and Bunny datasets, achieving competitive results for video compression with INRs. This achievement narrows the gap to autoencoder-based video coding, marking a significant stride in INR-based video compression research.

Implicit Neural Representations (INRs) have become an essential tool for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Popular architectures such as SIREN, WIRE, and FINER demonstrate the potential of INR for capturing fine-grained image details. However, traditional INRs often lack explicit geometric structure and have limited capabilities for local editing or integration with physical simulation, restricting their applicability in dynamic or interactive settings. To address these limitations, we propose GaINeR: Geometry-Aware Implicit Network Representation, a novel framework for 2D images that combines trainable Gaussian distributions with a neural network-based INR. For a given image coordinate, the model retrieves the K nearest Gaussians, aggregates distance-weighted embeddings, and predicts the RGB value via a neural network. This design enables continuous image representation, interpretable geometric structure, and flexible local editing, providing a foundation for physically aware and interactive image manipulation. The official implementation of our method is publicly available at https://github.com/WJakubowska/GaINeR.

Implicit Neural Representations (INRs) approximate discrete data through continuous functions and are commonly used for encoding 2D images. Traditional image-based INRs employ neural networks to map pixel coordinates to RGB values, capturing shapes, colors, and textures within the network's weights. Recently, GaussianImage has been proposed as an alternative, using Gaussian functions instead of neural networks to achieve comparable quality and compression. Such a solution obtains a quality and compression ratio similar to classical INR models but does not allow image modification. In contrast, our work introduces a novel method, MiraGe, which uses mirror reflections to perceive 2D images in 3D space and employs flat-controlled Gaussians for precise 2D image editing. Our approach improves the rendering quality and allows realistic image modifications, including human-inspired perception of photos in the 3D world. Thanks to modeling images in 3D space, we obtain the illusion of 3D-based modification in 2D images. We also show that our Gaussian representation can be easily combined with a physics engine to produce physics-based modification of 2D images. Consequently, MiraGe allows for better quality than the standard approach and natural modification of 2D images

Implicit Neural Representations (INRs) employ neural networks to approximate discrete data as continuous functions. In the context of video data, such models can be utilized to transform the coordinates of pixel locations along with frame occurrence times (or indices) into RGB color values. Although INRs facilitate effective compression, they are unsuitable for editing purposes. One potential solution is to use a 3D Gaussian Splatting (3DGS) based model, such as the Video Gaussian Representation (VGR), which is capable of encoding video as a multitude of 3D Gaussians and is applicable for numerous video processing operations, including editing. Nevertheless, in this case, the capacity for modification is constrained to a limited set of basic transformations. To address this issue, we introduce the Video Gaussian Splatting (VeGaS) model, which enables realistic modifications of video data. To construct VeGaS, we propose a novel family of Folded-Gaussian distributions designed to capture nonlinear dynamics in a video stream and model consecutive frames by 2D Gaussians obtained as respective conditional distributions. Our experiments demonstrate that VeGaS outperforms state-of-the-art solutions in frame reconstruction tasks and allows realistic modifications of video data. The code is available at: https://github.com/gmum/VeGaS.

Ultra-high-resolution image generation poses great challenges, such as increased semantic planning complexity and detail synthesis difficulties, alongside substantial training resource demands. We present UltraPixel, a novel architecture utilizing cascade diffusion models to generate high-quality images at multiple resolutions (e.g., 1K to 6K) within a single model, while maintaining computational efficiency. UltraPixel leverages semantics-rich representations of lower-resolution images in the later denoising stage to guide the whole generation of highly detailed high-resolution images, significantly reducing complexity. Furthermore, we introduce implicit neural representations for continuous upsampling and scale-aware normalization layers adaptable to various resolutions. Notably, both low- and high-resolution processes are performed in the most compact space, sharing the majority of parameters with less than 3% additional parameters for high-resolution outputs, largely enhancing training and inference efficiency. Our model achieves fast training with reduced data requirements, producing photo-realistic high-resolution images and demonstrating state-of-the-art performance in extensive experiments.

Modeling the bidirectional correspondence between external sensory stimuli and internal neural activity has emerged as a critical frontier in neuroscience. However, existing approaches predominantly treat brain encoding and decoding as isolated tasks, relying heavily on unimodal alignment and external priors while overlooking the brain's intrinsic nature as a multimodal integration system. To address these limitations, we propose BrainJanus, the first unified brain model that integrates brain, vision, and language within a single framework. Specifically, we introduce a Unified Brain Tokenizer to quantize continuous neural dynamics into discrete tokens aligned with visual and linguistic representations in a shared Omni space. Building on this, we utilize an All-in-One autoregressive architecture that leverages next-token prediction to enable seamless any-to-any generation, which encompasses image-to-brain and text-to-brain encoding, and brain-to-image and brain-to-text decoding. Extensive experiments demonstrate that BrainJanus achieves superior performance across diverse benchmarks. Furthermore, our framework exhibits zero-shot generalization and preserves interpretable biological topography, highlighting its potential as a general-purpose brain modeling paradigm. The code is available at https://github.com/HaitaoWuTJU/BrainJanus{GitHub}.

Humans rely on their visual and tactile senses to develop a comprehensive 3D understanding of their physical environment. Recently, there has been a growing interest in exploring and manipulating objects using data-driven approaches that utilise high-resolution vision-based tactile sensors. However, 3D shape reconstruction using tactile sensing has lagged behind visual shape reconstruction because of limitations in existing techniques, including the inability to generalise over unseen shapes, the absence of real-world testing, and limited expressive capacity imposed by discrete representations. To address these challenges, we propose TouchSDF, a Deep Learning approach for tactile 3D shape reconstruction that leverages the rich information provided by a vision-based tactile sensor and the expressivity of the implicit neural representation DeepSDF. Our technique consists of two components: (1) a Convolutional Neural Network that maps tactile images into local meshes representing the surface at the touch location, and (2) an implicit neural function that predicts a signed distance function to extract the desired 3D shape. This combination allows TouchSDF to reconstruct smooth and continuous 3D shapes from tactile inputs in simulation and real-world settings, opening up research avenues for robust 3D-aware representations and improved multimodal perception in robotics. Code and supplementary material are available at: https://touchsdf.github.io/

In recent years, huge progress has been made on learning neural implicit representations from multi-view images for 3D reconstruction. As an additional input complementing coordinates, using sinusoidal functions as positional encodings plays a key role in revealing high frequency details with coordinate-based neural networks. However, high frequency positional encodings make the optimization unstable, which results in noisy reconstructions and artifacts in empty space. To resolve this issue in a general sense, we introduce to learn neural implicit representations with quantized coordinates, which reduces the uncertainty and ambiguity in the field during optimization. Instead of continuous coordinates, we discretize continuous coordinates into discrete coordinates using nearest interpolation among quantized coordinates which are obtained by discretizing the field in an extremely high resolution. We use discrete coordinates and their positional encodings to learn implicit functions through volume rendering. This significantly reduces the variations in the sample space, and triggers more multi-view consistency constraints on intersections of rays from different views, which enables to infer implicit function in a more effective way. Our quantized coordinates do not bring any computational burden, and can seamlessly work upon the latest methods. Our evaluations under the widely used benchmarks show our superiority over the state-of-the-art. Our code is available at https://github.com/MachinePerceptionLab/CQ-NIR.

Recent advances in Neural Fields have enabled powerful, discretization-invariant methods for learning neural operators that approximate solutions of Partial Differential Equations (PDEs) on general geometries. Building on these developments, we introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations with non-parameterized geometric variability, based on recently proposed Equivariant Neural Field architectures. In enf2enf, input geometries are encoded into latent point cloud embeddings that inherently preserve geometric grounding and capture local phenomena. The resulting representations are then combined with global parameters and directly decoded into continuous output fields, thus efficiently modeling the coupling between geometry and physics. By leveraging the inductive biases of locality and translation invariance, our approach is able to capture fine-scale physical features as well as complex shape variations, thereby enhancing generalization and physical compliance. Extensive experiments on a high-fidelity aerodynamic dataset, a hyper-elastic material benchmark, and multi-element airfoil geometries, demonstrate that the proposed model achieves superior or competitive performance compared to state-of-the-art graph based, operator learning, and neural field methods. Notably, our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes while maintaining high accuracy on full-scale discretizations.

Humans represent scenes and objects in rich feature spaces, carrying information that allows us to generalise about category memberships and abstract functions with few examples. What determines whether a neural network model generalises like a human? We tested how well the representations of 86 pretrained neural network models mapped to human learning trajectories across two tasks where humans had to learn continuous relationships and categories of natural images. In these tasks, both human participants and neural networks successfully identified the relevant stimulus features within a few trials, demonstrating effective generalisation. We found that while training dataset size was a core determinant of alignment with human choices, contrastive training with multi-modal data (text and imagery) was a common feature of currently publicly available models that predicted human generalisation. Intrinsic dimensionality of representations had different effects on alignment for different model types. Lastly, we tested three sets of human-aligned representations and found no consistent improvements in predictive accuracy compared to the baselines. In conclusion, pretrained neural networks can serve to extract representations for cognitive models, as they appear to capture some fundamental aspects of cognition that are transferable across tasks. Both our paradigms and modelling approach offer a novel way to quantify alignment between neural networks and humans and extend cognitive science into more naturalistic domains.

Neural implicit representations are drawing a lot of attention from the robotics community recently, as they are expressive, continuous and compact. However, city-scale continual implicit dense mapping based on sparse LiDAR input is still an under-explored challenge. To this end, we successfully build a city-scale continual neural mapping system with a panoptic representation that consists of environment-level and instance-level modelling. Given a stream of sparse LiDAR point cloud, it maintains a dynamic generative model that maps 3D coordinates to signed distance field (SDF) values. To address the difficulty of representing geometric information at different levels in city-scale space, we propose a tailored three-layer sampling strategy to dynamically sample the global, local and near-surface domains. Meanwhile, to realize high fidelity mapping of instance under incomplete observation, category-specific prior is introduced to better model the geometric details. We evaluate on the public SemanticKITTI dataset and demonstrate the significance of the newly proposed three-layer sampling strategy and panoptic representation, using both quantitative and qualitative results. Codes and model will be publicly available.

