Daily Papers

Causal video generators must predict from the past, but they need not learn only from it. In streaming autoregressive video diffusion, each emitted segment becomes a commitment that future segments must preserve. Standard training, however, only asks each causal state to explain the present. This creates what we call a representation-level planning gap: states that fit the current segment may discard identity, layout, and motion information needed for a consistent future. We introduce Video-Mirai, a training-only method that closes this gap without changing causal inference: the generator rolls out causally, a frozen foresight encoder reads the completed rollout non-causally, and a lightweight predictor distills the resulting stopped-gradient targets into causal states. Future frames supervise representations, never generator inputs. At inference, the encoder and predictor are discarded, leaving the original architecture, per-step FLOPs, and KV-cache behavior unchanged. Video-Mirai improves a strong Causal-Forcing baseline on 5-second VBench from 83.8 to 84.6 in terms of Total Score. On 30-second rollouts beyond the training horizon, subject consistency improves from 84.9 to 88.5 and background consistency from 90.2 to 91.9. Ablations identify future-conditioned targets as the key ingredient, and probes show that future frames become more decodable from current features. Causality should constrain inference, not representation supervision. Our study highlights that visual autoregressive models need foresight. Project page: https://y0uroy.github.io/Video-Mirai.

Early stopping monitors global validation loss and halts all parameter updates simultaneously, which is computationally costly for large transformers due to the extended time required for validation inference. We propose GradES, a novel gradient-based early stopping approach that operates within transformer components (attention projections and Feed-Forward layer matrices). We found that different components converge at varying rates during fine-tuning. GradES tracks the magnitude of gradients in backpropagation for these matrices during training. When a projection matrix's gradients fall below a convergence threshold tau, we exclude that projection matrix from further updates individually, eliminating costly validation passes while allowing slow converging matrices to continue learning. By strategically freezing parameters when their gradients converge, GradES speeds up training time by 1.57--7.22times while simultaneously enhancing generalization through early prevention of overfitting, resulting in 1.2% higher average accuracy.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of introducing gradient delay, which impedes optimization and can lead to lower final model performance. We introduce Adaptive Braking (AB), a modification for momentum-based optimizers that mitigates the effects of gradient delay. AB dynamically scales the gradient based on the alignment of the gradient and the velocity. This can dampen oscillations along high curvature directions of the loss surface, stabilizing and accelerating asynchronous training. We show that applying AB on top of SGD with momentum enables training ResNets on CIFAR-10 and ImageNet-1k with delays D geq 32 update steps with minimal drop in final test accuracy.

Training neural networks requires significant computational resources and energy. Methods like mixed-precision and quantization-aware training reduce bit usage, yet they still depend heavily on computationally expensive gradient-based optimization. In this work, we propose a paradigm shift: eliminate gradients altogether. One might hope that, in a finite quantized space, finding optimal weights with out gradients would be easier but we theoretically prove that this problem is NP-hard even in simple settings where the continuous case is efficiently solvable. To address this, we introduce a novel heuristic optimization framework that avoids full weight updates and significantly improves efficiency. Empirically, our method achieves performance comparable to that of full-precision gradient-based training on standard datasets and architectures, while using up to 3x less energy and requiring up to 5x fewer parameter updates.

The Automatic Identification System (AIS) enables data-driven maritime surveillance but suffers from reliability issues and irregular intervals. We address vessel destination estimation using global-scope AIS data by proposing a differentiated approach that recasts long port-to-port trajectories as a nested sequence structure. Using spatial grids, this method mitigates spatio-temporal bias while preserving detailed resolution. We introduce a novel deep learning architecture, WAY, designed to process these reformulated trajectories for long-term destination estimation days to weeks in advance. WAY comprises a trajectory representation layer and Channel-Aggregative Sequential Processing (CASP) blocks. The representation layer generates multi-channel vector sequences from kinematic and non-kinematic features. CASP blocks utilize multi-headed channel- and self-attention for aggregation and sequential information delivery. Additionally, we propose a task-specialized Gradient Dropout (GD) technique to enable many-to-many training on single labels, preventing biased feedback surges by stochastically blocking gradient flow based on sample length. Experiments on 5-year AIS data demonstrate WAY's superiority over conventional spatial grid-based approaches regardless of trajectory progression. Results further confirm that adopting GD leads to performance gains. Finally, we explore WAY's potential for real-world application through multitask learning for ETA estimation.

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the value of the objective function; instead, the line search can operate on merit functions. In this report, we explore an alternative line-search method which is applicable to this case; it particulary addresses the damping of the step length in tight valleys. We propose a line-search criterion based on the divergence of the field of Newton step vectors. The visualization of the criterion for two-dimensional test functions reveals a network of ravines with flat bottom at the zero points of the criterion. The ravines are typically connected to stationary points. To traverse this ravine network in order to approach a stationary point, a zigzag strategy is devised. Numerical experiments demonstrate that the novel line-search strategy succeeds from most starting points in all test functions, but only exhibits the desired damping of the step length in some situations. At the present stage it is therefore difficult to appraise the utility of this contribution.

Most existing approaches to referring segmentation achieve strong performance only through fine-tuning or by composing multiple pre-trained models, often at the cost of additional training and architectural modifications. Meanwhile, large-scale generative diffusion models encode rich semantic information, making them attractive as general-purpose feature extractors. In this work, we introduce a new method that directly exploits features, attention scores, from diffusion transformers for downstream tasks, requiring neither architectural modifications nor additional training. To systematically evaluate these features, we extend benchmarks with vision-language grounding tasks spanning both images and videos. Our key insight is that stop words act as attention magnets: they accumulate surplus attention and can be filtered to reduce noise. Moreover, we identify global attention sinks (GAS) emerging in deeper layers and show that they can be safely suppressed or redirected onto auxiliary tokens, leading to sharper and more accurate grounding maps. We further propose an attention redistribution strategy, where appended stop words partition background activations into smaller clusters, yielding sharper and more localized heatmaps. Building on these findings, we develop RefAM, a simple training-free grounding framework that combines cross-attention maps, GAS handling, and redistribution. Across zero-shot referring image and video segmentation benchmarks, our approach consistently outperforms prior methods, establishing a new state of the art without fine-tuning or additional components.

Wasserstein Gradient Flows (WGF) with respect to specific functionals have been widely used in the machine learning literature. Recently, neural networks have been adopted to approximate certain intractable parts of the underlying Wasserstein gradient flow and result in efficient inference procedures. In this paper, we introduce the Neural Sinkhorn Gradient Flow (NSGF) model, which parametrizes the time-varying velocity field of the Wasserstein gradient flow w.r.t. the Sinkhorn divergence to the target distribution starting a given source distribution. We utilize the velocity field matching training scheme in NSGF, which only requires samples from the source and target distribution to compute an empirical velocity field approximation. Our theoretical analyses show that as the sample size increases to infinity, the mean-field limit of the empirical approximation converges to the true underlying velocity field. To further enhance model efficiency on high-dimensional tasks, a two-phase NSGF++ model is devised, which first follows the Sinkhorn flow to approach the image manifold quickly (le 5 NFEs) and then refines the samples along a simple straight flow. Numerical experiments with synthetic and real-world benchmark datasets support our theoretical results and demonstrate the effectiveness of the proposed methods.

Continuously adapting pre-trained models to local data on resource constrained edge devices is the last mile for model deployment. However, as models increase in size and depth, backpropagation requires a large amount of memory, which becomes prohibitive for edge devices. In addition, most existing low power neural processing engines (e.g., NPUs, DSPs, MCUs, etc.) are designed as fixed-point inference accelerators, without training capabilities. Forward gradients, solely based on directional derivatives computed from two forward calls, have been recently used for model training, with substantial savings in computation and memory. However, the performance of quantized training with fixed-point forward gradients remains unclear. In this paper, we investigate the feasibility of on-device training using fixed-point forward gradients, by conducting comprehensive experiments across a variety of deep learning benchmark tasks in both vision and audio domains. We propose a series of algorithm enhancements that further reduce the memory footprint, and the accuracy gap compared to backpropagation. An empirical study on how training with forward gradients navigates in the loss landscape is further explored. Our results demonstrate that on the last mile of model customization on edge devices, training with fixed-point forward gradients is a feasible and practical approach.

Classifier-free guidance (CFG) is a widely used technique for controllable generation in diffusion and flow-based models. Despite its empirical success, CFG relies on a heuristic linear extrapolation that is often sensitive to the guidance scale. In this work, we provide a principled interpretation of CFG through the lens of optimization. We demonstrate that the velocity field in flow matching corresponds to the gradient of a sequence of smoothed distance functions, which guides latent variables toward the scaled target image set. This perspective reveals that the standard CFG formulation is an approximation of this gradient, where the prediction gap, the discrepancy between conditional and unconditional outputs, governs guidance sensitivity. Leveraging this insight, we reformulate the CFG sampling as a homotopy optimization with a manifold constraint. This formulation necessitates a manifold projection step, which we implement via an incremental gradient descent scheme during sampling. To improve computational efficiency and stability, we further enhance this iterative process with Anderson Acceleration without requiring additional model evaluations. Our proposed methods are training-free and consistently refine generation fidelity, prompt alignment, and robustness to the guidance scale. We validate their effectiveness across diverse benchmarks, demonstrating significant improvements on large-scale models such as DiT-XL-2-256, Flux, and Stable Diffusion 3.5.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

We investigate the theoretical foundations of classifier-free guidance (CFG). CFG is the dominant method of conditional sampling for text-to-image diffusion models, yet unlike other aspects of diffusion, it remains on shaky theoretical footing. In this paper, we disprove common misconceptions, by showing that CFG interacts differently with DDPM (Ho et al., 2020) and DDIM (Song et al., 2021), and neither sampler with CFG generates the gamma-powered distribution p(x|c)^gamma p(x)^{1-gamma}. Then, we clarify the behavior of CFG by showing that it is a kind of predictor-corrector method (Song et al., 2020) that alternates between denoising and sharpening, which we call predictor-corrector guidance (PCG). We prove that in the SDE limit, CFG is actually equivalent to combining a DDIM predictor for the conditional distribution together with a Langevin dynamics corrector for a gamma-powered distribution (with a carefully chosen gamma). Our work thus provides a lens to theoretically understand CFG by embedding it in a broader design space of principled sampling methods.

Object modeling has become a core part of recent tracking frameworks. Current popular tackers use Transformer attention to extract the template feature separately or interactively with the search region. However, separate template learning lacks communication between the template and search regions, which brings difficulty in extracting discriminative target-oriented features. On the other hand, interactive template learning produces hybrid template features, which may introduce potential distractors to the template via the cluttered search regions. To enjoy the merits of both methods, we propose a robust object modeling framework for visual tracking (ROMTrack), which simultaneously models the inherent template and the hybrid template features. As a result, harmful distractors can be suppressed by combining the inherent features of target objects with search regions' guidance. Target-related features can also be extracted using the hybrid template, thus resulting in a more robust object modeling framework. To further enhance robustness, we present novel variation tokens to depict the ever-changing appearance of target objects. Variation tokens are adaptable to object deformation and appearance variations, which can boost overall performance with negligible computation. Experiments show that our ROMTrack sets a new state-of-the-art on multiple benchmarks.

FSampler is a training free, sampler agnostic execution layer that accelerates diffusion sampling by reducing the number of function evaluations (NFE). FSampler maintains a short history of denoising signals (epsilon) from recent real model calls and extrapolates the next epsilon using finite difference predictors at second order, third order, or fourth order, falling back to lower order when history is insufficient. On selected steps the predicted epsilon substitutes the model call while keeping each sampler's update rule unchanged. Predicted epsilons are validated for finiteness and magnitude; a learning stabilizer rescales predictions on skipped steps to correct drift, and an optional gradient estimation stabilizer compensates local curvature. Protected windows, periodic anchors, and a cap on consecutive skips bound deviation over the trajectory. Operating at the sampler level, FSampler integrates with Euler/DDIM, DPM++ 2M/2S, LMS/AB2, and RES family exponential multistep methods and drops into standard workflows. FLUX.1 dev, Qwen Image, and Wan 2.2, FSampler reduces time by 8 to 22% and model calls by 15 to 25% at high fidelity (Structural Similarity Index (SSIM) 0.95 to 0.99), without altering sampler formulas. With an aggressive adaptive gate, reductions can reach 45 to 50% fewer model calls at lower fidelity (SSIM 0.73 to 0.74).

Robust validation metrics remain essential in contemporary deep learning, not only to detect overfitting and poor generalization, but also to monitor training dynamics. In the supervised classification setting, we investigate whether interactions between training data and model weights can yield such a metric that both tracks generalization during training and attributes performance to individual training samples. We introduce Gradient-Weight Alignment (GWA), quantifying the coherence between per-sample gradients and model weights. We show that effective learning corresponds to coherent alignment, while misalignment indicates deteriorating generalization. GWA is efficiently computable during training and reflects both sample-specific contributions and dataset-wide learning dynamics. Extensive experiments show that GWA accurately predicts optimal early stopping, enables principled model comparisons, and identifies influential training samples, providing a validation-set-free approach for model analysis directly from the training data.

Recently, there has been a growing interest in automating the process of neural architecture design, and the Differentiable Architecture Search (DARTS) method makes the process available within a few GPU days. However, the performance of DARTS is often observed to collapse when the number of search epochs becomes large. Meanwhile, lots of "{\em skip-connect}s" are found in the selected architectures. In this paper, we claim that the cause of the collapse is that there exists overfitting in the optimization of DARTS. Therefore, we propose a simple and effective algorithm, named "DARTS+", to avoid the collapse and improve the original DARTS, by "early stopping" the search procedure when meeting a certain criterion. We also conduct comprehensive experiments on benchmark datasets and different search spaces and show the effectiveness of our DARTS+ algorithm, and DARTS+ achieves 2.32% test error on CIFAR10, 14.87% on CIFAR100, and 23.7% on ImageNet. We further remark that the idea of "early stopping" is implicitly included in some existing DARTS variants by manually setting a small number of search epochs, while we give an {\em explicit} criterion for "early stopping".

A novel gradient boosting framework is proposed where shallow neural networks are employed as ``weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered outperforming results against state-of-the-art boosting methods in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of each model components and model hyperparameters.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

Negative guidance -- explicitly suppressing unwanted attributes -- remains a fundamental challenge in diffusion models, particularly in few-step sampling regimes. While Classifier-Free Guidance (CFG) works well in standard settings, it fails under aggressive sampling step compression due to divergent predictions between positive and negative branches. We present Normalized Attention Guidance (NAG), an efficient, training-free mechanism that applies extrapolation in attention space with L1-based normalization and refinement. NAG restores effective negative guidance where CFG collapses while maintaining fidelity. Unlike existing approaches, NAG generalizes across architectures (UNet, DiT), sampling regimes (few-step, multi-step), and modalities (image, video), functioning as a universal plug-in with minimal computational overhead. Through extensive experimentation, we demonstrate consistent improvements in text alignment (CLIP Score), fidelity (FID, PFID), and human-perceived quality (ImageReward). Our ablation studies validate each design component, while user studies confirm significant preference for NAG-guided outputs. As a model-agnostic inference-time approach requiring no retraining, NAG provides effortless negative guidance for all modern diffusion frameworks -- pseudocode in the Appendix!

Significant recent work has studied the ability of gradient descent to recover a hidden planted direction θ^star in S^{d-1} in different high-dimensional settings, including tensor PCA and single-index models. The key quantity that governs the ability of gradient descent to traverse these landscapes is the information exponent k^star (Ben Arous et al., (2021)), which corresponds to the order of the saddle at initialization in the population landscape. Ben Arous et al., (2021) showed that n gtrsim d^{max(1, k^star-1)} samples were necessary and sufficient for online SGD to recover θ^star, and Ben Arous et al., (2020) proved a similar lower bound for Langevin dynamics. More recently, Damian et al., (2023) showed it was possible to circumvent these lower bounds by running gradient descent on a smoothed landscape, and that this algorithm succeeds with n gtrsim d^{max(1, k^star/2)} samples, which is optimal in the worst case. This raises the question of whether it is possible to achieve the same rate without explicit smoothing. In this paper, we show that Langevin dynamics can succeed with n gtrsim d^{ k^star/2 } samples if one considers the average iterate, rather than the last iterate. The key idea is that the combination of noise-injection and iterate averaging is able to emulate the effect of landscape smoothing. We apply this result to both the tensor PCA and single-index model settings. Finally, we conjecture that minibatch SGD can also achieve the same rate without adding any additional noise.

Classifier-free guidance (CFG) is a core technique powering state-of-the-art image generation systems, yet its underlying mechanisms remain poorly understood. In this work, we begin by analyzing CFG in a simplified linear diffusion model, where we show its behavior closely resembles that observed in the nonlinear case. Our analysis reveals that linear CFG improves generation quality via three distinct components: (i) a mean-shift term that approximately steers samples in the direction of class means, (ii) a positive Contrastive Principal Components (CPC) term that amplifies class-specific features, and (iii) a negative CPC term that suppresses generic features prevalent in unconditional data. We then verify that these insights in real-world, nonlinear diffusion models: over a broad range of noise levels, linear CFG resembles the behavior of its nonlinear counterpart. Although the two eventually diverge at low noise levels, we discuss how the insights from the linear analysis still shed light on the CFG's mechanism in the nonlinear regime.

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value c >0. It is widely used for example for stabilizing the training of deep learning models (Goodfellow et al., 2016), or for enforcing differential privacy (Abadi et al., 2016). Despite popularity and simplicity of the clipping mechanism, its convergence guarantees often require specific values of c and strong noise assumptions. In this paper, we give convergence guarantees that show precise dependence on arbitrary clipping thresholds c and show that our guarantees are tight with both deterministic and stochastic gradients. In particular, we show that (i) for deterministic gradient descent, the clipping threshold only affects the higher-order terms of convergence, (ii) in the stochastic setting convergence to the true optimum cannot be guaranteed under the standard noise assumption, even under arbitrary small step-sizes. We give matching upper and lower bounds for convergence of the gradient norm when running clipped SGD, and illustrate these results with experiments.

The widespread use of vector graphics creates a significant demand for vectorization methods. While recent learning-based techniques have shown their capability to create vector images of clear topology, filling these primitives with gradients remains a challenge. In this paper, we propose a segmentation-guided vectorization framework to convert raster images into concise vector graphics with radial gradient fills. With the guidance of an embedded gradient-aware segmentation subroutine, our approach progressively appends gradient-filled B\'ezier paths to the output, where primitive parameters are initiated with our newly designed initialization technique and are optimized to minimize our novel loss function. We build our method on a differentiable renderer with traditional segmentation algorithms to develop it as a model-free tool for raster-to-vector conversion. It is tested on various inputs to demonstrate its feasibility, independent of datasets, to synthesize vector graphics with improved visual quality and layer-wise topology compared to prior work.

In spite of recent progress, image diffusion models still produce artifacts. A common solution is to leverage the feedback provided by quality assessment systems or human annotators to optimize the model, where images are generally rated in their entirety. In this work, we believe problem-solving starts with identification, yielding the request that the model should be aware of not just the presence of defects in an image, but their specific locations. Motivated by this, we propose DiffDoctor, a two-stage pipeline to assist image diffusion models in generating fewer artifacts. Concretely, the first stage targets developing a robust artifact detector, for which we collect a dataset of over 1M flawed synthesized images and set up an efficient human-in-the-loop annotation process, incorporating a carefully designed class-balance strategy. The learned artifact detector is then involved in the second stage to optimize the diffusion model by providing pixel-level feedback. Extensive experiments on text-to-image diffusion models demonstrate the effectiveness of our artifact detector as well as the soundness of our diagnose-then-treat design.

Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability p_0 is small. Using the Tsallis q-logarithm, we define a loss family J_Q that interpolates between RLVR (at q{=}0, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at q{=}1, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification P_{θ^{-q}} that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires Ω(1{p_0}) time to escape cold start, while the density-estimation pole escapes in Θbig(log(1{p_0})big); intermediate q trades escape speed against noise memorization. Because P_θ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias Obig(q{M P_θ^{q+1}}big); GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at q{=}0.75 substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low q dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at q{=}0.75 provides stable gradients (best overall on HotPotQA at 47.9 maj@16, +14.4 over GRPO).