Representing 3D surfaces as level sets of continuous functions over R^3 is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision tasks. In order to represent 3D motion within this framework, it is often assumed (either explicitly or implicitly) that the transformations which a surface may undergo are homeomorphic: this is not necessarily true, for instance, in the case of fluid dynamics. In order to represent more general classes of deformations, we propose to apply this theoretical framework as regularizers for the optimization of simple 4D implicit functions (such as signed distance fields). We show that our representation is capable of capturing both homeomorphic and topology-changing deformations, while also defining correspondences over the continuously-reconstructed surfaces.

Sparse autoencoders (SAEs) are widely used to extract interpretable features from neural network representations, often under the implicit assumption that concepts correspond to independent linear directions. However, a growing body of evidence suggests that many concepts are instead organized along low-dimensional manifolds encoding continuous geometric relationships. This raises three basic questions: what does it mean for an SAE to capture a manifold, when do existing SAE architectures do so, and how? We develop a theoretical framework that answers these questions and show that SAEs can capture manifolds in two fundamentally different ways: globally, by allocating a compact group of atoms whose linear span contains the entire manifold, or locally, by distributing it across features that each selectively tile a restricted region of the underlying geometry. Empirically, we find that SAEs suboptimally recover continuous structures, mixing the global subspace and local tiling solutions in a fragmented regime we call dilution. This explains why manifold structure is rarely visible at the level of individual concepts and motivates post-hoc unsupervised discovery methods that search for coherent groups of atoms rather than isolated directions. More broadly, our results suggest that future representation learning methods should treat geometric objects, not just individual directions, as the basic units of interpretability.

In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this to topological concepts such as homeomorphism and embedding. We then investigate what are continuous and discontinuous representations for 2D, 3D, and n-dimensional rotations. We demonstrate that for 3D rotations, all representations are discontinuous in the real Euclidean spaces of four or fewer dimensions. Thus, widely used representations such as quaternions and Euler angles are discontinuous and difficult for neural networks to learn. We show that the 3D rotations have continuous representations in 5D and 6D, which are more suitable for learning. We also present continuous representations for the general case of the n-dimensional rotation group SO(n). While our main focus is on rotations, we also show that our constructions apply to other groups such as the orthogonal group and similarity transforms. We finally present empirical results, which show that our continuous rotation representations outperform discontinuous ones for several practical problems in graphics and vision, including a simple autoencoder sanity test, a rotation estimator for 3D point clouds, and an inverse kinematics solver for 3D human poses.

Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

Neural implicit surface representation techniques are in high demand for advancing technologies in augmented reality/virtual reality, digital twins, autonomous navigation, and many other fields. With their ability to model object surfaces in a scene as a continuous function, such techniques have made remarkable strides recently, especially over classical 3D surface reconstruction methods, such as those that use voxels or point clouds. However, these methods struggle with scenes that have varied and complex surfaces principally because they model any given scene with a single encoder network that is tasked to capture all of low through high-surface frequency information in the scene simultaneously. In this work, we propose a novel, neural implicit surface representation approach called FreBIS to overcome this challenge. FreBIS works by stratifying the scene based on the frequency of surfaces into multiple frequency levels, with each level (or a group of levels) encoded by a dedicated encoder. Moreover, FreBIS encourages these encoders to capture complementary information by promoting mutual dissimilarity of the encoded features via a novel, redundancy-aware weighting module. Empirical evaluations on the challenging BlendedMVS dataset indicate that replacing the standard encoder in an off-the-shelf neural surface reconstruction method with our frequency-stratified encoders yields significant improvements. These enhancements are evident both in the quality of the reconstructed 3D surfaces and in the fidelity of their renderings from any viewpoint.

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However, these methods suffer from a slow inference due to the slow convergence of neural networks and the extensive calculation of distances to surface points, which limits them to small scale points. To resolve the scalability issue in surface reconstruction, we propose GridPull to improve the efficiency of learning implicit representations from large scale point clouds. Our novelty lies in the fast inference of a discrete distance field defined on grids without using any neural components. To remedy the lack of continuousness brought by neural networks, we introduce a loss function to encourage continuous distances and consistent gradients in the field during pulling queries onto the surface in grids near to the surface. We use uniform grids for a fast grid search to localize sampled queries, and organize surface points in a tree structure to speed up the calculation of distances to the surface. We do not rely on learning priors or normal supervision during optimization, and achieve superiority over the latest methods in terms of complexity and accuracy. We evaluate our method on shape and scene benchmarks, and report numerical and visual comparisons with the latest methods to justify our effectiveness and superiority. The code is available at https://github.com/chenchao15/GridPull.

Recent research in medical image analysis with deep learning almost exclusively focuses on grid- or voxel-based data representations. We challenge this common choice by introducing MedFuncta, a modality-agnostic continuous data representation based on neural fields. We demonstrate how to scale neural fields from single instances to large datasets by exploiting redundancy in medical signals and by applying an efficient meta-learning approach with a context reduction scheme. We further address the spectral bias in commonly used SIREN activations, by introducing an omega_0-schedule, improving reconstruction quality and convergence speed. We validate our proposed approach on a large variety of medical signals of different dimensions and modalities (1D: ECG; 2D: Chest X-ray, Retinal OCT, Fundus Camera, Dermatoscope, Colon Histopathology, Cell Microscopy; 3D: Brain MRI, Lung CT) and successfully demonstrate that we can solve relevant downstream tasks on these representations. We additionally release a large-scale dataset of > 550k annotated neural fields to promote research in this direction.

Although mission-critical applications require the use of deep neural networks (DNNs), their continuous execution at mobile devices results in a significant increase in energy consumption. While edge offloading can decrease energy consumption, erratic patterns in channel quality, network and edge server load can lead to severe disruption of the system's key operations. An alternative approach, called split computing, generates compressed representations within the model (called "bottlenecks"), to reduce bandwidth usage and energy consumption. Prior work has proposed approaches that introduce additional layers, to the detriment of energy consumption and latency. For this reason, we propose a new framework called BottleFit, which, in addition to targeted DNN architecture modifications, includes a novel training strategy to achieve high accuracy even with strong compression rates. We apply BottleFit on cutting-edge DNN models in image classification, and show that BottleFit achieves 77.1% data compression with up to 0.6% accuracy loss on ImageNet dataset, while state of the art such as SPINN loses up to 6% in accuracy. We experimentally measure the power consumption and latency of an image classification application running on an NVIDIA Jetson Nano board (GPU-based) and a Raspberry PI board (GPU-less). We show that BottleFit decreases power consumption and latency respectively by up to 49% and 89% with respect to (w.r.t.) local computing and by 37% and 55% w.r.t. edge offloading. We also compare BottleFit with state-of-the-art autoencoders-based approaches, and show that (i) BottleFit reduces power consumption and execution time respectively by up to 54% and 44% on the Jetson and 40% and 62% on Raspberry PI; (ii) the size of the head model executed on the mobile device is 83 times smaller. We publish the code repository for reproducibility of the results in this study.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

Recent successful applications of convolutional neural networks (CNNs) to audio classification and speech recognition have motivated the search for better input representations for more efficient training. Visual displays of an audio signal, through various time-frequency representations such as spectrograms offer a rich representation of the temporal and spectral structure of the original signal. In this letter, we compare various popular signal processing methods to obtain this representation, such as short-time Fourier transform (STFT) with linear and Mel scales, constant-Q transform (CQT) and continuous Wavelet transform (CWT), and assess their impact on the classification performance of two environmental sound datasets using CNNs. This study supports the hypothesis that time-frequency representations are valuable in learning useful features for sound classification. Moreover, the actual transformation used is shown to impact the classification accuracy, with Mel-scaled STFT outperforming the other discussed methods slightly and baseline MFCC features to a large degree. Additionally, we observe that the optimal window size during transformation is dependent on the characteristics of the audio signal and architecturally, 2D convolution yielded better results in most cases compared to 1D.

Neural audio codecs (NACs) provide compact latent speech representations in the form of sequences of continuous vectors or discrete tokens. In this work, we investigate how these two types of speech representations compare when used as training targets for supervised speech enhancement. We consider both autoregressive and non-autoregressive speech enhancement models based on the Conformer architecture, as well as a simple baseline where the NAC encoder is simply fine-tuned for speech enhancement. Our experiments reveal three key findings: predicting continuous latent representations consistently outperforms discrete token prediction; autoregressive models achieve higher quality but at the expense of intelligibility and efficiency, making non-autoregressive models more attractive in practice; and adding encoder fine-tuning yields the strongest enhancement metrics overall, though at the cost of degraded codec reconstruction. The code and audio samples are available online.

Recent 4D shape representations model continuous temporal evolution of implicit shapes by (1) learning query flows without leveraging shape and articulation priors or (2) decoding shape occupancies separately for each time value. Thus, they do not effectively capture implicit correspondences between articulated shapes or regularize jittery temporal deformations. In this work, we present FourierHandFlow, which is a spatio-temporally continuous representation for human hands that combines a 3D occupancy field with articulation-aware query flows represented as Fourier series. Given an input RGB sequence, we aim to learn a fixed number of Fourier coefficients for each query flow to guarantee smooth and continuous temporal shape dynamics. To effectively model spatio-temporal deformations of articulated hands, we compose our 4D representation based on two types of Fourier query flow: (1) pose flow that models query dynamics influenced by hand articulation changes via implicit linear blend skinning and (2) shape flow that models query-wise displacement flow. In the experiments, our method achieves state-of-the-art results on video-based 4D reconstruction while being computationally more efficient than the existing 3D/4D implicit shape representations. We additionally show our results on motion inter- and extrapolation and texture transfer using the learned correspondences of implicit shapes. To the best of our knowledge, FourierHandFlow is the first neural 4D continuous hand representation learned from RGB videos. The code will be publicly accessible.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being sensitive to how the function is sampled. We present a new framework for understanding and designing discretization invariant neural networks (DI-Nets), which generalizes many discrete networks such as convolutional neural networks as well as continuous networks such as neural operators. Our analysis establishes upper bounds on the deviation in model outputs under different finite discretizations, and highlights the central role of point set discrepancy in characterizing such bounds. This insight leads to the design of a family of neural networks driven by numerical integration via quasi-Monte Carlo sampling with discretizations of low discrepancy. We prove by construction that DI-Nets universally approximate a large class of maps between integrable function spaces, and show that discretization invariance also describes backpropagation through such models. Applied to neural fields, convolutional DI-Nets can learn to classify and segment visual data under various discretizations, and sometimes generalize to new types of discretizations at test time. Code: https://github.com/clintonjwang/DI-net.