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

Optimization analyses for cross-entropy training rely on local Taylor models of the loss to predict whether a proposed step will decrease the objective. These surrogates are reliable only inside the Taylor convergence radius of the true loss along the update direction. That radius is set not by real-line curvature alone but by the nearest complex singularity. For cross-entropy, the softmax partition function F=sum_j exp(z_j) has complex zeros -- ``ghosts of softmax'' -- that induce logarithmic singularities in the loss and cap this radius. To make this geometry usable, we derive closed-form expressions under logit linearization along the proposed update direction. In the binary case, the exact radius is ρ^*=δ^2+ π^2/Δ_a. In the multiclass case, we obtain the lower bound ρ_a=π/Δ_a, where Δ_a=max_k a_k-min_k a_k is the spread of directional logit derivatives a_k=nabla z_kcdot v. This bound costs one Jacobian-vector product and reveals what makes a step fragile: samples that are both near a decision flip and highly sensitive to the proposed direction tighten the radius. The normalized step size r=τ/ρ_a separates safe from dangerous updates. Across six tested architectures and multiple step directions, no model fails for r<1, yet collapse appears once rge 1. Temperature scaling confirms the mechanism: normalizing by ρ_a shrinks the onset-threshold spread from standard deviation 0.992 to 0.164. A controller that enforces τleρ_a survives learning-rate spikes up to 10{,} 000times in our tests, where gradient clipping still collapses. Together, these results identify a geometric constraint on cross-entropy optimization that operates through Taylor convergence rather than Hessian curvature.

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation in the presence of stragglers. In this paper, we consider the distributed computation of a sequence of gradients {g(1),g(2),ldots,g(J)}, where processing of each gradient g(t) starts in round-t and finishes by round-(t+T). Here Tgeq 0 denotes a delay parameter. For the GC scheme, coding is only across computing nodes and this results in a solution where T=0. On the other hand, having T>0 allows for designing schemes which exploit the temporal dimension as well. In this work, we propose two schemes that demonstrate improved performance compared to GC. Our first scheme combines GC with selective repetition of previously unfinished tasks and achieves improved straggler mitigation. In our second scheme, which constitutes our main contribution, we apply GC to a subset of the tasks and repetition for the remainder of the tasks. We then multiplex these two classes of tasks across workers and rounds in an adaptive manner, based on past straggler patterns. Using theoretical analysis, we demonstrate that our second scheme achieves significant reduction in the computational load. In our experiments, we study a practical setting of concurrently training multiple neural networks over an AWS Lambda cluster involving 256 worker nodes, where our framework naturally applies. We demonstrate that the latter scheme can yield a 16\% improvement in runtime over the baseline GC scheme, in the presence of naturally occurring, non-simulated stragglers.

Diffusion models have demonstrated strong generative performance when using guidance methods such as classifier-free guidance (CFG), which enhance output quality by modifying the sampling trajectory. These methods typically improve a target output by intentionally degrading another, often the unconditional output, using heuristic perturbation functions such as identity mixing or blurred conditions. However, these approaches lack a principled foundation and rely on manually designed distortions. In this work, we propose Adversarial Sinkhorn Attention Guidance (ASAG), a novel method that reinterprets attention scores in diffusion models through the lens of optimal transport and intentionally disrupt the transport cost via Sinkhorn algorithm. Instead of naively corrupting the attention mechanism, ASAG injects an adversarial cost within self-attention layers to reduce pixel-wise similarity between queries and keys. This deliberate degradation weakens misleading attention alignments and leads to improved conditional and unconditional sample quality. ASAG shows consistent improvements in text-to-image diffusion, and enhances controllability and fidelity in downstream applications such as IP-Adapter and ControlNet. The method is lightweight, plug-and-play, and improves reliability without requiring any model retraining.

Recent diffusion models achieve the state-of-the-art performance in image generation, but often suffer from semantic inconsistencies or hallucinations. While various inference-time guidance methods can enhance generation, they often operate indirectly by relying on external signals or architectural modifications, which introduces additional computational overhead. In this paper, we propose Tangential Amplifying Guidance (TAG), a more efficient and direct guidance method that operates solely on trajectory signals without modifying the underlying diffusion model. TAG leverages an intermediate sample as a projection basis and amplifies the tangential components of the estimated scores with respect to this basis to correct the sampling trajectory. We formalize this guidance process by leveraging a first-order Taylor expansion, which demonstrates that amplifying the tangential component steers the state toward higher-probability regions, thereby reducing inconsistencies and enhancing sample quality. TAG is a plug-and-play, architecture-agnostic module that improves diffusion sampling fidelity with minimal computational addition, offering a new perspective on diffusion guidance.

This paper is on Few-Shot Object Detection (FSOD), where given a few templates (examples) depicting a novel class (not seen during training), the goal is to detect all of its occurrences within a set of images. From a practical perspective, an FSOD system must fulfil the following desiderata: (a) it must be used as is, without requiring any fine-tuning at test time, (b) it must be able to process an arbitrary number of novel objects concurrently while supporting an arbitrary number of examples from each class and (c) it must achieve accuracy comparable to a closed system. Towards satisfying (a)-(c), in this work, we make the following contributions: We introduce, for the first time, a simple, yet powerful, few-shot detection transformer (FS-DETR) based on visual prompting that can address both desiderata (a) and (b). Our system builds upon the DETR framework, extending it based on two key ideas: (1) feed the provided visual templates of the novel classes as visual prompts during test time, and (2) ``stamp'' these prompts with pseudo-class embeddings (akin to soft prompting), which are then predicted at the output of the decoder. Importantly, we show that our system is not only more flexible than existing methods, but also, it makes a step towards satisfying desideratum (c). Specifically, it is significantly more accurate than all methods that do not require fine-tuning and even matches and outperforms the current state-of-the-art fine-tuning based methods on the most well-established benchmarks (PASCAL VOC & MSCOCO).

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine learning practitioners, our goal is to accelerate generalization of a model under grokking phenomenon. By regarding a series of gradients of a parameter over training iterations as a random signal over time, we can spectrally decompose the parameter trajectories under gradient descent into two components: the fast-varying, overfitting-yielding component and the slow-varying, generalization-inducing component. This analysis allows us to accelerate the grokking phenomenon more than times 50 with only a few lines of code that amplifies the slow-varying components of gradients. The experiments show that our algorithm applies to diverse tasks involving images, languages, and graphs, enabling practical availability of this peculiar artifact of sudden generalization. Our code is available at https://github.com/ironjr/grokfast.

Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i.i.d. instances. As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times. Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94% of timesteps used for classification while achieving rigorous accuracy gap control.

Attention sinks and massive activations are recurring and closely related phenomena in Transformer models. Existing studies have largely focused on the forward pass, making it unclear whether their connection is direct or mediated by a training-time mechanism. We study this question from the perspective of backpropagation. Empirically and theoretically, we show that under causal mask, attention sinks can induce pronounced gradient concentration, which we term gradient sinks. Furthermore, in pre-norm architectures with RMSNorm, massive activations can be understood as an adaptive response to this localized gradient pressure during training. To test this hypothesis, we introduce V-scale, a modification that adjusts value-path backpropagated gradients. In pretrained V-scale models, attention sinks are preserved whereas massive activations are suppressed. These results support the interpretation that gradient sink is a key training-time mediator linking attention sinks and massive activations.

Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple warm restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where we demonstrate new state-of-the-art results at 3.14% and 16.21%, respectively. We also demonstrate its advantages on a dataset of EEG recordings and on a downsampled version of the ImageNet dataset. Our source code is available at https://github.com/loshchil/SGDR

Classifier-free guidance (CFG) is a cornerstone of text-to-image diffusion models, yet its effectiveness is limited by the use of static guidance scales. This "one-size-fits-all" approach fails to adapt to the diverse requirements of different prompts; moreover, prior solutions like gradient-based correction or fixed heuristic schedules introduce additional complexities and fail to generalize. In this work, we challeng this static paradigm by introducing a framework for dynamic CFG scheduling. Our method leverages online feedback from a suite of general-purpose and specialized small-scale latent-space evaluations, such as CLIP for alignment, a discriminator for fidelity and a human preference reward model, to assess generation quality at each step of the reverse diffusion process. Based on this feedback, we perform a greedy search to select the optimal CFG scale for each timestep, creating a unique guidance schedule tailored to every prompt and sample. We demonstrate the effectiveness of our approach on both small-scale models and the state-of-the-art Imagen 3, showing significant improvements in text alignment, visual quality, text rendering and numerical reasoning. Notably, when compared against the default Imagen 3 baseline, our method achieves up to 53.8% human preference win-rate for overall preference, a figure that increases up to to 55.5% on prompts targeting specific capabilities like text rendering. Our work establishes that the optimal guidance schedule is inherently dynamic and prompt-dependent, and provides an efficient and generalizable framework to achieve it.

Camouflaged object segmentation presents unique challenges compared to traditional segmentation tasks, primarily due to the high similarity in patterns and colors between camouflaged objects and their backgrounds. Effective solutions to this problem have significant implications in critical areas such as pest control, defect detection, and lesion segmentation in medical imaging. Prior research has predominantly emphasized supervised or unsupervised pre-training methods, leaving zero-shot approaches significantly underdeveloped. Existing zero-shot techniques commonly utilize the Segment Anything Model (SAM) in automatic mode or rely on vision-language models to generate cues for segmentation; however, their performances remain unsatisfactory, due to the similarity of the camouflaged object and the background. This work studies how to avoid training by integrating large pre-trained models like SAM-2 and Owl-v2 with temporal information into a modular pipeline. Evaluated on the MoCA-Mask dataset, our approach achieves outstanding performance improvements, significantly outperforming existing zero-shot methods by raising the F-measure (F_beta^w) from 0.296 to 0.628. Our approach also surpasses supervised methods, increasing the F-measure from 0.476 to 0.628. Additionally, evaluation on the MoCA-Filter dataset demonstrates an increase in the success rate from 0.628 to 0.697 when compared with FlowSAM, a supervised transfer method. A thorough ablation study further validates the individual contributions of each component. Besides our main contributions, we also highlight inconsistencies in previous work regarding metrics and settings. Code can be found in https://github.com/weathon/vcos.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars: whole training loss curves can *collapse* onto a universal trajectory after a simple normalization. What remains unclear is whether this phenomenon persists for LLM families trained under *practical scaling recipes*, where width, depth, learning rate, batch size, and weight decay are scaled jointly. We show that it does: loss curves collapse across scales precisely when optimization hyperparameters are set optimally for the given data budget, in accordance with recent empirical scaling laws. Collapse therefore emerges as a signature of compute-efficient training. We demonstrate two applications at scale: (1) deviation-from-collapse provides a sensitive, early diagnostic of training pathologies, and (2) predictability of collapsed curves enables early stopping in large-scale hyperparameter tuning. Finally, we train a competitive LLM family, *Celerity*, using these insights, establishing collapse as an effective tool for developing efficient LLMs.

Early stopping based on hold-out data is a popular regularization technique designed to mitigate overfitting and increase the predictive accuracy of neural networks. Models trained with early stopping often provide relatively accurate predictions, but they generally still lack precise statistical guarantees unless they are further calibrated using independent hold-out data. This paper addresses the above limitation with conformalized early stopping: a novel method that combines early stopping with conformal calibration while efficiently recycling the same hold-out data. This leads to models that are both accurate and able to provide exact predictive inferences without multiple data splits nor overly conservative adjustments. Practical implementations are developed for different learning tasks -- outlier detection, multi-class classification, regression -- and their competitive performance is demonstrated on real data.

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This accounts for gradients being local linear approximations which lose their relevance as the iterate moves along the loss landscape. This work questions the use of a single EMA to accumulate past gradients and empirically demonstrates how this choice can be sub-optimal: a single EMA cannot simultaneously give a high weight to the immediate past, and a non-negligible weight to older gradients. Building on this observation, we propose AdEMAMix, a simple modification of the Adam optimizer with a mixture of two EMAs to better take advantage of past gradients. Our experiments on language modeling and image classification show -- quite surprisingly -- that gradients can stay relevant for tens of thousands of steps. They help to converge faster, and often to lower minima: e.g., a 1.3B parameter AdEMAMix LLM trained on 101B tokens performs comparably to an AdamW model trained on 197B tokens (+95%). Moreover, our method significantly slows-down model forgetting during training. Our work motivates further exploration of different types of functions to leverage past gradients, beyond EMAs.

Denoising diffusion models excel at generating high-quality images conditioned on text prompts, yet their effectiveness heavily relies on careful guidance during the sampling process. Classifier-Free Guidance (CFG) provides a widely used mechanism for steering generation by setting the guidance scale, which balances image quality and prompt alignment. However, the choice of the guidance scale has a critical impact on the convergence toward a visually appealing and prompt-adherent image. In this work, we propose an annealing guidance scheduler which dynamically adjusts the guidance scale over time based on the conditional noisy signal. By learning a scheduling policy, our method addresses the temperamental behavior of CFG. Empirical results demonstrate that our guidance scheduler significantly enhances image quality and alignment with the text prompt, advancing the performance of text-to-image generation. Notably, our novel scheduler requires no additional activations or memory consumption, and can seamlessly replace the common classifier-free guidance, offering an improved trade-off between prompt alignment and quality.

Siamese networks have become a common structure in various recent models for unsupervised visual representation learning. These models maximize the similarity between two augmentations of one image, subject to certain conditions for avoiding collapsing solutions. In this paper, we report surprising empirical results that simple Siamese networks can learn meaningful representations even using none of the following: (i) negative sample pairs, (ii) large batches, (iii) momentum encoders. Our experiments show that collapsing solutions do exist for the loss and structure, but a stop-gradient operation plays an essential role in preventing collapsing. We provide a hypothesis on the implication of stop-gradient, and further show proof-of-concept experiments verifying it. Our "SimSiam" method achieves competitive results on ImageNet and downstream tasks. We hope this simple baseline will motivate people to rethink the roles of Siamese architectures for unsupervised representation learning. Code will be made available.

Infrared small target detection (IRSTD) is critical for defense and surveillance but remains challenging due to (1) target loss from minimal features, (2) false alarms in cluttered environments, (3) missed detections from low saliency, and (4) high computational costs. To address these issues, we propose TY-RIST, an optimized YOLOv12n architecture that integrates (1) a stride-aware backbone with fine-grained receptive fields, (2) a high-resolution detection head, (3) cascaded coordinate attention blocks, and (4) a branch pruning strategy that reduces computational cost by about 25.5% while marginally improving accuracy and enabling real-time inference. We also incorporate the Normalized Gaussian Wasserstein Distance (NWD) to enhance regression stability. Extensive experiments on four benchmarks and across 20 different models demonstrate state-of-the-art performance, improving mAP at 0.5 IoU by +7.9%, Precision by +3%, and Recall by +10.2%, while achieving up to 123 FPS on a single GPU. Cross-dataset validation on a fifth dataset further confirms strong generalization capability. Additional results and resources are available at https://www.github.com/moured/TY-RIST

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SmoothGrad, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/GradientPathologiesPINNs.

Recent advancements in latent diffusion models (LDMs) have markedly enhanced text-to-audio generation, yet their iterative sampling processes impose substantial computational demands, limiting practical deployment. While recent methods utilizing consistency-based distillation aim to achieve few-step or single-step inference, their one-step performance is constrained by curved trajectories, preventing them from surpassing traditional diffusion models. In this work, we introduce FlashAudio with rectified flows to learn straight flow for fast simulation. To alleviate the inefficient timesteps allocation and suboptimal distribution of noise, FlashAudio optimizes the time distribution of rectified flow with Bifocal Samplers and proposes immiscible flow to minimize the total distance of data-noise pairs in a batch vias assignment. Furthermore, to address the amplified accumulation error caused by the classifier-free guidance (CFG), we propose Anchored Optimization, which refines the guidance scale by anchoring it to a reference trajectory. Experimental results on text-to-audio generation demonstrate that FlashAudio's one-step generation performance surpasses the diffusion-based models with hundreds of sampling steps on audio quality and enables a sampling speed of 400x faster than real-time on a single NVIDIA 4090Ti GPU.

Balancing efficiency and accuracy is a long-standing problem for deploying deep learning models. The trade-off is even more important for real-time safety-critical systems like autonomous vehicles. In this paper, we propose an effective approach for accelerating transformer-based 3D object detectors by dynamically halting tokens at different layers depending on their contribution to the detection task. Although halting a token is a non-differentiable operation, our method allows for differentiable end-to-end learning by leveraging an equivalent differentiable forward-pass. Furthermore, our framework allows halted tokens to be reused to inform the model's predictions through a straightforward token recycling mechanism. Our method significantly improves the Pareto frontier of efficiency versus accuracy when compared with the existing approaches. By halting tokens and increasing model capacity, we are able to improve the baseline model's performance without increasing the model's latency on the Waymo Open Dataset.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning fields. The validity of existing works heavily rely on either a restrictive Lower- Level Strong Convexity (LLSC) condition or on solving a series of approximation subproblems with high accuracy or both. In this work, by averaging the upper and lower level objectives, we propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for BLO that is simple yet efficient for large-scale BLO and gets rid of the limited LLSC restriction. We further provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption, which is always required by others. Thus our theory safely captures a wider variety of applications in deep learning, especially where the upper-level objective is quadratic w.r.t. the lower-level variable. Experimental results demonstrate the superiority of our method.

Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256x256 resolution (2.22 FID) and 512x512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural intrinsic connection between Hessian approximation and the linearization of the gradient. Importantly, Gradient-Normalized Smoothness does not depend on the specific problem class of the objective functions, while effectively translating local information about the gradient field and Hessian approximation into the global behavior of the method. This new concept equips approximate second-order algorithms with universal global convergence guarantees, recovering state-of-the-art rates for functions with H\"older-continuous Hessians and third derivatives, quasi-self-concordant functions, as well as smooth classes in first-order optimization. These rates are achieved automatically and extend to broader classes, such as generalized self-concordant functions. We demonstrate direct applications of our results for global linear rates in logistic regression and softmax problems with approximate Hessians, as well as in non-convex optimization using Fisher and Gauss-Newton approximations.

3D Gaussian Splatting (3DGS) enables real-time, photorealistic novel view synthesis, making it a highly attractive representation for model-based video tracking. However, leveraging the differentiability of the 3DGS renderer "in the wild" remains notoriously fragile. A fundamental bottleneck lies in the compact, local support of the Gaussian primitives. Standard photometric objectives implicitly rely on spatial overlap; if severe camera misalignment places the rendered object outside the target's local footprint, gradients strictly vanish, leaving the optimizer stranded. We introduce SpectralSplats, a robust tracking framework that resolves this "vanishing gradient" problem by shifting the optimization objective from the spatial to the frequency domain. By supervising the rendered image via a set of global complex sinusoidal features (Spectral Moments), we construct a global basin of attraction, ensuring that a valid, directional gradient toward the target exists across the entire image domain, even when pixel overlap is completely nonexistent. To harness this global basin without introducing periodic local minima associated with high frequencies, we derive a principled Frequency Annealing schedule from first principles, gracefully transitioning the optimizer from global convexity to precise spatial alignment. We demonstrate that SpectralSplats acts as a seamless, drop-in replacement for spatial losses across diverse deformation parameterizations (from MLPs to sparse control points), successfully recovering complex deformations even from severely misaligned initializations where standard appearance-based tracking catastrophically fails.

Recent studies have demonstrated that diffusion models are capable of generating high-quality samples, but their quality heavily depends on sampling guidance techniques, such as classifier guidance (CG) and classifier-free guidance (CFG). These techniques are often not applicable in unconditional generation or in various downstream tasks such as image restoration. In this paper, we propose a novel sampling guidance, called Perturbed-Attention Guidance (PAG), which improves diffusion sample quality across both unconditional and conditional settings, achieving this without requiring additional training or the integration of external modules. PAG is designed to progressively enhance the structure of samples throughout the denoising process. It involves generating intermediate samples with degraded structure by substituting selected self-attention maps in diffusion U-Net with an identity matrix, by considering the self-attention mechanisms' ability to capture structural information, and guiding the denoising process away from these degraded samples. In both ADM and Stable Diffusion, PAG surprisingly improves sample quality in conditional and even unconditional scenarios. Moreover, PAG significantly improves the baseline performance in various downstream tasks where existing guidances such as CG or CFG cannot be fully utilized, including ControlNet with empty prompts and image restoration such as inpainting and deblurring.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance via projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical of these two techniques relative to the continuous ideal gradients. Motivated by this analysis we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients. We then validate this work on several inverse image problems and property-guided molecular generation.