The current electroencephalogram (EEG) based deep learning models are typically designed for specific datasets and applications in brain-computer interaction (BCI), limiting the scale of the models and thus diminishing their perceptual capabilities and generalizability. Recently, Large Language Models (LLMs) have achieved unprecedented success in text processing, prompting us to explore the capabilities of Large EEG Models (LEMs). We hope that LEMs can break through the limitations of different task types of EEG datasets, and obtain universal perceptual capabilities of EEG signals through unsupervised pre-training. Then the models can be fine-tuned for different downstream tasks. However, compared to text data, the volume of EEG datasets is generally small and the format varies widely. For example, there can be mismatched numbers of electrodes, unequal length data samples, varied task designs, and low signal-to-noise ratio. To overcome these challenges, we propose a unified foundation model for EEG called Large Brain Model (LaBraM). LaBraM enables cross-dataset learning by segmenting the EEG signals into EEG channel patches. Vector-quantized neural spectrum prediction is used to train a semantically rich neural tokenizer that encodes continuous raw EEG channel patches into compact neural codes. We then pre-train neural Transformers by predicting the original neural codes for the masked EEG channel patches. The LaBraMs were pre-trained on about 2,500 hours of various types of EEG signals from around 20 datasets and validated on multiple different types of downstream tasks. Experiments on abnormal detection, event type classification, emotion recognition, and gait prediction show that our LaBraM outperforms all compared SOTA methods in their respective fields. Our code is available at https://github.com/935963004/LaBraM.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

For computer vision systems to operate in dynamic situations, they need to be able to represent and reason about object permanence. We introduce a framework for learning to estimate 4D visual representations from monocular RGB-D, which is able to persist objects, even once they become obstructed by occlusions. Unlike traditional video representations, we encode point clouds into a continuous representation, which permits the model to attend across the spatiotemporal context to resolve occlusions. On two large video datasets that we release along with this paper, our experiments show that the representation is able to successfully reveal occlusions for several tasks, without any architectural changes. Visualizations show that the attention mechanism automatically learns to follow occluded objects. Since our approach can be trained end-to-end and is easily adaptable, we believe it will be useful for handling occlusions in many video understanding tasks. Data, code, and models are available at https://occlusions.cs.columbia.edu/.

Large Lanugage Models (LLMs) are gaining increasing popularity in a variety of use cases, from language understanding and writing to assistance in application development. One of the most important aspects for optimal funcionality of LLMs is embedding layers. Word embeddings are distributed representations of words in a continuous vector space. In the context of LLMs, words or tokens from the input text are transformed into high-dimensional vectors using unique algorithms specific to the model. Our research examines the embedding algorithms from leading companies in the industry, such as OpenAI, Google's PaLM, and BERT. Using medical data, we have analyzed similarity scores of each embedding layer, observing differences in performance among each algorithm. To enhance each model and provide an additional encoding layer, we also implemented Siamese Neural Networks. After observing changes in performance with the addition of the model, we measured the carbon footage per epoch of training. The carbon footprint associated with large language models (LLMs) is a significant concern, and should be taken into consideration when selecting algorithms for a variety of use cases. Overall, our research compared the accuracy different, leading embedding algorithms and their carbon footage, allowing for a holistic review of each embedding algorithm.

In this paper, we study the problem of continuous 3D shape representations. The majority of existing successful methods are coordinate-based implicit neural representations. However, they are inefficient to render novel views or recover explicit surface points. A few works start to formulate 3D shapes as ray-based neural functions, but the learned structures are inferior due to the lack of multi-view geometry consistency. To tackle these challenges, we propose a new framework called RayDF. It consists of three major components: 1) the simple ray-surface distance field, 2) the novel dual-ray visibility classifier, and 3) a multi-view consistency optimization module to drive the learned ray-surface distances to be multi-view geometry consistent. We extensively evaluate our method on three public datasets, demonstrating remarkable performance in 3D surface point reconstruction on both synthetic and challenging real-world 3D scenes, clearly surpassing existing coordinate-based and ray-based baselines. Most notably, our method achieves a 1000x faster speed than coordinate-based methods to render an 800x800 depth image, showing the superiority of our method for 3D shape representation. Our code and data are available at https://github.com/vLAR-group/RayDF

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.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Policy gradient methods are an appealing approach in reinforcement learning because they directly optimize the cumulative reward and can straightforwardly be used with nonlinear function approximators such as neural networks. The two main challenges are the large number of samples typically required, and the difficulty of obtaining stable and steady improvement despite the nonstationarity of the incoming data. We address the first challenge by using value functions to substantially reduce the variance of policy gradient estimates at the cost of some bias, with an exponentially-weighted estimator of the advantage function that is analogous to TD(lambda). We address the second challenge by using trust region optimization procedure for both the policy and the value function, which are represented by neural networks. Our approach yields strong empirical results on highly challenging 3D locomotion tasks, learning running gaits for bipedal and quadrupedal simulated robots, and learning a policy for getting the biped to stand up from starting out lying on the ground. In contrast to a body of prior work that uses hand-crafted policy representations, our neural network policies map directly from raw kinematics to joint torques. Our algorithm is fully model-free, and the amount of simulated experience required for the learning tasks on 3D bipeds corresponds to 1-2 weeks of real time.

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

Diffusion models have emerged as the state-of-the-art for image generation, among other tasks. Here, we present an efficient diffusion-based model for 3D-aware generation of neural fields. Our approach pre-processes training data, such as ShapeNet meshes, by converting them to continuous occupancy fields and factoring them into a set of axis-aligned triplane feature representations. Thus, our 3D training scenes are all represented by 2D feature planes, and we can directly train existing 2D diffusion models on these representations to generate 3D neural fields with high quality and diversity, outperforming alternative approaches to 3D-aware generation. Our approach requires essential modifications to existing triplane factorization pipelines to make the resulting features easy to learn for the diffusion model. We demonstrate state-of-the-art results on 3D generation on several object classes from ShapeNet.

In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we propose Neural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output. NDF allow to extract the surface as very dense point clouds and as meshes. We also show that NDF allow for surface normal calculation and can be rendered using a slight modification of sphere tracing. We find NDF can be used for multi-target regression (multiple outputs for one input) with techniques that have been exclusively used for rendering in graphics. Experiments on ShapeNet show that NDF, while simple, is the state-of-the art, and allows to reconstruct shapes with inner structures, such as the chairs inside a bus. Notably, we show that NDF are not restricted to 3D shapes, and can approximate more general open surfaces such as curves, manifolds, and functions. Code is available for research at https://virtualhumans.mpi-inf.mpg.de/ndf/.

Neural autoencoders underpin generative models. Practical, large-scale use of neural autoencoders for generative modeling necessitates fast encoding, low latent rates, and a single model across representations. Existing approaches are reconstruction-first: they incur high latent rates, slow encoding, and separate architectures for discrete vs. continuous latents and for different audio channel formats, hindering workflows from preprocessing to inference conditioning. We introduce a generative-first architecture for audio autoencoding that increases temporal downsampling from 2048x to 3360x and supports continuous and discrete representations and common audio channel formats in one model. By balancing compression, quality, and speed, it delivers 10x faster encoding, 1.6x lower rates, and eliminates channel-format-specific variants while maintaining competitive reconstruction quality. This enables applications previously constrained by processing costs: a 60-second mono signal compresses to 788 tokens, making generative modeling more tractable.

This paper addresses the task of space-time video super-resolution (ST-VSR). Existing methods generally suffer from inaccurate motion estimation and motion compensation (MEMC) problems for large motions. Inspired by recent progress in physics-informed neural networks, we model the challenges of MEMC in ST-VSR as a mapping between two continuous function spaces. Specifically, our approach transforms independent low-resolution representations in the coarse-grained continuous function space into refined representations with enriched spatiotemporal details in the fine-grained continuous function space. To achieve efficient and accurate MEMC, we design a Galerkin-type attention function to perform frame alignment and temporal interpolation. Due to the linear complexity of the Galerkin-type attention mechanism, our model avoids patch partitioning and offers global receptive fields, enabling precise estimation of large motions. The experimental results show that the proposed method surpasses state-of-the-art techniques in both fixed-size and continuous space-time video super-resolution tasks.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

Speech enhancement systems are typically trained using pairs of clean and noisy speech. In audio-visual speech enhancement (AVSE), there is not as much ground-truth clean data available; most audio-visual datasets are collected in real-world environments with background noise and reverberation, hampering the development of AVSE. In this work, we introduce AV2Wav, a resynthesis-based audio-visual speech enhancement approach that can generate clean speech despite the challenges of real-world training data. We obtain a subset of nearly clean speech from an audio-visual corpus using a neural quality estimator, and then train a diffusion model on this subset to generate waveforms conditioned on continuous speech representations from AV-HuBERT with noise-robust training. We use continuous rather than discrete representations to retain prosody and speaker information. With this vocoding task alone, the model can perform speech enhancement better than a masking-based baseline. We further fine-tune the diffusion model on clean/noisy utterance pairs to improve the performance. Our approach outperforms a masking-based baseline in terms of both automatic metrics and a human listening test and is close in quality to the target speech in the listening test. Audio samples can be found at https://home.ttic.edu/~jcchou/demo/avse/avse_demo.html.

Radiance of real-world scenes typically spans a much wider dynamic range than what standard cameras can capture. While conventional HDR methods merge alternating-exposure frames, these approaches are inherently constrained to 2D pixel-level alignment, often leading to ghosting artifacts and temporal inconsistency in dynamic scenes. To address these limitations, we present HDR-NSFF, a paradigm shift from 2D-based merging to 4D spatio-temporal modeling. Our framework reconstructs dynamic HDR radiance fields from alternating-exposure monocular videos by representing the scene as a continuous function of space and time, and is compatible with both neural radiance field and 4D Gaussian Splatting (4DGS) based dynamic representations. This unified end-to-end pipeline explicitly models HDR radiance, 3D scene flow, geometry, and tone-mapping, ensuring physical plausibility and global coherence. We further enhance robustness by (i) extending semantic-based optical flow with DINO features to achieve exposure-invariant motion estimation, and (ii) incorporating a generative prior as a regularizer to compensate for limited observation in monocular captures and saturation-induced information loss. To evaluate HDR space-time view synthesis, we present the first real-world HDR-GoPro dataset specifically designed for dynamic HDR scenes. Experiments demonstrate that HDR-NSFF recovers fine radiance details and coherent dynamics even under challenging exposure variations, thereby achieving state-of-the-art performance in novel space-time view synthesis. Project page: https://shin-dong-yeon.github.io/HDR-NSFF/

Proteins move and deform to ensure their biological functions. Despite significant progress in protein structure prediction, approximating conformational ensembles at physiological conditions remains a fundamental open problem. This paper presents a novel perspective on the problem by directly targeting continuous compact representations of protein motions inferred from sparse experimental observations. We develop a task-specific loss function enforcing data symmetries, including scaling and permutation operations. Our method PETIMOT (Protein sEquence and sTructure-based Inference of MOTions) leverages transfer learning from pre-trained protein language models through an SE(3)-equivariant graph neural network. When trained and evaluated on the Protein Data Bank, PETIMOT shows superior performance in time and accuracy, capturing protein dynamics, particularly large/slow conformational changes, compared to state-of-the-art flow-matching approaches and traditional physics-based models.

Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to poor generalization when extrapolating beyond trained spatiotemporal regions. This work presents SPIKE (Sparse Physics-Informed Koopman-Enhanced), a framework that regularizes PINNs with continuous-time Koopman operators to learn parsimonious dynamics representations. By enforcing linear dynamics dz/dt = Az in a learned observable space, both PIKE (without explicit sparsity) and SPIKE (with L1 regularization on A) learn sparse generator matrices, embodying the parsimony principle that complex dynamics admit low-dimensional structure. Experiments across parabolic, hyperbolic, dispersive, and stiff PDEs, including fluid dynamics (Navier-Stokes) and chaotic ODEs (Lorenz), demonstrate consistent improvements in temporal extrapolation, spatial generalization, and long-term prediction accuracy. The continuous-time formulation with matrix exponential integration provides unconditional stability for stiff systems while avoiding diagonal dominance issues inherent in discrete-time Koopman operators.

Continuous space-time video super-resolution (C-STVSR) endeavors to upscale videos simultaneously at arbitrary spatial and temporal scales, which has recently garnered increasing interest. However, prevailing methods struggle to yield satisfactory videos at out-of-distribution spatial and temporal scales. On the other hand, event streams characterized by high temporal resolution and high dynamic range, exhibit compelling promise in vision tasks. This paper presents EvEnhancer, an innovative approach that marries the unique advantages of event streams to elevate effectiveness, efficiency, and generalizability for C-STVSR. Our approach hinges on two pivotal components: 1) Event-adapted synthesis capitalizes on the spatiotemporal correlations between frames and events to discern and learn long-term motion trajectories, enabling the adaptive interpolation and fusion of informative spatiotemporal features; 2) Local implicit video transformer integrates local implicit video neural function with cross-scale spatiotemporal attention to learn continuous video representations utilized to generate plausible videos at arbitrary resolutions and frame rates. Experiments show that EvEnhancer achieves superiority on synthetic and real-world datasets and preferable generalizability on out-of-distribution scales against state-of-the-art methods. Code is available at https://github.com/W-Shuoyan/EvEnhancer.

Reconstructing high-fidelity, animatable 3D head avatars from effortlessly captured monocular videos is a pivotal yet formidable challenge. Although significant progress has been made in rendering performance and manipulation capabilities, notable challenges remain, including incomplete reconstruction and inefficient Gaussian representation. To address these challenges, we introduce FATE, a novel method for reconstructing an editable full-head avatar from a single monocular video. FATE integrates a sampling-based densification strategy to ensure optimal positional distribution of points, improving rendering efficiency. A neural baking technique is introduced to convert discrete Gaussian representations into continuous attribute maps, facilitating intuitive appearance editing. Furthermore, we propose a universal completion framework to recover non-frontal appearance, culminating in a 360^circ-renderable 3D head avatar. FATE outperforms previous approaches in both qualitative and quantitative evaluations, achieving state-of-the-art performance. To the best of our knowledge, FATE is the first animatable and 360^circ full-head monocular reconstruction method for a 3D head avatar. The code will be publicly released upon publication.

With the development of Deep Neural Networks (DNNs), many efforts have been made to handle medical image segmentation. Traditional methods such as nnUNet train specific segmentation models on the individual datasets. Plenty of recent methods have been proposed to adapt the foundational Segment Anything Model (SAM) to medical image segmentation. However, they still focus on discrete representations to generate pixel-wise predictions, which are spatially inflexible and scale poorly to higher resolution. In contrast, implicit methods learn continuous representations for segmentation, which is crucial for medical image segmentation. In this paper, we propose I-MedSAM, which leverages the benefits of both continuous representations and SAM, to obtain better cross-domain ability and accurate boundary delineation. Since medical image segmentation needs to predict detailed segmentation boundaries, we designed a novel adapter to enhance the SAM features with high-frequency information during Parameter-Efficient Fine-Tuning (PEFT). To convert the SAM features and coordinates into continuous segmentation output, we utilize Implicit Neural Representation (INR) to learn an implicit segmentation decoder. We also propose an uncertainty-guided sampling strategy for efficient learning of INR. Extensive evaluations on 2D medical image segmentation tasks have shown that our proposed method with only 1.6M trainable parameters outperforms existing methods including discrete and implicit methods. The code will be available at: https://github.com/ucwxb/I-MedSAM.

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume representation at a fixed dimension or resolution, which may be inefficient for simple tasks and ineffective for more complicated tasks. In this work, we investigate how to learn dynamic and adaptive representations at different levels of abstraction to achieve the optimal trade-off between efficiency and effectiveness. Specifically, we construct dynamic-resolution particle representations of the environment and learn a unified dynamics model using graph neural networks (GNNs) that allows continuous selection of the abstraction level. During test time, the agent can adaptively determine the optimal resolution at each model-predictive control (MPC) step. We evaluate our method in object pile manipulation, a task we commonly encounter in cooking, agriculture, manufacturing, and pharmaceutical applications. Through comprehensive evaluations both in the simulation and the real world, we show that our method achieves significantly better performance than state-of-the-art fixed-resolution baselines at the gathering, sorting, and redistribution of granular object piles made with various instances like coffee beans, almonds, corn, etc.

The task of information retrieval is an important component of many natural language processing systems, such as open domain question answering. While traditional methods were based on hand-crafted features, continuous representations based on neural networks recently obtained competitive results. A challenge of using such methods is to obtain supervised data to train the retriever model, corresponding to pairs of query and support documents. In this paper, we propose a technique to learn retriever models for downstream tasks, inspired by knowledge distillation, and which does not require annotated pairs of query and documents. Our approach leverages attention scores of a reader model, used to solve the task based on retrieved documents, to obtain synthetic labels for the retriever. We evaluate our method on question answering, obtaining state-of-the-art results.

Representing visual signals by coordinate-based deep fully-connected networks has been shown advantageous in fitting complex details and solving inverse problems than discrete grid-based representation. However, acquiring such a continuous Implicit Neural Representation (INR) requires tedious per-scene training on tons of signal measurements, which limits its practicality. In this paper, we present a generic INR framework that achieves both data and training efficiency by learning a Neural Implicit Dictionary (NID) from a data collection and representing INR as a functional combination of basis sampled from the dictionary. Our NID assembles a group of coordinate-based subnetworks which are tuned to span the desired function space. After training, one can instantly and robustly acquire an unseen scene representation by solving the coding coefficients. To parallelly optimize a large group of networks, we borrow the idea from Mixture-of-Expert (MoE) to design and train our network with a sparse gating mechanism. Our experiments show that, NID can improve reconstruction of 2D images or 3D scenes by 2 orders of magnitude faster with up to 98% less input data. We further demonstrate various applications of NID in image inpainting and occlusion removal, which are considered to be challenging with vanilla INR. Our codes are available in https://github.com/VITA-Group/Neural-Implicit-Dict.

We propose pixelNeRF, a learning framework that predicts a continuous neural scene representation conditioned on one or few input images. The existing approach for constructing neural radiance fields involves optimizing the representation to every scene independently, requiring many calibrated views and significant compute time. We take a step towards resolving these shortcomings by introducing an architecture that conditions a NeRF on image inputs in a fully convolutional manner. This allows the network to be trained across multiple scenes to learn a scene prior, enabling it to perform novel view synthesis in a feed-forward manner from a sparse set of views (as few as one). Leveraging the volume rendering approach of NeRF, our model can be trained directly from images with no explicit 3D supervision. We conduct extensive experiments on ShapeNet benchmarks for single image novel view synthesis tasks with held-out objects as well as entire unseen categories. We further demonstrate the flexibility of pixelNeRF by demonstrating it on multi-object ShapeNet scenes and real scenes from the DTU dataset. In all cases, pixelNeRF outperforms current state-of-the-art baselines for novel view synthesis and single image 3D reconstruction. For the video and code, please visit the project website: https://alexyu.net/pixelnerf

Non-line-of-sight (NLOS) imaging is conducted to infer invisible scenes from indirect light on visible objects. The neural transient field (NeTF) was proposed for representing scenes as neural radiance fields in NLOS scenes. We propose NLOS neural implicit surface (NLOS-NeuS), which extends the NeTF to neural implicit surfaces with a signed distance function (SDF) for reconstructing three-dimensional surfaces in NLOS scenes. We introduce two constraints as loss functions for correctly learning an SDF to avoid non-zero level-set surfaces. We also introduce a lower bound constraint of an SDF based on the geometry of the first-returning photons. The experimental results indicate that these constraints are essential for learning a correct SDF in NLOS scenes. Compared with previous methods with discretized representation, NLOS-NeuS with the neural continuous representation enables us to reconstruct smooth surfaces while preserving fine details in NLOS scenes. To the best of our knowledge, this is the first study on neural implicit surfaces with volume rendering in NLOS scenes.