Camouflaged object detection segments objects with intrinsic similarity and edge disruption. Current detection methods rely on accumulated complex components. Each approach adds components such as boundary modules, attention mechanisms, and multi-scale processors independently. This accumulation creates a computational burden without proportional gains. To manage this complexity, they process at reduced resolutions, eliminating fine details essential for camouflage. We present SPEGNet, addressing fragmentation through a unified design. The architecture integrates multi-scale features via channel calibration and spatial enhancement. Boundaries emerge directly from context-rich representations, maintaining semantic-spatial alignment. Progressive refinement implements scale-adaptive edge modulation with peak influence at intermediate resolutions. This design strikes a balance between boundary precision and regional consistency. SPEGNet achieves 0.887 S_alpha on CAMO, 0.890 on COD10K, and 0.895 on NC4K, with real-time inference speed. Our approach excels across scales, from tiny, intricate objects to large, pattern-similar ones, while handling occlusion and ambiguous boundaries. Code, model weights, and results are available on https://github.com/Baber-Jan/SPEGNet{https://github.com/Baber-Jan/SPEGNet}.

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this "hypergradient" needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.

Recent approaches have yielded promising results in distilling multi-step text-to-image diffusion models into one-step ones. The state-of-the-art efficient distillation technique, i.e., SwiftBrushv2 (SBv2), even surpasses the teacher model's performance with limited resources. However, our study reveals its instability when handling different diffusion model backbones due to using a fixed guidance scale within the Variational Score Distillation (VSD) loss. Another weakness of the existing one-step diffusion models is the missing support for negative prompt guidance, which is crucial in practical image generation. This paper presents SNOOPI, a novel framework designed to address these limitations by enhancing the guidance in one-step diffusion models during both training and inference. First, we effectively enhance training stability through Proper Guidance-SwiftBrush (PG-SB), which employs a random-scale classifier-free guidance approach. By varying the guidance scale of both teacher models, we broaden their output distributions, resulting in a more robust VSD loss that enables SB to perform effectively across diverse backbones while maintaining competitive performance. Second, we propose a training-free method called Negative-Away Steer Attention (NASA), which integrates negative prompts into one-step diffusion models via cross-attention to suppress undesired elements in generated images. Our experimental results show that our proposed methods significantly improve baseline models across various metrics. Remarkably, we achieve an HPSv2 score of 31.08, setting a new state-of-the-art benchmark for one-step diffusion models.

Introduced by Hinton et al. in 2012, dropout has stood the test of time as a regularizer for preventing overfitting in neural networks. In this study, we demonstrate that dropout can also mitigate underfitting when used at the start of training. During the early phase, we find dropout reduces the directional variance of gradients across mini-batches and helps align the mini-batch gradients with the entire dataset's gradient. This helps counteract the stochasticity of SGD and limit the influence of individual batches on model training. Our findings lead us to a solution for improving performance in underfitting models - early dropout: dropout is applied only during the initial phases of training, and turned off afterwards. Models equipped with early dropout achieve lower final training loss compared to their counterparts without dropout. Additionally, we explore a symmetric technique for regularizing overfitting models - late dropout, where dropout is not used in the early iterations and is only activated later in training. Experiments on ImageNet and various vision tasks demonstrate that our methods consistently improve generalization accuracy. Our results encourage more research on understanding regularization in deep learning and our methods can be useful tools for future neural network training, especially in the era of large data. Code is available at https://github.com/facebookresearch/dropout.

Camouflaged object detection is an emerging and challenging computer vision task that requires identifying and segmenting objects that blend seamlessly into their environments due to high similarity in color, texture, and size. This task is further complicated by low-light conditions, partial occlusion, small object size, intricate background patterns, and multiple objects. While many sophisticated methods have been proposed for this task, current methods still struggle to precisely detect camouflaged objects in complex scenarios, especially with small and multiple objects, indicating room for improvement. We propose a Multi-Scale Recursive Network that extracts multi-scale features via a Pyramid Vision Transformer backbone and combines them via specialized Attention-Based Scale Integration Units, enabling selective feature merging. For more precise object detection, our decoder recursively refines features by incorporating Multi-Granularity Fusion Units. A novel recursive-feedback decoding strategy is developed to enhance global context understanding, helping the model overcome the challenges in this task. By jointly leveraging multi-scale learning and recursive feature optimization, our proposed method achieves performance gains, successfully detecting small and multiple camouflaged objects. Our model achieves state-of-the-art results on two benchmark datasets for camouflaged object detection and ranks second on the remaining two. Our codes, model weights, and results are available at https://github.com/linaagh98/MSRNet{https://github.com/linaagh98/MSRNet}.

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true one, with precision growing only with the square root of the batch size. A theoretical justification is with the help of stochastic approximation theory. However, the conditions for the validity of this theory are not satisfied in the usual learning rate schedules. Batch processing is also difficult to combine with efficient second-order optimization methods. This proposal is based on another hypothesis: the loss minimum of the training set can be expected to be well-approximated by the minima of its subsets. Such subset minima can be computed in a fraction of the time necessary for optimizing over the whole training set. This hypothesis has been tested with the help of the MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks, optionally extended by training data augmentation. The experiments have confirmed that results equivalent to conventional training can be reached. In summary, even small subsets are representative if the overdetermination ratio for the given model parameter set sufficiently exceeds unity. The computing expense can be reduced to a tenth or less.

Existing learning rate schedules that do not require specification of the optimization stopping step T are greatly out-performed by learning rate schedules that depend on T. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhibiting state-of-the-art performance compared to schedules across a wide family of problems ranging from convex problems to large-scale deep learning problems. Our Schedule-Free approach introduces no additional hyper-parameters over standard optimizers with momentum. Our method is a direct consequence of a new theory we develop that unifies scheduling and iterate averaging. An open source implementation of our method is available (https://github.com/facebookresearch/schedule_free).

Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to numerically implement the proximal step. The most challenging step, in this setup, is to evaluate functions involving density explicitly, such as entropy, in terms of samples. This paper builds on the recent works with a slight but crucial difference: we propose to utilize a variational formulation of the objective function formulated as maximization over a parametric class of functions. Theoretically, the proposed variational formulation allows the construction of gradient flows directly for empirical distributions with a well-defined and meaningful objective function. Computationally, this approach replaces the computationally expensive step in existing methods, to handle objective functions involving density, with inner loop updates that only require a small batch of samples and scale well with the dimension. The performance and scalability of the proposed method are illustrated with the aid of several numerical experiments involving high-dimensional synthetic and real datasets.

Customizing an LLM judge to a specific task or domain often involves optimizing its prompt across multiple evaluation criteria simultaneously. Textual gradient methods automate this for a single judge criterion, however they produce natural-language critiques, not numerical vectors. Thus, the conflict-resolution toolkit of multi-task learning (PCGrad, MGDA) doesn't apply to the multi-objective textual gradient setting. We test five decomposition modes of textual gradient optimizers by varying how much cross-task information the loss, gradient and optimizer LLMs share. In 6 of 10 configurations, we observe that optimization never improves over the initial prompt. Gradient specificity drops by 59% (from 9.0 to 3.7) when the gradient LLM processes multiple criteria jointly. Separately, we observe that naively combining per-task instructions into a single prompt degrades Spearman's rho by -5.3%. These results identify two separable failure modes: optimization-time gradient dilution and inference-time instruction interference, which together constrain the design space for multi-objective judge customization using textual feedback.

Pan-cancer screening in large-scale CT scans remains challenging for existing AI methods, primarily due to the difficulty of localizing diverse types of tiny lesions in large CT volumes. The extreme foreground-background imbalance significantly hinders models from focusing on diseased regions, while redundant focus on healthy regions not only decreases the efficiency but also increases false positives. Inspired by radiologists' glance and focus diagnostic strategy, we introduce GF-Screen, a Glance and Focus reinforcement learning framework for pan-cancer screening. GF-Screen employs a Glance model to localize the diseased regions and a Focus model to precisely segment the lesions, where segmentation results of the Focus model are leveraged to reward the Glance model via Reinforcement Learning (RL). Specifically, the Glance model crops a group of sub-volumes from the entire CT volume and learns to select the sub-volumes with lesions for the Focus model to segment. Given that the selecting operation is non-differentiable for segmentation training, we propose to employ the segmentation results to reward the Glance model. To optimize the Glance model, we introduce a novel group relative learning paradigm, which employs group relative comparison to prioritize high-advantage predictions and discard low-advantage predictions within sub-volume groups, not only improving efficiency but also reducing false positives. In this way, for the first time, we effectively extend cutting-edge RL techniques to tackle the specific challenges in pan-cancer screening. Extensive experiments on 16 internal and 7 external datasets across 9 lesion types demonstrated the effectiveness of GF-Screen. Notably, GF-Screen leads the public validation leaderboard of MICCAI FLARE25 pan-cancer challenge, surpassing the FLARE24 champion solution by a large margin (+25.6% DSC and +28.2% NSD).

In this paper, we introduce StreakNet-Arch, a novel signal processing architecture designed for Underwater Carrier LiDAR-Radar (UCLR) imaging systems, to address the limitations in scatter suppression and real-time imaging. StreakNet-Arch formulates the signal processing as a real-time, end-to-end binary classification task, enabling real-time image acquisition. To achieve this, we leverage Self-Attention networks and propose a novel Double Branch Cross Attention (DBC-Attention) mechanism that surpasses the performance of traditional methods. Furthermore, we present a method for embedding streak-tube camera images into attention networks, effectively acting as a learned bandpass filter. To facilitate further research, we contribute a publicly available streak-tube camera image dataset. The dataset contains 2,695,168 real-world underwater 3D point cloud data. These advancements significantly improve UCLR capabilities, enhancing its performance and applicability in underwater imaging tasks. The source code and dataset can be found at https://github.com/BestAnHongjun/StreakNet .

In this paper cum technical report, we present PHUDGE A fine tuned Phi3 model that achieved SOTA results in 4 tasks as Feedback Test, Feedback OOD, MT Human, Preference Test surpassing each and every existing model in latency and throughput. It shows very strong correlation not only with GPT4 but with Human annotators too in unseen data as well as in both absolute and relative grading tasks. We have not only addressed the usage of small LMs for cost effective production grade systems but have also shown that Causal modelling is not only slow in nature but sometimes it can hinder models learning capabilities and should be replaced by simpler tasks whenever we can to make the overall system faster and better. We show that by following systematic ML experimentation, thoughtful data augmentation and re purposing the problem itself, we can even beat 10x bigger models even with lesser training data. To the best of our knowledge, we are re the first one to experiment and showcase the usage of generalised version of Earth Movers Distance AKA Wasserstein distance by using Minkowski Distance with a penalty to control loss smoothing and can be used as a loss function instead of Cross Entropy to get stable training and better results for grading tasks.