How to represent an image? While the visual world is presented in a continuous manner, machines store and see the images in a discrete way with 2D arrays of pixels. In this paper, we seek to learn a continuous representation for images. Inspired by the recent progress in 3D reconstruction with implicit neural representation, we propose Local Implicit Image Function (LIIF), which takes an image coordinate and the 2D deep features around the coordinate as inputs, predicts the RGB value at a given coordinate as an output. Since the coordinates are continuous, LIIF can be presented in arbitrary resolution. To generate the continuous representation for images, we train an encoder with LIIF representation via a self-supervised task with super-resolution. The learned continuous representation can be presented in arbitrary resolution even extrapolate to x30 higher resolution, where the training tasks are not provided. We further show that LIIF representation builds a bridge between discrete and continuous representation in 2D, it naturally supports the learning tasks with size-varied image ground-truths and significantly outperforms the method with resizing the ground-truths.

Implicit neural representation (INR) has proven to be accurate and efficient in various domains. In this work, we explore how different neural networks can be designed as a new texture INR, which operates in a continuous manner rather than a discrete one over the input UV coordinate space. Through thorough experiments, we demonstrate that these INRs perform well in terms of image quality, with considerable memory usage and rendering inference time. We analyze the balance between these objectives. In addition, we investigate various related applications in real-time rendering and down-stream tasks, e.g. mipmap fitting and INR-space generation.

High-resolution (HR) image harmonization is of great significance in real-world applications such as image synthesis and image editing. However, due to the high memory costs, existing dense pixel-to-pixel harmonization methods are mainly focusing on processing low-resolution (LR) images. Some recent works resort to combining with color-to-color transformations but are either limited to certain resolutions or heavily depend on hand-crafted image filters. In this work, we explore leveraging the implicit neural representation (INR) and propose a novel image Harmonization method based on Implicit neural Networks (HINet), which to the best of our knowledge, is the first dense pixel-to-pixel method applicable to HR images without any hand-crafted filter design. Inspired by the Retinex theory, we decouple the MLPs into two parts to respectively capture the content and environment of composite images. A Low-Resolution Image Prior (LRIP) network is designed to alleviate the Boundary Inconsistency problem, and we also propose new designs for the training and inference process. Extensive experiments have demonstrated the effectiveness of our method compared with state-of-the-art methods. Furthermore, some interesting and practical applications of the proposed method are explored. Our code will be available at https://github.com/WindVChen/INR-Harmonization.

Super-resolution (SR) and image generation are important tasks in computer vision and are widely adopted in real-world applications. Most existing methods, however, generate images only at fixed-scale magnification and suffer from over-smoothing and artifacts. Additionally, they do not offer enough diversity of output images nor image consistency at different scales. Most relevant work applied Implicit Neural Representation (INR) to the denoising diffusion model to obtain continuous-resolution yet diverse and high-quality SR results. Since this model operates in the image space, the larger the resolution of image is produced, the more memory and inference time is required, and it also does not maintain scale-specific consistency. We propose a novel pipeline that can super-resolve an input image or generate from a random noise a novel image at arbitrary scales. The method consists of a pretrained auto-encoder, a latent diffusion model, and an implicit neural decoder, and their learning strategies. The proposed method adopts diffusion processes in a latent space, thus efficient, yet aligned with output image space decoded by MLPs at arbitrary scales. More specifically, our arbitrary-scale decoder is designed by the symmetric decoder w/o up-scaling from the pretrained auto-encoder, and Local Implicit Image Function (LIIF) in series. The latent diffusion process is learnt by the denoising and the alignment losses jointly. Errors in output images are backpropagated via the fixed decoder, improving the quality of output images. In the extensive experiments using multiple public benchmarks on the two tasks i.e. image super-resolution and novel image generation at arbitrary scales, the proposed method outperforms relevant methods in metrics of image quality, diversity and scale consistency. It is significantly better than the relevant prior-art in the inference speed and memory usage.

Enhancing low-resolution, low-frame-rate videos to high-resolution, high-frame-rate quality is essential for a seamless user experience, motivating advancements in Continuous Spatial-Temporal Video Super Resolution (C-STVSR). While prior methods employ Implicit Neural Representation (INR) for continuous encoding, they often struggle to capture the complexity of video data, relying on simple coordinate concatenation and pre-trained optical flow network for motion representation. Interestingly, we find that adding position encoding, contrary to common observations, does not improve-and even degrade performance. This issue becomes particularly pronounced when combined with pre-trained optical flow networks, which can limit the model's flexibility. To address these issues, we propose BF-STVSR, a C-STVSR framework with two key modules tailored to better represent spatial and temporal characteristics of video: 1) B-spline Mapper for smooth temporal interpolation, and 2) Fourier Mapper for capturing dominant spatial frequencies. Our approach achieves state-of-the-art PSNR and SSIM performance, showing enhanced spatial details and natural temporal consistency.

Current deep learning models for Multispectral and Hyperspectral Image Fusion (MS/HS fusion) are typically designed for fixed spectral bands and spatial scales, which limits their transferability across diverse sensors. To address this, we propose SSA, a universal framework for MS/HS fusion with spectral-band and fusion-scale agnosticism. Specifically, we introduce Matryoshka Kernel (MK), a novel operator that enables a single model to adapt to arbitrary numbers of spectral channels. Meanwhile, we build SSA upon an Implicit Neural Representation (INR) backbone that models the HS signal as a continuous function, enabling reconstruction at arbitrary spatial resolutions. Together, these two forms of agnosticism enable a single MS/HS fusion model that generalizes effectively to unseen sensors and spatial scales. Extensive experiments demonstrate that our single model achieves state-of-the-art performance while generalizing well to unseen sensors and scales, paving the way toward future HS foundation models.

The estimation of optical flow and 6-DoF ego-motion, two fundamental tasks in 3D vision, has typically been addressed independently. For neuromorphic vision (e.g., event cameras), however, the lack of robust data association makes solving the two problems separately an ill-posed challenge, especially in the absence of supervision via ground truth. Existing works mitigate this ill-posedness by either enforcing the smoothness of the flow field via an explicit variational regularizer or leveraging explicit structure-and-motion priors in the parametrization to improve event alignment. The former notably introduces bias in results and computational overhead, while the latter, which parametrizes the optical flow in terms of the scene depth and the camera motion, often converges to suboptimal local minima. To address these issues, we propose an unsupervised framework that jointly optimizes egomotion and optical flow via implicit spatial-temporal and geometric regularization. First, by modeling camera's egomotion as a continuous spline and optical flow as an implicit neural representation, our method inherently embeds spatial-temporal coherence through inductive biases. Second, we incorporate structure-and-motion priors through differential geometric constraints, bypassing explicit depth estimation while maintaining rigorous geometric consistency. As a result, our framework (called E-MoFlow) unifies egomotion and optical flow estimation via implicit regularization under a fully unsupervised paradigm. Experiments demonstrate its versatility to general 6-DoF motion scenarios, achieving state-of-the-art performance among unsupervised methods and competitive even with supervised approaches.

Learning useful representations without supervision remains a key challenge in machine learning. In this paper, we propose a simple yet powerful generative model that learns such discrete representations. Our model, the Vector Quantised-Variational AutoEncoder (VQ-VAE), differs from VAEs in two key ways: the encoder network outputs discrete, rather than continuous, codes; and the prior is learnt rather than static. In order to learn a discrete latent representation, we incorporate ideas from vector quantisation (VQ). Using the VQ method allows the model to circumvent issues of "posterior collapse" -- where the latents are ignored when they are paired with a powerful autoregressive decoder -- typically observed in the VAE framework. Pairing these representations with an autoregressive prior, the model can generate high quality images, videos, and speech as well as doing high quality speaker conversion and unsupervised learning of phonemes, providing further evidence of the utility of the learnt representations.

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of condensed-matter lattice models with coupled electronic and structural or magnetic degrees of freedom. However, most existing formulations rely on hand-crafted, symmetry-aware descriptors, whose construction is often system-specific and can hinder generality and transferability across different lattice Hamiltonians. Here we introduce a symmetry-preserving framework based on equivariant neural networks (ENNs) that provides a general, data-driven mapping from local configurations of dynamical variables to the associated on-site forces in a lattice Hamiltonian. In contrast to ENN architectures developed for molecular systems -- where continuous Euclidean symmetries dominate -- our approach aims to embed the discrete point-group and internal symmetries intrinsic to lattice models directly into the neural-network representation of the force field. As a proof of principle, we construct an ENN-based force-field model for the adiabatic dynamics of the Holstein Hamiltonian on a square lattice, a canonical system for electron-lattice physics. The resulting ML-enabled large-scale dynamical simulations faithfully capture mesoscale evolution of the symmetry-breaking phase, illustrating the utility of lattice-equivariant architectures for linking microscopic electronic processes to emergent dynamical behavior in condensed-matter lattice systems.

Efficient neural representations for dynamic video scenes are critical for applications ranging from video compression to interactive simulations. Yet, existing methods often face challenges related to high memory usage, lengthy training times, and temporal consistency. To address these issues, we introduce a novel neural video representation that combines 3D Gaussian splatting with continuous camera motion modeling. By leveraging Neural ODEs, our approach learns smooth camera trajectories while maintaining an explicit 3D scene representation through Gaussians. Additionally, we introduce a spatiotemporal hierarchical learning strategy, progressively refining spatial and temporal features to enhance reconstruction quality and accelerate convergence. This memory-efficient approach achieves high-quality rendering at impressive speeds. Experimental results show that our hierarchical learning, combined with robust camera motion modeling, captures complex dynamic scenes with strong temporal consistency, achieving state-of-the-art performance across diverse video datasets in both high- and low-motion scenarios.