Image labeling is a critical bottleneck in the development of computer vision technologies, often constraining machine learning performance due to the time-intensive nature of manual annotations. This work introduces a novel approach that leverages outpainting to mitigate annotated data scarcity by generating artificial contexts and annotations, significantly reducing labeling efforts. We apply this technique to a particularly acute challenge in autonomous driving, urban planning, and environmental monitoring: the lack of diverse, eye-level vehicle images from desired classes. Our dataset comprises AI-generated vehicle images obtained by detecting and cropping vehicles from manually selected seed images, which are then outpainted onto larger canvases to simulate varied real-world conditions. The outpainted images include detailed annotations, providing high-quality ground truth data. Advanced outpainting techniques and image quality assessments ensure visual fidelity and contextual relevance. Ablation results show that incorporating AIDOVECL improves overall detection performance by up to about 10%, and delivers gains of up to about 40% in settings with greater diversity of context, object scale, and placement, with underrepresented classes achieving up to about 50% higher true positives. AIDOVECL enhances vehicle detection by augmenting real training data and supporting evaluation across diverse scenarios. By demonstrating outpainting as an automatic annotation paradigm, it offers a practical and versatile solution for building fine-grained datasets with reduced labeling effort across multiple machine learning domains. The code and links to datasets are available for further research and replication at https://github.com/amir-kazemi/aidovecl.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

This paper introduces a novel one-stage end-to-end detector specifically designed to detect small lesions in medical images. Precise localization of small lesions presents challenges due to their appearance and the diverse contextual backgrounds in which they are found. To address this, our approach introduces a new type of pixel-based anchor that dynamically moves towards the targeted lesion for detection. We refer to this new architecture as GravityNet, and the novel anchors as gravity points since they appear to be "attracted" by the lesions. We conducted experiments on two well-established medical problems involving small lesions to evaluate the performance of the proposed approach: microcalcifications detection in digital mammograms and microaneurysms detection in digital fundus images. Our method demonstrates promising results in effectively detecting small lesions in these medical imaging tasks.

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

Open-world instance segmentation is a rising task, which aims to segment all objects in the image by learning from a limited number of base-category objects. This task is challenging, as the number of unseen categories could be hundreds of times larger than that of seen categories. Recently, the DETR-like models have been extensively studied in the closed world while stay unexplored in the open world. In this paper, we utilize the Transformer for open-world instance segmentation and present SWORD. Firstly, we introduce to attach the stop-gradient operation before classification head and further add IoU heads for discovering novel objects. We demonstrate that a simple stop-gradient operation not only prevents the novel objects from being suppressed as background, but also allows the network to enjoy the merit of heuristic label assignment. Secondly, we propose a novel contrastive learning framework to enlarge the representations between objects and background. Specifically, we maintain a universal object queue to obtain the object center, and dynamically select positive and negative samples from the object queries for contrastive learning. While the previous works only focus on pursuing average recall and neglect average precision, we show the prominence of SWORD by giving consideration to both criteria. Our models achieve state-of-the-art performance in various open-world cross-category and cross-dataset generalizations. Particularly, in VOC to non-VOC setup, our method sets new state-of-the-art results of 40.0% on ARb100 and 34.9% on ARm100. For COCO to UVO generalization, SWORD significantly outperforms the previous best open-world model by 5.9% on APm and 8.1% on ARm100.

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Efficient, reliable and reproducible target volume delineation is a key step in the effective planning of breast radiotherapy. However, post-operative breast target delineation is challenging as the contrast between the tumor bed volume (TBV) and normal breast tissue is relatively low in CT images. In this study, we propose to mimic the marker-guidance procedure in manual target delineation. We developed a saliency-based deep learning segmentation (SDL-Seg) algorithm for accurate TBV segmentation in post-operative breast irradiation. The SDL-Seg algorithm incorporates saliency information in the form of markers' location cues into a U-Net model. The design forces the model to encode the location-related features, which underscores regions with high saliency levels and suppresses low saliency regions. The saliency maps were generated by identifying markers on CT images. Markers' locations were then converted to probability maps using a distance-transformation coupled with a Gaussian filter. Subsequently, the CT images and the corresponding saliency maps formed a multi-channel input for the SDL-Seg network. Our in-house dataset was comprised of 145 prone CT images from 29 post-operative breast cancer patients, who received 5-fraction partial breast irradiation (PBI) regimen on GammaPod. The performance of the proposed method was compared against basic U-Net. Our model achieved mean (standard deviation) of 76.4 %, 6.76 mm, and 1.9 mm for DSC, HD95, and ASD respectively on the test set with computation time of below 11 seconds per one CT volume. SDL-Seg showed superior performance relative to basic U-Net for all the evaluation metrics while preserving low computation cost. The findings demonstrate that SDL-Seg is a promising approach for improving the efficiency and accuracy of the on-line treatment planning procedure of PBI, such as GammaPod based PBI.

Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with intuitions with regard to the behaviour of different algorithms that will allow her to put them to use. In the course of this overview, we look at different variants of gradient descent, summarize challenges, introduce the most common optimization algorithms, review architectures in a parallel and distributed setting, and investigate additional strategies for optimizing gradient descent.

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning rates affect the loss Hessian observed during training, we also analyze the effects of model initialization, architectural choices, and common training heuristics such as gradient clipping and learning rate warmup. Our results demonstrate that successful model and hyperparameter choices allow the early optimization trajectory to either avoid -- or navigate out of -- regions of high curvature and into flatter regions that tolerate a higher learning rate. Our results suggest a unifying perspective on how disparate mitigation strategies for training instability ultimately address the same underlying failure mode of neural network optimization, namely poor conditioning. Inspired by the conditioning perspective, we show that learning rate warmup can improve training stability just as much as batch normalization, layer normalization, MetaInit, GradInit, and Fixup initialization.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

Quantized neural network training optimizes a discrete, non-differentiable objective. The straight-through estimator (STE) enables backpropagation through surrogate gradients and is widely used. While previous studies have primarily focused on the properties of surrogate gradients and their convergence, the influence of quantization hyperparameters, such as bit width and quantization range, on learning dynamics remains largely unexplored. We theoretically show that in the high-dimensional limit, STE dynamics converge to a deterministic ordinary differential equation. This reveals that STE training exhibits a plateau followed by a sharp drop in generalization error, with plateau length depending on the quantization range. A fixed-point analysis quantifies the asymptotic deviation from the unquantized linear model. We also extend analytical techniques for stochastic gradient descent to nonlinear transformations of weights and inputs.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates (O-DICE) achieve SOTA performance and great robustness.

An algorithm to estimate the evolution of learning curves on the whole of a training data base, based on the results obtained from a portion and using a functional strategy, is introduced. We approximate iteratively the sought value at the desired time, independently of the learning technique used and once a point in the process, called prediction level, has been passed. The proposal proves to be formally correct with respect to our working hypotheses and includes a reliable proximity condition. This allows the user to fix a convergence threshold with respect to the accuracy finally achievable, which extends the concept of stopping criterion and seems to be effective even in the presence of distorting observations. Our aim is to evaluate the training effort, supporting decision making in order to reduce the need for both human and computational resources during the learning process. The proposal is of interest in at least three operational procedures. The first is the anticipation of accuracy gain, with the purpose of measuring how much work is needed to achieve a certain degree of performance. The second relates the comparison of efficiency between systems at training time, with the objective of completing this task only for the one that best suits our requirements. The prediction of accuracy is also a valuable item of information for customizing systems, since we can estimate in advance the impact of settings on both the performance and the development costs. Using the generation of part-of-speech taggers as an example application, the experimental results are consistent with our expectations.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

Distribution Matching Distillation (DMD) is a powerful acceleration paradigm, yet its stability is often compromised in Forbidden Zone, regions where the real teacher provides unreliable guidance while the fake teacher exerts insufficient repulsive force. In this work, we propose a unified optimization framework that reinterprets prior art as implicit strategies to avoid these corrupted regions. Based on this insight, we introduce Adaptive Matching Distillation (AMD), a self-correcting mechanism that utilizes reward proxies to explicitly detect and escape Forbidden Zones. AMD dynamically prioritizes corrective gradients via structural signal decomposition and introduces Repulsive Landscape Sharpening to enforce steep energy barriers against failure mode collapse. Extensive experiments across image and video generation tasks (e.g., SDXL, Wan2.1) and rigorous benchmarks (e.g., VBench, GenEval) demonstrate that AMD significantly enhances sample fidelity and training robustness. For instance, AMD improves the HPSv2 score on SDXL from 30.64 to 31.25, outperforming state-of-the-art baselines. These findings validate that explicitly rectifying optimization trajectories within Forbidden Zones is essential for pushing the performance ceiling of few-step generative models.

Classifier guidance -- using the gradients of an image classifier to steer the generations of a diffusion model -- has the potential to dramatically expand the creative control over image generation and editing. However, currently classifier guidance requires either training new noise-aware models to obtain accurate gradients or using a one-step denoising approximation of the final generation, which leads to misaligned gradients and sub-optimal control. We highlight this approximation's shortcomings and propose a novel guidance method: Direct Optimization of Diffusion Latents (DOODL), which enables plug-and-play guidance by optimizing diffusion latents w.r.t. the gradients of a pre-trained classifier on the true generated pixels, using an invertible diffusion process to achieve memory-efficient backpropagation. Showcasing the potential of more precise guidance, DOODL outperforms one-step classifier guidance on computational and human evaluation metrics across different forms of guidance: using CLIP guidance to improve generations of complex prompts from DrawBench, using fine-grained visual classifiers to expand the vocabulary of Stable Diffusion, enabling image-conditioned generation with a CLIP visual encoder, and improving image aesthetics using an aesthetic scoring network. Code at https://github.com/salesforce/DOODL.