We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at https://github.com/zknus/ICLR2024-FROND.

Token-based video representation has emerged as a promising approach for enabling large language models (LLMs) to interpret video content. However, existing token reduction techniques, such as pruning and merging, often disrupt essential positional embeddings and rely on continuous visual tokens sampled from nearby pixels with similar spatial-temporal locations. By removing only a small fraction of tokens, these methods still produce relatively lengthy continuous sequences, which falls short of the extreme compression required to balance computational efficiency and token count in video LLMs. In this paper, we introduce the novel task of Extreme Short Token Reduction, which aims to represent entire videos using a minimal set of discrete tokens. We propose VQToken, a neural discrete token representation framework that (i) applies adaptive vector quantization to continuous ViT embeddings to learn a compact codebook and (ii) preserves spatial-temporal positions via a token hash function by assigning each grid-level token to its nearest codebook entry. On the Extreme Short Token Reduction task, our VQToken compresses sequences to just 0.07 percent of their original length while incurring only a 0.66 percent drop in accuracy on the NextQA-MC benchmark. It also achieves comparable performance on ActNet-QA, Long Video Bench, and VideoMME. We further introduce the Token Information Density (TokDense) metric and formalize fixed-length and adaptive-length subtasks, achieving state-of-the-art results in both settings. Our approach dramatically lowers theoretical complexity, increases information density, drastically reduces token counts, and enables efficient video LLMs in resource-constrained environments.

NeRF-based techniques fit wide and deep multi-layer perceptrons (MLPs) to a continuous radiance field that can be rendered from any unseen viewpoint. However, the lack of surface and normals definition and high rendering times limit their usage in typical computer graphics applications. Such limitations have recently been overcome separately, but solving them together remains an open problem. We present KiloNeuS, a neural representation reconstructing an implicit surface represented as a signed distance function (SDF) from multi-view images and enabling real-time rendering by partitioning the space into thousands of tiny MLPs fast to inference. As we learn the implicit surface locally using independent models, resulting in a globally coherent geometry is non-trivial and needs to be addressed during training. We evaluate rendering performance on a GPU-accelerated ray-caster with in-shader neural network inference, resulting in an average of 46 FPS at high resolution, proving a satisfying tradeoff between storage costs and rendering quality. In fact, our evaluation for rendering quality and surface recovery shows that KiloNeuS outperforms its single-MLP counterpart. Finally, to exhibit the versatility of KiloNeuS, we integrate it into an interactive path-tracer taking full advantage of its surface normals. We consider our work a crucial first step toward real-time rendering of implicit neural representations under global illumination.

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.

We propose two novel model architectures for computing continuous vector representations of words from very large data sets. The quality of these representations is measured in a word similarity task, and the results are compared to the previously best performing techniques based on different types of neural networks. We observe large improvements in accuracy at much lower computational cost, i.e. it takes less than a day to learn high quality word vectors from a 1.6 billion words data set. Furthermore, we show that these vectors provide state-of-the-art performance on our test set for measuring syntactic and semantic word similarities.

Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based language models implicitly learn to represent sentences as continuous-time functions defined over a continuous input space. This phenomenon occurs in most state-of-the-art Large Language Models (LLMs), including Llama2, Llama3, Phi3, Gemma, Gemma2, and Mistral, and suggests that LLMs reason about language in ways that fundamentally differ from humans. Our work formally extends Transformers to capture the nuances of time and space continuity in both input and output space. Our results challenge the traditional interpretation of how LLMs understand language, with several linguistic and engineering implications.

We reformulate the problem of encoding a multi-scale representation of a sequence in a language model by casting it in a continuous learning framework. We propose a hierarchical multi-scale language model in which short time-scale dependencies are encoded in the hidden state of a lower-level recurrent neural network while longer time-scale dependencies are encoded in the dynamic of the lower-level network by having a meta-learner update the weights of the lower-level neural network in an online meta-learning fashion. We use elastic weights consolidation as a higher-level to prevent catastrophic forgetting in our continuous learning framework.

Existing neural reconstruction schemes such as Neural Radiance Field (NeRF) are largely focused on modeling opaque objects. We present a novel neural refractive field(NeReF) to recover wavefront of transparent fluids by simultaneously estimating the surface position and normal of the fluid front. Unlike prior arts that treat the reconstruction target as a single layer of the surface, NeReF is specifically formulated to recover a volumetric normal field with its corresponding density field. A query ray will be refracted by NeReF according to its accumulated refractive point and normal, and we employ the correspondences and uniqueness of refracted ray for NeReF optimization. We show NeReF, as a global optimization scheme, can more robustly tackle refraction distortions detrimental to traditional methods for correspondence matching. Furthermore, the continuous NeReF representation of wavefront enables view synthesis as well as normal integration. We validate our approach on both synthetic and real data and show it is particularly suitable for sparse multi-view acquisition. We hence build a small light field array and experiment on various surface shapes to demonstrate high fidelity NeReF reconstruction.

Signed networks allow us to model conflicting relationships and interactions, such as friend/enemy and support/oppose. These signed interactions happen in real-time. Modeling such dynamics of signed networks is crucial to understanding the evolution of polarization in the network and enabling effective prediction of the signed structure (i.e., link signs and signed weights) in the future. However, existing works have modeled either (static) signed networks or dynamic (unsigned) networks but not dynamic signed networks. Since both sign and dynamics inform the graph structure in different ways, it is non-trivial to model how to combine the two features. In this work, we propose a new Graph Neural Network (GNN)-based approach to model dynamic signed networks, named SEMBA: Signed link's Evolution using Memory modules and Balanced Aggregation. Here, the idea is to incorporate the signs of temporal interactions using separate modules guided by balance theory and to evolve the embeddings from a higher-order neighborhood. Experiments on 4 real-world datasets and 4 different tasks demonstrate that SEMBA consistently and significantly outperforms the baselines by up to 80% on the tasks of predicting signs of future links while matching the state-of-the-art performance on predicting the existence of these links in the future. We find that this improvement is due specifically to the superior performance of SEMBA on the minority negative class.

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs with static inputs and outputs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs employing piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

Before the deep learning revolution, many perception algorithms were based on runtime optimization in conjunction with a strong prior/regularization penalty. A prime example of this in computer vision is optical and scene flow. Supervised learning has largely displaced the need for explicit regularization. Instead, they rely on large amounts of labeled data to capture prior statistics, which are not always readily available for many problems. Although optimization is employed to learn the neural network, the weights of this network are frozen at runtime. As a result, these learning solutions are domain-specific and do not generalize well to other statistically different scenarios. This paper revisits the scene flow problem that relies predominantly on runtime optimization and strong regularization. A central innovation here is the inclusion of a neural scene flow prior, which uses the architecture of neural networks as a new type of implicit regularizer. Unlike learning-based scene flow methods, optimization occurs at runtime, and our approach needs no offline datasets -- making it ideal for deployment in new environments such as autonomous driving. We show that an architecture based exclusively on multilayer perceptrons (MLPs) can be used as a scene flow prior. Our method attains competitive -- if not better -- results on scene flow benchmarks. Also, our neural prior's implicit and continuous scene flow representation allows us to estimate dense long-term correspondences across a sequence of point clouds. The dense motion information is represented by scene flow fields where points can be propagated through time by integrating motion vectors. We demonstrate such a capability by accumulating a sequence of lidar point clouds.

Efficient reasoning about the semantic, spatial, and temporal structure of a scene is a crucial prerequisite for autonomous driving. We present NEural ATtention fields (NEAT), a novel representation that enables such reasoning for end-to-end imitation learning models. NEAT is a continuous function which maps locations in Bird's Eye View (BEV) scene coordinates to waypoints and semantics, using intermediate attention maps to iteratively compress high-dimensional 2D image features into a compact representation. This allows our model to selectively attend to relevant regions in the input while ignoring information irrelevant to the driving task, effectively associating the images with the BEV representation. In a new evaluation setting involving adverse environmental conditions and challenging scenarios, NEAT outperforms several strong baselines and achieves driving scores on par with the privileged CARLA expert used to generate its training data. Furthermore, visualizing the attention maps for models with NEAT intermediate representations provides improved interpretability.

Neural architecture search (NAS) has a great impact by automatically designing effective neural network architectures. However, the prohibitive computational demand of conventional NAS algorithms (e.g. 10^4 GPU hours) makes it difficult to directly search the architectures on large-scale tasks (e.g. ImageNet). Differentiable NAS can reduce the cost of GPU hours via a continuous representation of network architecture but suffers from the high GPU memory consumption issue (grow linearly w.r.t. candidate set size). As a result, they need to utilize~proxy tasks, such as training on a smaller dataset, or learning with only a few blocks, or training just for a few epochs. These architectures optimized on proxy tasks are not guaranteed to be optimal on the target task. In this paper, we present ProxylessNAS that can directly learn the architectures for large-scale target tasks and target hardware platforms. We address the high memory consumption issue of differentiable NAS and reduce the computational cost (GPU hours and GPU memory) to the same level of regular training while still allowing a large candidate set. Experiments on CIFAR-10 and ImageNet demonstrate the effectiveness of directness and specialization. On CIFAR-10, our model achieves 2.08\% test error with only 5.7M parameters, better than the previous state-of-the-art architecture AmoebaNet-B, while using 6times fewer parameters. On ImageNet, our model achieves 3.1\% better top-1 accuracy than MobileNetV2, while being 1.2times faster with measured GPU latency. We also apply ProxylessNAS to specialize neural architectures for hardware with direct hardware metrics (e.g. latency) and provide insights for efficient CNN architecture design.