DeepSeek-R1 has successfully enhanced Large Language Model (LLM) reasoning capabilities through its rule-based reward system. While it's a ''perfect'' reward system that effectively mitigates reward hacking, such reward functions are often discrete. Our experimental observations suggest that discrete rewards can lead to gradient anomaly, unstable optimization, and slow convergence. To address this issue, we propose ReDit (Reward Dithering), a method that dithers the discrete reward signal by adding simple random noise. With this perturbed reward, exploratory gradients are continuously provided throughout the learning process, enabling smoother gradient updates and accelerating convergence. The injected noise also introduces stochasticity into flat reward regions, encouraging the model to explore novel policies and escape local optima. Experiments across diverse tasks demonstrate the effectiveness and efficiency of ReDit. On average, ReDit achieves performance comparable to vanilla GRPO with only approximately 10% the training steps, and furthermore, still exhibits a 4% performance improvement over vanilla GRPO when trained for a similar duration. Visualizations confirm significant mitigation of gradient issues with ReDit. Moreover, theoretical analyses are provided to further validate these advantages.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Dynamic Tanh (DyT) removes LayerNorm by bounding activations with a learned tanh(alpha x). We show that this bounding is a regime-dependent implicit regularizer, not a uniformly beneficial replacement. Across GPT-2-family models spanning 64M to 3.78B parameters and 1M to 118M tokens, with Llama and ViT cross-checks, DyT improves validation loss by 27.3% at 64M/1M but worsens it by 18.8% at 64M/118M; the 1M benefit vanishes with capacity (+1.7% at 3.78B), while the 118M penalty reaches +27.9%. The mechanism is measurable: 49% of DyT activations saturate at 1M versus 23% at 118M, and a 500-step saturation heuristic classifies DyT's sign with 75% raw in-sample accuracy on the 12-cell GPT-2 calibration set (AUC 0.75; 64% when adding Scale 5 stress cells), correctly labels 3/3 Llama checks, but only reaches 50% raw leave-one-scale-out accuracy. Three interventions support the bounding explanation: HardTanh reproduces the regime pattern, increasing alpha at 118M monotonically reduces DyT's penalty, and vanilla+dropout(p=0.5) matches DyT's data-rich loss. We also localize Llama-DyT collapse to SwiGLU gating, where saturation separates collapse from convergence in a 3-seed component ablation (r=0.94). Scope: all experiments are compute-limited (T/P < 1.84), below Chinchilla-optimal training.

In this paper, we study a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. While restart strategies are commonly employed in first-order methods to achieve optimal convergence under strong convexity, they introduce structural complexity and practical overhead, making algorithm design and nesting cumbersome. To address this, we propose a restart-free stochastic gradient sliding algorithm that eliminates the need for explicit restart phases when the simple nonsmooth component is strongly convex. Through a novel and carefully designed parameter selection strategy, we prove that the proposed algorithm achieves an ε-solution with only O(log(1ε)) gradient evaluations for the smooth component and O(1ε) stochastic subgradient evaluations for the nonsmooth component, matching the optimal complexity of existing multi-phase (restart-based) methods. Moreover, for the case where the nonsmooth component is structured, allowing the overall problem to be reformulated as a bilinear saddle-point problem, we develop a restart-free accelerated stochastic gradient sliding algorithm. We show that the resulting method requires only O(log(1ε)) gradient computations for the smooth component while preserving an overall iteration complexity of O(1{sqrtε}) for solving the corresponding saddle-point problems. Our work thus provides simpler, restart-f

The success of the machine learning field has reliably depended on training on large datasets. While effective, this trend comes at an extraordinary cost. This is due to two deeply intertwined factors: the size of models and the size of datasets. While promising research efforts focus on reducing the size of models, the other half of the equation remains fairly mysterious. Indeed, it is surprising that the standard approach to training remains to iterate over and over, uniformly sampling the training dataset. In this paper we explore a series of alternative training paradigms that leverage insights from hard-data-mining and dropout, simple enough to implement and use that can become the new training standard. The proposed Progressive Data Dropout reduces the number of effective epochs to as little as 12.4% of the baseline. This savings actually do not come at any cost for accuracy. Surprisingly, the proposed method improves accuracy by up to 4.82%. Our approach requires no changes to model architecture or optimizer, and can be applied across standard training pipelines, thus posing an excellent opportunity for wide adoption. Code can be found here: https://github.com/bazyagami/LearningWithRevision

Automatic differentiation through digital signal processing algorithms for virtual analogue modelling has recently gained popularity. These algorithms are typically more computationally efficient than black-box neural networks that rely on dense matrix multiplications. Due to their differentiable nature, they can be integrated with neural networks and jointly trained using gradient descent algorithms, resulting in more efficient systems. Furthermore, signal processing algorithms have significantly fewer parameters than neural networks, allowing the application of the Newton-Raphson method. This method offers faster and more robust convergence than gradient descent at the cost of quadratic storage. This paper presents a method to emulate analogue levelling amplifiers using a feed-forward digital compressor with parameters optimised via the Newton-Raphson method. We demonstrate that a digital compressor can successfully approximate the behaviour of our target unit, the Teletronix LA-2A. Different strategies for computing the Hessian matrix are benchmarked. We leverage parallel algorithms for recursive filters to achieve efficient training on modern GPUs. The resulting model is made into a VST plugin and is open-sourced at https://github.com/aim-qmul/4a2a.

We present EGN, a stochastic second-order optimization algorithm that combines the generalized Gauss-Newton (GN) Hessian approximation with low-rank linear algebra to compute the descent direction. Leveraging the Duncan-Guttman matrix identity, the parameter update is obtained by factorizing a matrix which has the size of the mini-batch. This is particularly advantageous for large-scale machine learning problems where the dimension of the neural network parameter vector is several orders of magnitude larger than the batch size. Additionally, we show how improvements such as line search, adaptive regularization, and momentum can be seamlessly added to EGN to further accelerate the algorithm. Moreover, under mild assumptions, we prove that our algorithm converges to an epsilon-stationary point at a linear rate. Finally, our numerical experiments demonstrate that EGN consistently exceeds, or at most matches the generalization performance of well-tuned SGD, Adam, and SGN optimizers across various supervised and reinforcement learning tasks.

This paper comprehensively evaluates several recently proposed optimizers for 4-bit training, revealing that low-bit precision amplifies sensitivity to learning rates and often causes unstable gradient norms, leading to divergence at higher learning rates. Among these, SPAM, a recent optimizer featuring momentum reset and spike-aware gradient clipping, achieves the best performance across various bit levels, but struggles to stabilize gradient norms, requiring careful learning rate tuning. To address these limitations, we propose Stable-SPAM, which incorporates enhanced gradient normalization and clipping techniques. In particular, Stable-SPAM (1) adaptively updates the clipping threshold for spiked gradients by tracking their historical maxima; (2) normalizes the entire gradient matrix based on its historical l_2-norm statistics; and (3) inherits momentum reset from SPAM to periodically reset the first and second moments of Adam, mitigating the accumulation of spiked gradients. Extensive experiments show that Stable-SPAM effectively stabilizes gradient norms in 4-bit LLM training, delivering superior performance compared to Adam and SPAM. Notably, our 4-bit LLaMA-1B model trained with Stable-SPAM outperforms the BF16 LLaMA-1B trained with Adam by up to 2 perplexity. Furthermore, when both models are trained in 4-bit, Stable-SPAM achieves the same loss as Adam while requiring only about half the training steps. Code is available at https://github.com/TianjinYellow/StableSPAM.git.

Diffusion distillation, exemplified by Distribution Matching Distillation (DMD), has shown great promise in few-step generation but often sacrifices quality for sampling speed. While integrating Reinforcement Learning (RL) into distillation offers potential, a naive fusion of these two objectives relies on suboptimal raw sample evaluation. This sample-based scoring creates inherent conflicts with the distillation trajectory and produces unreliable rewards due to the noisy nature of early-stage generation. To overcome these limitations, we propose GDMD, a novel framework that redefines the reward mechanism by prioritizing distillation gradients over raw pixel outputs as the primary signal for optimization. By reinterpreting the DMD gradients as implicit target tensors, our framework enables existing reward models to directly evaluate the quality of distillation updates. This gradient-level guidance functions as an adaptive weighting that synchronizes the RL policy with the distillation objective, effectively neutralizing optimization divergence. Empirical results show that GDMD sets a new SOTA for few-step generation. Specifically, our 4-step models outperform the quality of their multi-step teacher and substantially exceed previous DMDR results in GenEval and human-preference metrics, exhibiting strong scalability potential.

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we present Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast O(n^2) per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein W_1, W_2 distance of discretized densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Recently, diffusion models have emerged as promising newcomers in the field of generative models, shining brightly in image generation. However, when employed for object removal tasks, they still encounter issues such as generating random artifacts and the incapacity to repaint foreground object areas with appropriate content after removal. To tackle these problems, we propose Attentive Eraser, a tuning-free method to empower pre-trained diffusion models for stable and effective object removal. Firstly, in light of the observation that the self-attention maps influence the structure and shape details of the generated images, we propose Attention Activation and Suppression (ASS), which re-engineers the self-attention mechanism within the pre-trained diffusion models based on the given mask, thereby prioritizing the background over the foreground object during the reverse generation process. Moreover, we introduce Self-Attention Redirection Guidance (SARG), which utilizes the self-attention redirected by ASS to guide the generation process, effectively removing foreground objects within the mask while simultaneously generating content that is both plausible and coherent. Experiments demonstrate the stability and effectiveness of Attentive Eraser in object removal across a variety of pre-trained diffusion models, outperforming even training-based methods. Furthermore, Attentive Eraser can be implemented in various diffusion model architectures and checkpoints, enabling excellent scalability. Code is available at https://github.com/Anonym0u3/AttentiveEraser.

As deep learning continues to advance, the transparency of neural network decision-making remains a critical challenge, limiting trust and applicability in high-stakes domains. Class Activation Mapping (CAM) techniques have emerged as a key approach toward visualizing model decisions, yet existing methods face inherent trade-offs. Gradient-based CAM variants suffer from sensitivity to gradient perturbations due to gradient noise, leading to unstable and unreliable explanations. Conversely, gradient-free approaches mitigate gradient instability but incur significant computational overhead and inference latency. To address these limitations, we propose a Cluster Filter Class Activation Map (CF-CAM) technique, a novel framework that reintroduces gradient-based weighting while enhancing robustness against gradient noise. CF-CAM utilizes hierarchical importance weighting strategy to balance discriminative feature preservation and noise elimination. A density-aware channel clustering method via Density-Based Spatial Clustering of Applications with Noise (DBSCAN) groups semantically relevant feature channels and discard noise-prone activations. Additionally, cluster-conditioned gradient filtering leverages Gaussian filters to refine gradient signals, preserving edge-aware localization while suppressing noise impact. Experiment results demonstrate that CF-CAM achieves superior interpretability performance while enhancing computational efficiency, outperforming state-of-the-art CAM methods in faithfulness and robustness. By effectively mitigating gradient instability without excessive computational cost, CF-CAM provides a competitive solution for enhancing the interpretability of deep neural networks in critical applications such as autonomous driving and medical diagnosis.