Graph Neural Networks (GNNs) excel at learning from structured data, yet fairness in regression tasks remains underexplored. Existing approaches mainly target classification and representation-level debiasing, which cannot fully address the continuous nature of node-level regression. We propose FnRGNN, a fairness-aware in-processing framework for GNN-based node regression that applies interventions at three levels: (i) structure-level edge reweighting, (ii) representation-level alignment via MMD, and (iii) prediction-level normalization through Sinkhorn-based distribution matching. This multi-level strategy ensures robust fairness under complex graph topologies. Experiments on four real-world datasets demonstrate that FnRGNN reduces group disparities without sacrificing performance. Code is available at https://github.com/sybeam27/FnRGNN.

The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and trajectory inference. However, these methods consider cells as independent data points of population distributions. With spatial transcriptomics, we can represent cellular organization, along with dynamic cell-cell interactions that lead to changes in cell state. Still, key computational advances are necessary to enable the data-driven learning of such complex interactive cellular dynamics. While agent-based modeling (ABM) provides a powerful framework, traditional approaches rely on handcrafted rules derived from domain knowledge rather than data-driven approaches. To address this, we introduce Spatio Temporal Agent-Based Graph Evolution Dynamics(STAGED) integrating ABM with deep learning to model intercellular communication, and its effect on the intracellular gene regulatory network. Using graph ODE networks (GDEs) with shared weights per cell type, our approach represents genes as vertices and interactions as directed edges, dynamically learning their strengths through a designed attention mechanism. Trained to match continuous trajectories of simulated as well as inferred trajectories from spatial transcriptomics data, the model captures both intercellular and intracellular interactions, enabling a more adaptive and accurate representation of cellular dynamics.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Procedural text, which describes entities and their interactions as they undergo some process, depicts entities in a uniquely nuanced way. First, each entity may have some observable discrete attributes, such as its state or location; modeling these involves imposing global structure and enforcing consistency. Second, an entity may have properties which are not made explicit but can be effectively induced and tracked by neural networks. In this paper, we propose a structured neural architecture that reflects this dual nature of entity evolution. The model tracks each entity recurrently, updating its hidden continuous representation at each step to contain relevant state information. The global discrete state structure is explicitly modeled with a neural CRF over the changing hidden representation of the entity. This CRF can explicitly capture constraints on entity states over time, enforcing that, for example, an entity cannot move to a location after it is destroyed. We evaluate the performance of our proposed model on QA tasks over process paragraphs in the ProPara dataset and find that our model achieves state-of-the-art results.

Biological brains demonstrate complex neural activity, where the timing and interplay between neurons is critical to how brains process information. Most deep learning architectures simplify neural activity by abstracting away temporal dynamics. In this paper we challenge that paradigm. By incorporating neuron-level processing and synchronization, we can effectively reintroduce neural timing as a foundational element. We present the Continuous Thought Machine (CTM), a model designed to leverage neural dynamics as its core representation. The CTM has two core innovations: (1) neuron-level temporal processing, where each neuron uses unique weight parameters to process a history of incoming signals; and (2) neural synchronization employed as a latent representation. The CTM aims to strike a balance between oversimplified neuron abstractions that improve computational efficiency, and biological realism. It operates at a level of abstraction that effectively captures essential temporal dynamics while remaining computationally tractable for deep learning. We demonstrate the CTM's strong performance and versatility across a range of challenging tasks, including ImageNet-1K classification, solving 2D mazes, sorting, parity computation, question-answering, and RL tasks. Beyond displaying rich internal representations and offering a natural avenue for interpretation owing to its internal process, the CTM is able to perform tasks that require complex sequential reasoning. The CTM can also leverage adaptive compute, where it can stop earlier for simpler tasks, or keep computing when faced with more challenging instances. The goal of this work is to share the CTM and its associated innovations, rather than pushing for new state-of-the-art results. To that end, we believe the CTM represents a significant step toward developing more biologically plausible and powerful artificial intelligence systems.

Speech codecs that convert continuous speech signals into discrete tokens have become essential for speech language models (SLMs). However, existing codecs struggle to balance high-quality reconstruction with semantically rich representations, limiting their effectiveness in both generative and understanding tasks. In this work, we propose SAC, a neural speech codec with semantic-acoustic dual-stream quantization. By disentangling semantic and acoustic modeling into two dedicated streams, SAC enables each to be optimized for its respective role. Comprehensive evaluations show that SAC achieves strong reconstruction performance across diverse bitrates under both clean and noisy conditions, with particularly high scores on UTMOS and WER, demonstrating superior perceptual quality and intelligibility. Moreover, SAC substantially outperforms state-of-the-art codecs in semantic representation, achieving a level comparable to that of self-supervised learning (SSL) continuous embeddings. Finally, our analysis of speech disentanglement highlights the effectiveness of the dual-stream design, offering new potential for controllable speech applications.

Neural fields are increasingly used as a light-weight, continuous, and differentiable signal representation in (bio)medical imaging. However, unlike discrete signal representations such as voxel grids, neural fields cannot be easily extended. As neural fields are, in essence, neural networks, prior signals represented in a neural field will degrade when the model is presented with new data due to catastrophic forgetting. This work examines the extent to which different neural field approaches suffer from catastrophic forgetting and proposes a strategy to mitigate this issue. We consider the scenario in which data becomes available incrementally, with only the most recent data available for neural field fitting. In a series of experiments on cardiac cine MRI data, we demonstrate how knowledge distillation mitigates catastrophic forgetting when the spatiotemporal domain is enlarged or the dimensionality of the represented signal is increased. We find that the amount of catastrophic forgetting depends, to a large extent, on the neural fields model used, and that distillation could enable continual learning in neural fields.

Neural architecture search (NAS) is a hard computationally expensive optimization problem with a discrete, vast, and spiky search space. One of the key research efforts dedicated to this space focuses on accelerating NAS via certain proxy evaluations of neural architectures. Different from the prevalent predictor-based methods using surrogate models and differentiable architecture search via supernetworks, we propose an optimization proxy to streamline the NAS as an end-to-end optimization framework, named OptiProxy-NAS. In particular, using a proxy representation, the NAS space is reformulated to be continuous, differentiable, and smooth. Thereby, any differentiable optimization method can be applied to the gradient-based search of the relaxed architecture parameters. Our comprehensive experiments on 12 NAS tasks of 4 search spaces across three different domains including computer vision, natural language processing, and resource-constrained NAS fully demonstrate the superior search results and efficiency. Further experiments on low-fidelity scenarios verify the flexibility.

Neural implicit surface learning has shown significant progress in multi-view 3D reconstruction, where an object is represented by multilayer perceptrons that provide continuous implicit surface representation and view-dependent radiance. However, current methods often fail to accurately reconstruct reflective surfaces, leading to severe ambiguity. To overcome this issue, we propose Ref-NeuS, which aims to reduce ambiguity by attenuating the effect of reflective surfaces. Specifically, we utilize an anomaly detector to estimate an explicit reflection score with the guidance of multi-view context to localize reflective surfaces. Afterward, we design a reflection-aware photometric loss that adaptively reduces ambiguity by modeling rendered color as a Gaussian distribution, with the reflection score representing the variance. We show that together with a reflection direction-dependent radiance, our model achieves high-quality surface reconstruction on reflective surfaces and outperforms the state-of-the-arts by a large margin. Besides, our model is also comparable on general surfaces.

Medical image arbitrary-scale super-resolution (MIASSR) has recently gained widespread attention, aiming to super sample medical volumes at arbitrary scales via a single model. However, existing MIASSR methods face two major limitations: (i) reliance on high-resolution (HR) volumes and (ii) limited generalization ability, which restricts their application in various scenarios. To overcome these limitations, we propose Cube-based Neural Radiance Field (CuNeRF), a zero-shot MIASSR framework that can yield medical images at arbitrary scales and viewpoints in a continuous domain. Unlike existing MIASSR methods that fit the mapping between low-resolution (LR) and HR volumes, CuNeRF focuses on building a coordinate-intensity continuous representation from LR volumes without the need for HR references. This is achieved by the proposed differentiable modules: including cube-based sampling, isotropic volume rendering, and cube-based hierarchical rendering. Through extensive experiments on magnetic resource imaging (MRI) and computed tomography (CT) modalities, we demonstrate that CuNeRF outperforms state-of-the-art MIASSR methods. CuNeRF yields better visual verisimilitude and reduces aliasing artifacts at various upsampling factors. Moreover, our CuNeRF does not need any LR-HR training pairs, which is more flexible and easier to be used than others. Our code will be publicly available soon.

Neural speech codecs have recently emerged as a focal point in the fields of speech compression and generation. Despite this progress, achieving high-quality speech reconstruction under low-bitrate scenarios remains a significant challenge. In this paper, we propose PSCodec, a series of neural speech codecs based on prompt encoders, comprising PSCodec-Base, PSCodec-DRL-ICT, and PSCodec-CasAN, which are capable of delivering high-performance speech reconstruction with low bandwidths. Specifically, we first introduce PSCodec-Base, which leverages a pretrained speaker verification model-based prompt encoder (VPP-Enc) and a learnable Mel-spectrogram-based prompt encoder (MelP-Enc) to effectively disentangle and integrate voiceprint and Mel-related features in utterances. To further enhance feature utilization efficiency, we propose PSCodec-DRL-ICT, incorporating a structural similarity (SSIM) based disentangled representation loss (DRL) and an incremental continuous training (ICT) strategy. While PSCodec-DRL-ICT demonstrates impressive performance, its reliance on extensive hyperparameter tuning and multi-stage training makes it somewhat labor-intensive. To circumvent these limitations, we propose PSCodec-CasAN, utilizing an advanced cascaded attention network (CasAN) to enhance representational capacity of the entire system. Extensive experiments show that our proposed PSCodec-Base, PSCodec-DRL-ICT, and PSCodec-CasAN all significantly outperform several state-of-the-art neural codecs, exhibiting substantial improvements in both speech reconstruction quality and speaker similarity under low-bitrate conditions.

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.

We present DietNeRF, a 3D neural scene representation estimated from a few images. Neural Radiance Fields (NeRF) learn a continuous volumetric representation of a scene through multi-view consistency, and can be rendered from novel viewpoints by ray casting. While NeRF has an impressive ability to reconstruct geometry and fine details given many images, up to 100 for challenging 360{\deg} scenes, it often finds a degenerate solution to its image reconstruction objective when only a few input views are available. To improve few-shot quality, we propose DietNeRF. We introduce an auxiliary semantic consistency loss that encourages realistic renderings at novel poses. DietNeRF is trained on individual scenes to (1) correctly render given input views from the same pose, and (2) match high-level semantic attributes across different, random poses. Our semantic loss allows us to supervise DietNeRF from arbitrary poses. We extract these semantics using a pre-trained visual encoder such as CLIP, a Vision Transformer trained on hundreds of millions of diverse single-view, 2D photographs mined from the web with natural language supervision. In experiments, DietNeRF improves the perceptual quality of few-shot view synthesis when learned from scratch, can render novel views with as few as one observed image when pre-trained on a multi-view dataset, and produces plausible completions of completely unobserved regions.

We propose VidStyleODE, a spatiotemporally continuous disentangled Video representation based upon StyleGAN and Neural-ODEs. Effective traversal of the latent space learned by Generative Adversarial Networks (GANs) has been the basis for recent breakthroughs in image editing. However, the applicability of such advancements to the video domain has been hindered by the difficulty of representing and controlling videos in the latent space of GANs. In particular, videos are composed of content (i.e., appearance) and complex motion components that require a special mechanism to disentangle and control. To achieve this, VidStyleODE encodes the video content in a pre-trained StyleGAN W_+ space and benefits from a latent ODE component to summarize the spatiotemporal dynamics of the input video. Our novel continuous video generation process then combines the two to generate high-quality and temporally consistent videos with varying frame rates. We show that our proposed method enables a variety of applications on real videos: text-guided appearance manipulation, motion manipulation, image animation, and video interpolation and extrapolation. Project website: https://cyberiada.github.io/VidStyleODE

Modeling the time-varying 3D appearance of plants during growth poses unique challenges: unlike most dynamic scenes, plants continuously generate new geometry as they expand, branch, and differentiate. Existing dynamic scene representations are ill-suited to this setting: deformation fields provide insufficient constraints to yield physically plausible scene dynamics, and 4D Gaussian splatting represents the same physical structures with different Gaussian primitives at different times, breaking temporal consistency. We introduce GrowFlow, a dynamic representation that couples 3D Gaussian primitives with a neural ordinary differential equation to model plant growth as a continuous flow field over geometric parameters (position, scale, and orientation). Our representation enables consistent appearance rendering and models nonlinear, continuous-time growth dynamics with full temporal correspondences for every primitive. To initialize a sufficient set of Gaussian primitives, we first reconstruct the mature plant and then learn a reverse-growth process, effectively simulating the plant's developmental history in reverse. GrowFlow achieves superior image quality and geometric coherence compared to prior methods on a new, multi-view timelapse dataset of plant growth, and provides the first temporally coherent representation for appearance modeling of growing 3D structures.

Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to O(n n). We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same architecture to model images, audio, and text from raw bytes, setting a new state of the art for density modeling of Enwik8, CIFAR-10, and ImageNet-64. We generate unconditional samples that demonstrate global coherence and great diversity, and show it is possible in principle to use self-attention to model sequences of length one million or more.

Can neural networks systematically capture discrete, compositional task structure despite their continuous, distributed nature? The impressive capabilities of large-scale neural networks suggest that the answer to this question is yes. However, even for the most capable models, there are still frequent failure cases that raise doubts about their compositionality. Here, we seek to understand what it takes for a standard neural network to generalize over tasks that share compositional structure. We find that simply scaling data and model size leads to compositional generalization. We show that this holds across different task encodings as long as the training distribution sufficiently covers the task space. In line with this finding, we prove that standard multilayer perceptrons can approximate a general class of compositional task families to arbitrary precision using only a linear number of neurons with respect to the number of task modules. Finally, we uncover that if networks successfully compositionally generalize, the constituents of a task can be linearly decoded from their hidden activations. We show that this metric correlates with failures of text-to-image generation models to compose known concepts.

We propose NEURONA, a neuro-symbolic framework for fMRI decoding and concept grounding in neural activity. Leveraging image- and video-based fMRI question-answering datasets, NEURONA learns to decode interacting concepts from visual stimuli based on patterns of fMRI responses, integrating symbolic reasoning and compositional execution with fMRI grounding across brain regions. We demonstrate that incorporating structural priors (e.g., compositional predicate-argument dependencies between concepts) into the decoding process significantly improves both decoding accuracy over precise queries, and notably, generalization to unseen queries at test time. With NEURONA, we highlight neuro-symbolic frameworks as promising tools for understanding neural activity.

Catastrophic forgetting in neural networks is a significant problem for continual learning. A majority of the current methods replay previous data during training, which violates the constraints of an ideal continual learning system. Additionally, current approaches that deal with forgetting ignore the problem of catastrophic remembering, i.e. the worsening ability to discriminate between data from different tasks. In our work, we introduce Relevance Mapping Networks (RMNs) which are inspired by the Optimal Overlap Hypothesis. The mappings reflects the relevance of the weights for the task at hand by assigning large weights to essential parameters. We show that RMNs learn an optimized representational overlap that overcomes the twin problem of catastrophic forgetting and remembering. Our approach achieves state-of-the-art performance across all common continual learning datasets, even significantly outperforming data replay methods while not violating the constraints for an ideal continual learning system. Moreover, RMNs retain the ability to detect data from new tasks in an unsupervised manner, thus proving their resilience against catastrophic remembering.

Deep representation learning methods struggle with continual learning, suffering from both catastrophic forgetting of useful units and loss of plasticity, often due to rigid and unuseful units. While many methods address these two issues separately, only a few currently deal with both simultaneously. In this paper, we introduce Utility-based Perturbed Gradient Descent (UPGD) as a novel approach for the continual learning of representations. UPGD combines gradient updates with perturbations, where it applies smaller modifications to more useful units, protecting them from forgetting, and larger modifications to less useful units, rejuvenating their plasticity. We use a challenging streaming learning setup where continual learning problems have hundreds of non-stationarities and unknown task boundaries. We show that many existing methods suffer from at least one of the issues, predominantly manifested by their decreasing accuracy over tasks. On the other hand, UPGD continues to improve performance and surpasses or is competitive with all methods in all problems. Finally, in extended reinforcement learning experiments with PPO, we show that while Adam exhibits a performance drop after initial learning, UPGD avoids it by addressing both continual learning issues.

We create a reusable Transformer, BrainBERT, for intracranial recordings bringing modern representation learning approaches to neuroscience. Much like in NLP and speech recognition, this Transformer enables classifying complex concepts, i.e., decoding neural data, with higher accuracy and with much less data by being pretrained in an unsupervised manner on a large corpus of unannotated neural recordings. Our approach generalizes to new subjects with electrodes in new positions and to unrelated tasks showing that the representations robustly disentangle the neural signal. Just like in NLP where one can study language by investigating what a language model learns, this approach opens the door to investigating the brain by what a model of the brain learns. As a first step along this path, we demonstrate a new analysis of the intrinsic dimensionality of the computations in different areas of the brain. To construct these representations, we combine a technique for producing super-resolution spectrograms of neural data with an approach designed for generating contextual representations of audio by masking. In the future, far more concepts will be decodable from neural recordings by using representation learning, potentially unlocking the brain like language models unlocked language.

Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural biases. However, traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. Several extensions have been proposed to overcome this limitation. Nevertheless, these extensions tend to rely on surrogate gradients or reinforcement learning at the cost of higher bias or variance. In this work, we propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative to address the aforementioned limitations. This is done by incorporating a continuous relaxation to the induced structure. We demonstrate that CRvNN achieves strong performance in challenging synthetic tasks such as logical inference and ListOps. We also show that CRvNN performs comparably or better than prior latent structure models on real-world tasks such as sentiment analysis and natural language inference.

We introduce a new test of how well language models capture meaning in children's books. Unlike standard language modelling benchmarks, it distinguishes the task of predicting syntactic function words from that of predicting lower-frequency words, which carry greater semantic content. We compare a range of state-of-the-art models, each with a different way of encoding what has been previously read. We show that models which store explicit representations of long-term contexts outperform state-of-the-art neural language models at predicting semantic content words, although this advantage is not observed for syntactic function words. Interestingly, we find that the amount of text encoded in a single memory representation is highly influential to the performance: there is a sweet-spot, not too big and not too small, between single words and full sentences that allows the most meaningful information in a text to be effectively retained and recalled. Further, the attention over such window-based memories can be trained effectively through self-supervision. We then assess the generality of this principle by applying it to the CNN QA benchmark, which involves identifying named entities in paraphrased summaries of news articles, and achieve state-of-the-art performance.

Performant Convolutional Neural Network (CNN) architectures must be tailored to specific tasks in order to consider the length, resolution, and dimensionality of the input data. In this work, we tackle the need for problem-specific CNN architectures. We present the Continuous Convolutional Neural Network (CCNN): a single CNN able to process data of arbitrary resolution, dimensionality and length without any structural changes. Its key component are its continuous convolutional kernels which model long-range dependencies at every layer, and thus remove the need of current CNN architectures for task-dependent downsampling and depths. We showcase the generality of our method by using the same architecture for tasks on sequential (1{rm D}), visual (2{rm D}) and point-cloud (3{rm D}) data. Our CCNN matches and often outperforms the current state-of-the-art across all tasks considered.

In this work we propose a simple and efficient framework for learning sentence representations from unlabelled data. Drawing inspiration from the distributional hypothesis and recent work on learning sentence representations, we reformulate the problem of predicting the context in which a sentence appears as a classification problem. Given a sentence and its context, a classifier distinguishes context sentences from other contrastive sentences based on their vector representations. This allows us to efficiently learn different types of encoding functions, and we show that the model learns high-quality sentence representations. We demonstrate that our sentence representations outperform state-of-the-art unsupervised and supervised representation learning methods on several downstream NLP tasks that involve understanding sentence semantics while achieving an order of magnitude speedup in training time.