Reward guidance has been applied to great success in the test-time adaptation of continuous diffusion models; it updates each denoising step using the gradients from a downstream reward model. We study reward guidance for discrete diffusion language models, where one cannot differentiate through the natural outputs of the model because they are discrete tokens. Existing approaches either replace these discrete tokens with continuous relaxations, or employ techniques like the straight-through estimator. In this work, we show the downsides of both these methods. The former degrades gradient feedback because the reward model has never been trained with continuous inputs. The latter involves incorrect optimization because the gradient evaluated at discrete tokens is used to update continuous logits. Our key innovation is to go beyond this tradeoff by introducing a novel mechanism called EntRGi: Entropy aware Reward Guidance that dynamically regulates the gradients from the reward model. By modulating the continuous relaxation using the model's confidence, our approach substantially improves reward guidance while providing reliable inputs to the reward model. We empirically validate our approach on a 7B-parameter diffusion language model across 3 diverse reward models and 3 multi-skill benchmarks, showing consistent improvements over state-of-the-art methods.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Guidance in conditional diffusion generation is of great importance for sample quality and controllability. However, existing guidance schemes are to be desired. On one hand, mainstream methods such as classifier guidance and classifier-free guidance both require extra training with labeled data, which is time-consuming and unable to adapt to new conditions. On the other hand, training-free methods such as universal guidance, though more flexible, have yet to demonstrate comparable performance. In this work, through a comprehensive investigation into the design space, we show that it is possible to achieve significant performance improvements over existing guidance schemes by leveraging off-the-shelf classifiers in a training-free fashion, enjoying the best of both worlds. Employing calibration as a general guideline, we propose several pre-conditioning techniques to better exploit pretrained off-the-shelf classifiers for guiding diffusion generation. Extensive experiments on ImageNet validate our proposed method, showing that state-of-the-art diffusion models (DDPM, EDM, DiT) can be further improved (up to 20%) using off-the-shelf classifiers with barely any extra computational cost. With the proliferation of publicly available pretrained classifiers, our proposed approach has great potential and can be readily scaled up to text-to-image generation tasks. The code is available at https://github.com/AlexMaOLS/EluCD/tree/main.

This paper investigates the distinctions between gradient methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) designed for differentiable functions. First, we demonstrate significant differences in the convergence properties of NGDMs compared to GDs, challenging the applicability of the extensive neural network convergence literature based on L-smoothness to non-smooth neural networks. Next, we demonstrate the paradoxical nature of NGDM solutions for L_{1}-regularized problems, showing that increasing the regularization penalty leads to an increase in the L_{1} norm of optimal solutions in NGDMs. Consequently, we show that widely adopted L_{1} penalization-based techniques for network pruning do not yield expected results. Finally, we explore the Edge of Stability phenomenon, indicating its inapplicability even to Lipschitz continuous convex differentiable functions, leaving its relevance to non-convex non-differentiable neural networks inconclusive. Our analysis exposes misguided interpretations of NGDMs in widely referenced papers and texts due to an overreliance on strong smoothness assumptions, emphasizing the necessity for a nuanced understanding of foundational assumptions in the analysis of these systems.

Image generation using diffusion models have demonstrated outstanding learning capabilities, effectively capturing the full distribution of the training dataset. They are known to generate wide variations in sampled images, albeit with a trade-off in image fidelity. Guided sampling methods, such as classifier guidance (CG) and classifier-free guidance (CFG), focus sampling in well-learned high-probability regions to generate images of high fidelity, but each has its limitations. CG is computationally expensive due to the use of back-propagation for classifier gradient descent, while CFG, being gradient-free, is more efficient but compromises class label alignment compared to CG. In this work, we propose an efficient guidance method that fully utilizes a pre-trained classifier without using gradient descent. By using the classifier solely in inference mode, a time-adaptive reference class label and corresponding guidance scale are determined at each time step for guided sampling. Experiments on both class-conditioned and text-to-image generation diffusion models demonstrate that the proposed Gradient-free Classifier Guidance (GFCG) method consistently improves class prediction accuracy. We also show GFCG to be complementary to other guided sampling methods like CFG. When combined with the state-of-the-art Autoguidance (ATG), without additional computational overhead, it enhances image fidelity while preserving diversity. For ImageNet 512times512, we achieve a record FD_{DINOv2} of 23.09, while simultaneously attaining a higher classification Precision (94.3%) compared to ATG (90.2%)

We introduce Gradient Agreement Filtering (GAF) to improve on gradient averaging in distributed deep learning optimization. Traditional distributed data-parallel stochastic gradient descent involves averaging gradients of microbatches to calculate a macrobatch gradient that is then used to update model parameters. We find that gradients across microbatches are often orthogonal or negatively correlated, especially in late stages of training, which leads to memorization of the training set, reducing generalization. In this paper, we introduce a simple, computationally effective way to reduce gradient variance by computing the cosine distance between micro-gradients during training and filtering out conflicting updates prior to averaging. We improve validation accuracy with significantly smaller microbatch sizes. We also show this reduces memorizing noisy labels. We demonstrate the effectiveness of this technique on standard image classification benchmarks including CIFAR-100 and CIFAR-100N-Fine. We show this technique consistently outperforms validation accuracy, in some cases by up to 18.2\% compared to traditional training approaches while reducing the computation required nearly an order of magnitude because we can now rely on smaller microbatch sizes without destabilizing training.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

In RL, given a prompt, we sample a group of completions from a model and score them. Two questions follow: which completions should gain probability mass, and how should the parameters move to realize that change? Standard policy-gradient methods answer both at once, so the update can overshoot or undershoot depending on the learning rate, clipping, and other optimizer choices. We introduce Target Policy Optimization (TPO), which separates the two questions. Given scored completions, TPO constructs a target distribution q_i propto p_i^{,old} exp(u_i) and fits the policy to it by cross-entropy. The loss gradient on sampled-completion logits is p^θ- q, which vanishes once the policy matches the target. On tabular bandits, transformer sequence tasks, and billion-parameter LLM RLVR, TPO matches PG, PPO, GRPO, and DG on easy tasks and substantially outperforms them under sparse reward. Code is available at https://github.com/JeanKaddour/tpo.

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of training. A simple argument then suggests that gradient descent may happen mostly in this subspace. We give an example of this effect in a solvable model of classification, and we comment on possible implications for optimization and learning.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the filter and its gradients computation while supporting parallelism. C++/CUDA implementations in PyTorch achieve at least 1000x speedup over naive Python implementations and consistently run fastest on the GPU. For the low-order filters commonly used in practice, exact time-domain filtering with analytical gradients outperforms the frequency-domain method in terms of speed. The source code is available at https://github.com/yoyolicoris/philtorch.

Probing studies what information is encoded in a frozen LLM's layer representations by training a lightweight predictor on top of them. Beyond analysis, probes are often used operationally in probe-then-steer pipelines: a learned concept vector is extracted from a probe and injected via additive activation steering by adding it to a layer representation during the forward pass. The effectiveness of this pipeline hinges on estimating concept vectors that are accurate, directionally stable under ablation, and inexpensive to obtain. Motivated by these desiderata, we propose RAPTOR (Ridge-Adaptive Logistic Probe), a simple L2-regularized logistic probe whose validation-tuned ridge strength yields concept vectors from normalized weights. Across extensive experiments on instruction-tuned LLMs and human-written concept datasets, RAPTOR matches or exceeds strong baselines in accuracy while achieving competitive directional stability and substantially lower training cost; these quantitative results are supported by qualitative downstream steering demonstrations. Finally, using the Convex Gaussian Min-max Theorem (CGMT), we provide a mechanistic characterization of ridge logistic regression in an idealized Gaussian teacher-student model in the high-dimensional few-shot regime, explaining how penalty strength mediates probe accuracy and concept-vector stability and yielding structural predictions that qualitatively align with trends observed on real LLM embeddings.

Neural Radiance Fields (NeRFs) have recently emerged as a powerful paradigm for the representation of natural, complex 3D scenes. NeRFs represent continuous volumetric density and RGB values in a neural network, and generate photo-realistic images from unseen camera viewpoints through ray tracing. We propose an algorithm for navigating a robot through a 3D environment represented as a NeRF using only an on-board RGB camera for localization. We assume the NeRF for the scene has been pre-trained offline, and the robot's objective is to navigate through unoccupied space in the NeRF to reach a goal pose. We introduce a trajectory optimization algorithm that avoids collisions with high-density regions in the NeRF based on a discrete time version of differential flatness that is amenable to constraining the robot's full pose and control inputs. We also introduce an optimization based filtering method to estimate 6DoF pose and velocities for the robot in the NeRF given only an onboard RGB camera. We combine the trajectory planner with the pose filter in an online replanning loop to give a vision-based robot navigation pipeline. We present simulation results with a quadrotor robot navigating through a jungle gym environment, the inside of a church, and Stonehenge using only an RGB camera. We also demonstrate an omnidirectional ground robot navigating through the church, requiring it to reorient to fit through the narrow gap. Videos of this work can be found at https://mikh3x4.github.io/nerf-navigation/ .

We introduce Gradient Descent with Adaptive Momentum Scaling (Grams), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We establish a global convergence guarantee for Grams and validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficient optimization in large-scale machine learning.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is clearly harmful toward the beginning of the chain (high noise levels), largely unnecessary toward the end (low noise levels), and only beneficial in the middle. We thus restrict it to a specific range of noise levels, improving both the inference speed and result quality. This limited guidance interval improves the record FID in ImageNet-512 significantly, from 1.81 to 1.40. We show that it is quantitatively and qualitatively beneficial across different sampler parameters, network architectures, and datasets, including the large-scale setting of Stable Diffusion XL. We thus suggest exposing the guidance interval as a hyperparameter in all diffusion models that use guidance.

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial