Daily Papers

Pre-trained Transformers often exhibit over-confidence in source patterns and difficulty in forming new target-domain patterns during fine-tuning. We formalize the mechanism of output saturation leading to gradient suppression through standard cross-entropy and softmax analysis, showing that gradient suppression at inflection layers confines adaptation to high-level recombination of existing features while preventing low-level reconstruction. We introduce a set of layer-wise diagnostic metrics -- attention entropy (saturation proxy), activation gradient norm, parameter gradient norm, and Delta-CKA under a shared PCA basis -- to identify inflection layers characterized by both low attention entropy and steep gradient decay. Building on these findings, we propose a diagnose-first, inject-light fine-tuning strategy: selectively inserting LoRA adapters at inflection layers to restore suppressed backward signals with minimal parameter overhead. Experiments on BERT-base transfer from SST-2 to Rotten Tomatoes under under-trained and over-trained source regimes reveal that over-trained initialization benefits from inflection-layer LoRA injection, while under-trained initialization suffers performance degradation. When base features are strong, unblocking inflection layers facilitates high-level compositional adaptation; when base features are weak, full-pathway unblocking is required for low-level reconstruction, as supported by joint analysis of layer-wise activation gradients and Delta-CKA dynamics.

In large language model (LLM)-based recommendation systems, direct preference optimization (DPO) effectively aligns recommendations with user preferences, requiring multi-negative objective functions to leverage abundant implicit-feedback negatives and sharpen preference boundaries. However, our empirical analyses reveal a counterintuitive phenomenon, preference optimization collapse, where increasing the number of negative samples can lead to performance degradation despite a continuously decreasing training loss. We further theoretically demonstrate that this collapse arises from gradient suppression, caused by the dominance of easily discriminable negatives over boundary-critical negatives that truly define user preference boundaries. As a result, boundary-relevant signals are under-optimized, weakening the model's decision boundary. Motivated by these observations, we propose DynamicPO (Dynamic Preference Optimization), a lightweight and plug-and-play framework comprising two adaptive mechanisms: Dynamic Boundary Negative Selection, which identifies and prioritizes informative negatives near the model's decision boundary, and Dual-Margin Dynamic beta Adjustment, which calibrates optimization strength per sample according to boundary ambiguity. Extensive experiments on three public datasets show that DynamicPO effectively prevents optimization collapse and improves recommendation accuracy on multi-negative preference optimization methods, with negligible computational overhead. Our code and datasets are available at https://github.com/xingyuHuxingyu/DynamicPO.

End-to-end training of multi-agent systems offers significant advantages in improving multi-task performance. However, training such models remains challenging and requires extensive manual design and monitoring. In this work, we introduce TurboTrain, a novel and efficient training framework for multi-agent perception and prediction. TurboTrain comprises two key components: a multi-agent spatiotemporal pretraining scheme based on masked reconstruction learning and a balanced multi-task learning strategy based on gradient conflict suppression. By streamlining the training process, our framework eliminates the need for manually designing and tuning complex multi-stage training pipelines, substantially reducing training time and improving performance. We evaluate TurboTrain on a real-world cooperative driving dataset, V2XPnP-Seq, and demonstrate that it further improves the performance of state-of-the-art multi-agent perception and prediction models. Our results highlight that pretraining effectively captures spatiotemporal multi-agent features and significantly benefits downstream tasks. Moreover, the proposed balanced multi-task learning strategy enhances detection and prediction.

Although convolutional neural networks (CNNs) have been proposed to remove adverse weather conditions in single images using a single set of pre-trained weights, they fail to restore weather videos due to the absence of temporal information. Furthermore, existing methods for removing adverse weather conditions (e.g., rain, fog, and snow) from videos can only handle one type of adverse weather. In this work, we propose the first framework for restoring videos from all adverse weather conditions by developing a video adverse-weather-component suppression network (ViWS-Net). To achieve this, we first devise a weather-agnostic video transformer encoder with multiple transformer stages. Moreover, we design a long short-term temporal modeling mechanism for weather messenger to early fuse input adjacent video frames and learn weather-specific information. We further introduce a weather discriminator with gradient reversion, to maintain the weather-invariant common information and suppress the weather-specific information in pixel features, by adversarially predicting weather types. Finally, we develop a messenger-driven video transformer decoder to retrieve the residual weather-specific feature, which is spatiotemporally aggregated with hierarchical pixel features and refined to predict the clean target frame of input videos. Experimental results, on benchmark datasets and real-world weather videos, demonstrate that our ViWS-Net outperforms current state-of-the-art methods in terms of restoring videos degraded by any weather condition.

Distributed optimization problems usually face inexact communication issues induced by communication quantization, differential privacy protection, or channels noise. Most existing algorithms need two-timescale setting of the stepsize of gradient descent and the parameter of noise suppression to ensure the convergence to the optimal solution. In this paper, we propose two single-timescale algorithms, VRA-DGT and VRA--DSGT, for distributed deterministic and stochastic optimization problems with inexact communication respectively. VRA-DGT integrates the Variance-Reduced Aggregation (VRA) mechanism with the distributed gradient tracking framework, which achieves a convergence rate of Oleft(k^{-1}right) in the mean-square sense when the objective function is strongly convex and smooth. For distributed stochastic optimization problem,VRA-DSGT, where a hybrid variance reduction technique has been introduced in VRA-DGT, VRA-DGT,, maintains the convergence rate of Oleft(k^{-1}right) for strongly convex and smooth objective function. Simulated experiments on logistic regression problem with real-world data verify the effectiveness of the proposed algorithms.

This paper introduces a new biologically-inspired training method named Continual Learning through Adjustment Suppression and Sparsity Promotion (CLASSP). CLASSP is based on two main principles observed in neuroscience, particularly in the context of synaptic transmission and Long-Term Potentiation (LTP). The first principle is a decay rate over the weight adjustment, which is implemented as a generalization of the AdaGrad optimization algorithm. This means that weights that have received many updates should have lower learning rates as they likely encode important information about previously seen data. However, this principle results in a diffuse distribution of updates throughout the model, as it promotes updates for weights that haven't been previously updated, while a sparse update distribution is preferred to leave weights unassigned for future tasks. Therefore, the second principle introduces a threshold on the loss gradient. This promotes sparse learning by updating a weight only if the loss gradient with respect to that weight is above a certain threshold, i.e. only updating weights with a significant impact on the current loss. Both principles reflect phenomena observed in LTP, where a threshold effect and a gradual saturation of potentiation have been observed. CLASSP is implemented in a Python/PyTorch class, making it applicable to any model. When compared with Elastic Weight Consolidation (EWC) using Computer Vision and sentiment analysis datasets, CLASSP demonstrates superior performance in terms of accuracy and memory footprint.

Table structure recognition is a key task in document analysis. However, the geometric deformation in deformed tables causes a weak correlation between content information and structure, resulting in downstream tasks not being able to obtain accurate content information. To obtain fine-grained spatial coordinates of cells, we propose the OG-HFYOLO model, which enhances the edge response by Gradient Orientation-aware Extractor, combines a Heterogeneous Kernel Cross Fusion module and a scale-aware loss function to adapt to multi-scale objective features, and introduces mask-driven non-maximal suppression in the post-processing, which replaces the traditional bounding box suppression mechanism. Furthermore, we also propose a data generator, filling the gap in the dataset for fine-grained deformation table cell spatial coordinate localization, and derive a large-scale dataset named Deformation Wired Table (DWTAL). Experiments show that our proposed model demonstrates excellent segmentation accuracy on all mainstream instance segmentation models. The dataset and the source code are open source: https://github.com/justliulong/OGHFYOLO.

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient updates through the lens of signal processing and reveal that fixed momentum coefficients inherently distort the balance between bias and variance, leading to skewed or suboptimal parameter updates. To address this, we propose SGDF (SGD with Filter), an optimizer inspired by the principles of Optimal Linear Filtering. SGDF computes an online, time-varying gain to dynamically refine gradient estimation by minimizing the mean-squared error, thereby achieving an optimal trade-off between noise suppression and signal preservation. Furthermore, our approach could extend to other optimizers, showcasing its broad applicability to optimization frameworks. Extensive experiments across diverse architectures and benchmarks demonstrate SGDF surpasses conventional momentum methods and achieves performance on par with or surpassing state-of-the-art optimizers.

Contrastive learning (CL) has emerged as a powerful technique for representation learning, with or without label supervision. However, supervised CL is prone to collapsing representations of subclasses within a class by not capturing all their features, and unsupervised CL may suppress harder class-relevant features by focusing on learning easy class-irrelevant features; both significantly compromise representation quality. Yet, there is no theoretical understanding of class collapse or feature suppression at test time. We provide the first unified theoretically rigorous framework to determine which features are learnt by CL. Our analysis indicate that, perhaps surprisingly, bias of (stochastic) gradient descent towards finding simpler solutions is a key factor in collapsing subclass representations and suppressing harder class-relevant features. Moreover, we present increasing embedding dimensionality and improving the quality of data augmentations as two theoretically motivated solutions to {feature suppression}. We also provide the first theoretical explanation for why employing supervised and unsupervised CL together yields higher-quality representations, even when using commonly-used stochastic gradient methods.

Is the standard weight decay in AdamW truly optimal? Although AdamW decouples weight decay from adaptive gradient scaling, a fundamental conflict remains: the Radial Tug-of-War. In deep learning, gradients tend to increase parameter norms to expand effective capacity while steering directions to learn features, whereas weight decay indiscriminately suppresses norm growth. This push--pull interaction induces radial oscillations, injecting noise into Adam's second-moment estimates and potentially degrading delicate tangential feature learning. We argue that magnitude and direction play distinct roles and should be decoupled in optimizer dynamics. We propose Orthogonal Dynamics Decoupling and instantiate it as AdamO: an SGD-style update handles the one-dimensional norm control, while Adam's adaptive preconditioning is confined to the tangential subspace. AdamO further incorporates curvature-adaptive radial step sizing and architecture-aware rules and projections for scale-invariant layers and low-dimensional parameters. Experiments on vision and language tasks show that AdamO improves generalization and stability over AdamW without introducing additional complex constraints.

The quadratic complexity of full attention limits efficient long-context processing in large language models (LLMs). Sparse attention mitigates this cost by restricting each query to attend to a subset of previous tokens; however, training-free approaches often lead to severe performance degradation. Native sparse-attention methods (e.g., NSA, MoBA) alleviate this issue, yet exhibit a critical paradox: they produce lower attention sparsity than full-attention models, despite aiming to approximate full attention, which may constrain their effectiveness. We attribute this paradox to gradient update deficiency: low-ranked key-value pairs excluded during sparse training receive neither forward contribution nor backward gradients, and thus never learn proper suppression. To overcome this limitation, we propose SSA (Sparse Sparse Attention), a unified training framework that considers both sparse and full attention and enforces bidirectional alignment at every layer. This design preserves gradient flow to all tokens while explicitly encouraging sparse-attention outputs to align with their full-attention counterparts, thereby promoting stronger sparsity. As a result, SSA achieves state-of-the-art performance under both sparse and full attention inference across multiple commonsense benchmarks. Furthermore, SSA enables models to adapt smoothly to varying sparsity budgets; performance improves consistently as more tokens are allowed to attend, supporting flexible compute-performance trade-offs at inference time. Finally, we show that native sparse-attention training surprisingly improves long-context extrapolation by mitigating the over-allocation of attention values in sink areas, with SSA demonstrating the strongest extrapolation capability.

Unlearning has been proposed to remove copyrighted and privacy-sensitive data from Large Language Models (LLMs). Existing approaches primarily rely on fine-tuning-based methods, which can be categorized into gradient ascent-based (GA-based) and suppression-based methods. However, they often degrade model utility (the ability to respond to normal prompts). In this work, we aim to develop a general framework that enhances the utility of fine-tuning-based unlearning methods. To achieve this goal, we first investigate the common property between GA-based and suppression-based methods. We unveil that GA-based methods unlearn by distinguishing the target data (i.e., the data to be removed) and suppressing related generations, which is essentially the same strategy employed by suppression-based methods. Inspired by this finding, we introduce Gated Representation UNlearning (GRUN) which has two components: a soft gate function for distinguishing target data and a suppression module using Representation Fine-tuning (ReFT) to adjust representations rather than model parameters. Experiments show that GRUN significantly improves the unlearning and utility. Meanwhile, it is general for fine-tuning-based methods, efficient and promising for sequential unlearning.

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.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

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.

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.

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.

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.

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.

Large language models (LLMs) have revolutionized lots of fields of research. Although it is well-known that fine-tuning is essential for enhancing the capabilities of LLMs, existing research suggests that there is potential redundancy in the fine-tuning process and therefore proposes to update only a subset of parameters. However, these methods fail to leverage the task-specific information to identify important parameters during training. Based on the insight that gradients inherently contain information on task-specific data, we propose Gradient-Mask Tuning (GMT), a method that selectively updates parameters during training based on their gradient information. Specifically, we compute the absolute values of the gradients and apply masking to those with relatively smaller magnitudes. Our empirical results across various tasks demonstrate that GMT not only outperforms traditional fine-tuning methods but also elevates the upper limits of LLM performance. Further analysis indicates that GMT exhibits insensitivity to mask ratio and possesses computational efficiency comparable to vanilla SFT.

LLM unlearning has emerged as a promising approach, aiming to enable models to forget hazardous/undesired knowledge at low cost while preserving as much model utility as possible. Among existing techniques, the most straightforward method is performing Gradient Ascent (GA) w.r.t. the forget data, thereby forcing the model to unlearn the forget dataset. However, GA suffers from severe instability, as it drives updates in a divergent direction, often resulting in drastically degraded model utility. To address this issue, we propose Smoothed Gradient Ascent (SGA). SGA combines the forget data with multiple constructed normal data through a tunable smoothing rate. Intuitively, this extends GA from learning solely on the forget data to jointly learning across both forget and normal data, enabling more stable unlearning while better preserving model utility. Theoretically, we provide the theoretical guidance on the selection of the optimal smoothing rate. Empirically, we evaluate SGA on three benchmarks: TOFU, Harry Potter, and MUSE-NEWS. Experimental results demonstrate that SGA consistently outperforms the original Gradient Ascent (GA) method across all metrics and achieves top-2 performance among all baseline methods on several key metrics.

This paper presents a comprehensive study on the role of Classifier-Free Guidance (CFG) in text-conditioned diffusion models from the perspective of inference efficiency. In particular, we relax the default choice of applying CFG in all diffusion steps and instead search for efficient guidance policies. We formulate the discovery of such policies in the differentiable Neural Architecture Search framework. Our findings suggest that the denoising steps proposed by CFG become increasingly aligned with simple conditional steps, which renders the extra neural network evaluation of CFG redundant, especially in the second half of the denoising process. Building upon this insight, we propose "Adaptive Guidance" (AG), an efficient variant of CFG, that adaptively omits network evaluations when the denoising process displays convergence. Our experiments demonstrate that AG preserves CFG's image quality while reducing computation by 25%. Thus, AG constitutes a plug-and-play alternative to Guidance Distillation, achieving 50% of the speed-ups of the latter while being training-free and retaining the capacity to handle negative prompts. Finally, we uncover further redundancies of CFG in the first half of the diffusion process, showing that entire neural function evaluations can be replaced by simple affine transformations of past score estimates. This method, termed LinearAG, offers even cheaper inference at the cost of deviating from the baseline model. Our findings provide insights into the efficiency of the conditional denoising process that contribute to more practical and swift deployment of text-conditioned diffusion models.

Label Smoothing (LS) is widely adopted to curb overconfidence in neural network predictions and enhance generalization. However, previous research shows that LS can force feature representations into excessively tight clusters, eroding intra-class distinctions. More recent findings suggest that LS also induces overconfidence in misclassifications, yet the precise mechanism remained unclear. In this work, we decompose the loss term introduced by LS, revealing two key components: (i) a regularization term that functions only when the prediction is correct, and (ii) an error-enhancement term that emerges under misclassifications. This latter term compels the model to reinforce incorrect predictions with exaggerated certainty, further collapsing the feature space. To address these issues, we propose Max Suppression (MaxSup), which uniformly applies the intended regularization to both correct and incorrect predictions by penalizing the top-1 logit instead of the ground-truth logit. Through feature analyses, we show that MaxSup restores intra-class variation and sharpens inter-class boundaries. Extensive experiments on image classification and downstream tasks confirm that MaxSup is a more robust alternative to LS. Code is available at: https://github.com/ZhouYuxuanYX/Maximum-Suppression-Regularization.

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.

Backpropagation provides a generalized configuration for overcoming catastrophic forgetting. Like, SGD and Adam are commonly used for weight updates in continual learning and continual pre-training. In practice, permission to access gradient information is not always granted (the gradient ban), such as black-box APIs, hardware limitations, and non-differentiable systems. To bridge this gap, we introduce the first benchmark ZeroFlow to evaluate gradient-free optimization algorithms for overcoming forgetting. This benchmark examines a suite of forward pass methods across multiple methods, forgetting scenarios, and datasets. We find that forward passes alone are enough to overcome forgetting. Our findings reveal new optimization principles that highlight the potential of forward-pass in mitigating forgetting, managing task conflicts, and reducing memory demands, alongside novel enhancements that further mitigate forgetting with just one forward pass. This work provides essential insights and tools for advancing forward pass methods to overcome forgetting.

We consider the training of the first layer of vision models and notice the clear relationship between pixel values and gradient update magnitudes: the gradients arriving at the weights of a first layer are by definition directly proportional to (normalized) input pixel values. Thus, an image with low contrast has a smaller impact on learning than an image with higher contrast, and a very bright or very dark image has a stronger impact on the weights than an image with moderate brightness. In this work, we propose performing gradient descent on the embeddings produced by the first layer of the model. However, switching to discrete inputs with an embedding layer is not a reasonable option for vision models. Thus, we propose the conceptual procedure of (i) a gradient descent step on first layer activations to construct an activation proposal, and (ii) finding the optimal weights of the first layer, i.e., those weights which minimize the squared distance to the activation proposal. We provide a closed form solution of the procedure and adjust it for robust stochastic training while computing everything efficiently. Empirically, we find that TrAct (Training Activations) speeds up training by factors between 1.25x and 4x while requiring only a small computational overhead. We demonstrate the utility of TrAct with different optimizers for a range of different vision models including convolutional and transformer architectures.

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.

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.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

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 introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

As large language models (LLMs) are increasingly deployed across various applications, privacy and copyright concerns have heightened the need for more effective LLM unlearning techniques. Many existing unlearning methods aim to suppress undesirable outputs through additional training (e.g., gradient ascent), which reduces the probability of generating such outputs. While such suppression-based approaches can control model outputs, they may not eliminate the underlying knowledge embedded in the model's internal activations; muting a response is not the same as forgetting it. Moreover, such suppression-based methods often suffer from model collapse. To address these issues, we propose a novel unlearning method that directly intervenes in the model's internal activations. In our formulation, forgetting is defined as a state in which the activation of a forgotten target is indistinguishable from that of ``unknown'' entities. Our method introduces an unlearning objective that modifies the activation of the target entity away from those of known entities and toward those of unknown entities in a sparse autoencoder latent space. By aligning the target's internal activation with those of unknown entities, we shift the model's recognition of the target entity from ``known'' to ``unknown'', achieving genuine forgetting while avoiding over-suppression and model collapse. Empirically, we show that our method effectively aligns the internal activations of the forgotten target, a result that the suppression-based approaches do not reliably achieve. Additionally, our method effectively reduces the model's recall of target knowledge in question-answering tasks without significant damage to the non-target knowledge.

Sparse training is emerging as a promising avenue for reducing the computational cost of training neural networks. Several recent studies have proposed pruning methods using learnable thresholds to efficiently explore the non-uniform distribution of sparsity inherent within the models. In this paper, we propose Gradient Annealing (GA), where gradients of masked weights are scaled down in a non-linear manner. GA provides an elegant trade-off between sparsity and accuracy without the need for additional sparsity-inducing regularization. We integrated GA with the latest learnable pruning methods to create an automated sparse training algorithm called AutoSparse, which achieves better accuracy and/or training/inference FLOPS reduction than existing learnable pruning methods for sparse ResNet50 and MobileNetV1 on ImageNet-1K: AutoSparse achieves (2x, 7x) reduction in (training,inference) FLOPS for ResNet50 on ImageNet at 80% sparsity. Finally, AutoSparse outperforms sparse-to-sparse SotA method MEST (uniform sparsity) for 80% sparse ResNet50 with similar accuracy, where MEST uses 12% more training FLOPS and 50% more inference FLOPS.

Group-based policy optimization methods like GRPO and GSPO have become standard for training multimodal models, leveraging group-wise rollouts and relative advantage estimation. However, they suffer from a critical gradient vanishing problem when all responses within a group receive identical rewards, causing advantage estimates to collapse and training signals to diminish. Existing attempts to mitigate this issue fall into two paradigms: filtering-based and sampling-based methods. Filtering-based methods first generate rollouts broadly and then retroactively filter out uninformative groups, leading to substantial computational overhead. Sampling-based methods proactively select effective samples before rollout but rely on static criteria or prior dataset knowledge, lacking real-time adaptability. To address these issues, we propose VADE, a Variance-Aware Dynamic sampling framework via online sample-level difficulty Estimation. Our framework integrates three key components: online sample-level difficulty estimation using Beta distributions, a Thompson sampler that maximizes information gain through the estimated correctness probability, and a two-scale prior decay mechanism that maintains robust estimation under policy evolution. This three components design enables VADE to dynamically select the most informative samples, thereby amplifying training signals while eliminating extra rollout costs. Extensive experiments on multimodal reasoning benchmarks show that VADE consistently outperforms strong baselines in both performance and sample efficiency, while achieving a dramatic reduction in computational overhead. More importantly, our framework can serves as a plug-and-play component to be seamlessly integrated into existing group-based RL algorithms. Code and models are available at https://VADE-RL.github.io.

In multi-task learning (MTL), gradient conflict poses a significant challenge. Effective methods for addressing this problem, including PCGrad, CAGrad, and GradNorm, in their original implementations are computationally demanding, which significantly limits their application in modern large models and transformers. We propose Gradient Conductor (GCond), a method that builds upon PCGrad principles by combining them with gradient accumulation and an adaptive arbitration mechanism. We evaluated GCond on self-supervised learning tasks using MobileNetV3-Small and ConvNeXt architectures on the ImageNet 1K dataset and a combined head and neck CT scan dataset, comparing the proposed method against baseline linear combinations and state-of-the-art gradient conflict resolution methods. The stochastic mode of GCond achieved a two-fold computational speedup while maintaining optimization quality, and demonstrated superior performance across all evaluated metrics, achieving lower L1 and SSIM losses compared to other methods on both datasets. GCond exhibited high scalability, being successfully applied to both compact models (MobileNetV3-Small) and large architectures (ConvNeXt-tiny and ConvNeXt-Base). It also showed compatibility with modern optimizers such as AdamW and Lion/LARS. Therefore, GCond offers a scalable and efficient solution to the problem of gradient conflicts in multi-task learning.

Beyond minimizing a single training loss, many deep learning estimation pipelines rely on an auxiliary objective to quantify and encourage desirable properties of the model (e.g. performance on another dataset, robustness, agreement with a prior). Although the simplest approach to incorporating an auxiliary loss is to sum it with the training loss as a regularizer, recent works have shown that one can improve performance by blending the gradients beyond a simple sum; this is known as gradient surgery. We cast the problem as a constrained minimization problem where the auxiliary objective is minimized among the set of minimizers of the training loss. To solve this bilevel problem, we follow a parameter update direction that combines the training loss gradient and the orthogonal projection of the auxiliary gradient to the training gradient. In a setting where gradients come from mini-batches, we explain how, using a moving average of the training loss gradients, we can carefully maintain this critical orthogonality property. We demonstrate that our method, Bloop, can lead to much better performances on NLP and vision experiments than other gradient surgery methods without EMA.

Machine unlearning in foundation models (e.g., language and vision transformers) is essential for privacy and safety; however, existing approaches are unstable and unreliable. A widely used strategy, the gradient difference method, applies gradient descent to retained data while performing gradient ascent on forgotten data. When combined with cross-entropy, this procedure can trigger the unbounded growth of weights and gradients, degrading both forgetting and retention. We provide a theoretical framework that explains this failure by showing how ascent destabilizes optimization in transformer feedforward MLP layers. Guided by this insight, we propose *Bounded Parameter-Efficient Unlearning*, which stabilizes LoRA-based fine-tuning by applying bounded functions to MLP adapters. This controls the weight dynamics during ascent and enables reliable convergence. We validate the approach on Vision Transformer class deletion on CIFAR-100, where GD+Sine is the only evaluated method to achieve both high forget quality and model utility across ViT-B/16, ViT-L/14, and DeiT-S architectures, and demonstrate generality on language-model benchmarks (TOFU, TDEC, MUSE) across architectures from 22M to 8B parameters, achieving improved forgetting while preserving utility.

Aligning diffusion models to downstream tasks often requires finetuning new models or gradient-based guidance at inference time to enable sampling from the reward-tilted posterior. In this work, we explore a simple inference-time gradient-free guidance approach, called controlled denoising (CoDe), that circumvents the need for differentiable guidance functions and model finetuning. CoDe is a blockwise sampling method applied during intermediate denoising steps, allowing for alignment with downstream rewards. Our experiments demonstrate that, despite its simplicity, CoDe offers a favorable trade-off between reward alignment, prompt instruction following, and inference cost, achieving a competitive performance against the state-of-the-art baselines. Our code is available at: https://github.com/anujinho/code.

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.

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.

Classifier-free guidance (CFG) is crucial for improving both generation quality and alignment between the input condition and final output in diffusion models. While a high guidance scale is generally required to enhance these aspects, it also causes oversaturation and unrealistic artifacts. In this paper, we revisit the CFG update rule and introduce modifications to address this issue. We first decompose the update term in CFG into parallel and orthogonal components with respect to the conditional model prediction and observe that the parallel component primarily causes oversaturation, while the orthogonal component enhances image quality. Accordingly, we propose down-weighting the parallel component to achieve high-quality generations without oversaturation. Additionally, we draw a connection between CFG and gradient ascent and introduce a new rescaling and momentum method for the CFG update rule based on this insight. Our approach, termed adaptive projected guidance (APG), retains the quality-boosting advantages of CFG while enabling the use of higher guidance scales without oversaturation. APG is easy to implement and introduces practically no additional computational overhead to the sampling process. Through extensive experiments, we demonstrate that APG is compatible with various conditional diffusion models and samplers, leading to improved FID, recall, and saturation scores while maintaining precision comparable to CFG, making our method a superior plug-and-play alternative to standard classifier-free guidance.

Large Language Models increasingly possess capabilities that carry dual-use risks. While data filtering has emerged as a pretraining-time mitigation, it faces significant challenges: labeling whether data is harmful is expensive at scale, and given improving sample efficiency with larger models, even small amounts of mislabeled content could give rise to dangerous capabilities. To address risks associated with mislabeled harmful content, prior work proposed Gradient Routing (Cloud et al., 2024) -- a technique that localizes target knowledge into a dedicated subset of model parameters so they can later be removed. We explore an improved variant of Gradient Routing, which we call Selective GradienT Masking (SGTM), with particular focus on evaluating its robustness to label noise. SGTM zero-masks selected gradients such that target domain examples only update their dedicated parameters. We test SGTM's effectiveness in two applications: removing knowledge of one language from a model trained on a bilingual synthetic dataset, and removing biology knowledge from a model trained on English Wikipedia. In both cases SGTM provides better retain/forget trade-off in the presence of labeling errors compared to both data filtering and a previously proposed instantiation of Gradient Routing. Unlike shallow unlearning approaches that can be quickly undone through fine-tuning, SGTM exhibits strong robustness to adversarial fine-tuning, requiring seven times more fine-tuning steps to reach baseline performance on the forget set compared to a finetuning-based unlearning method (RMU). Our results suggest SGTM provides a promising pretraining-time complement to existing safety mitigations, particularly in settings where label noise is unavoidable.

In this article, we introduce a novel normalization technique for neural network weight matrices, which we term weight conditioning. This approach aims to narrow the gap between the smallest and largest singular values of the weight matrices, resulting in better-conditioned matrices. The inspiration for this technique partially derives from numerical linear algebra, where well-conditioned matrices are known to facilitate stronger convergence results for iterative solvers. We provide a theoretical foundation demonstrating that our normalization technique smoothens the loss landscape, thereby enhancing convergence of stochastic gradient descent algorithms. Empirically, we validate our normalization across various neural network architectures, including Convolutional Neural Networks (CNNs), Vision Transformers (ViT), Neural Radiance Fields (NeRF), and 3D shape modeling. Our findings indicate that our normalization method is not only competitive but also outperforms existing weight normalization techniques from the literature.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

The canonical deep learning approach for learning requires computing a gradient term at each layer by back-propagating the error signal from the output towards each learnable parameter. Given the stacked structure of neural networks, where each layer builds on the representation of the layer below, this approach leads to hierarchical representations. More abstract features live on the top layers of the model, while features on lower layers are expected to be less abstract. In contrast to this, we introduce a new learning method named NoProp, which does not rely on either forward or backwards propagation. Instead, NoProp takes inspiration from diffusion and flow matching methods, where each layer independently learns to denoise a noisy target. We believe this work takes a first step towards introducing a new family of gradient-free learning methods, that does not learn hierarchical representations -- at least not in the usual sense. NoProp needs to fix the representation at each layer beforehand to a noised version of the target, learning a local denoising process that can then be exploited at inference. We demonstrate the effectiveness of our method on MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks. Our results show that NoProp is a viable learning algorithm which achieves superior accuracy, is easier to use and computationally more efficient compared to other existing back-propagation-free methods. By departing from the traditional gradient based learning paradigm, NoProp alters how credit assignment is done within the network, enabling more efficient distributed learning as well as potentially impacting other characteristics of the learning process.

We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A particular challenge has been to design universal initialization strategies which provably lead to implicit regularization in gradient-descent methods. At the same time, it has been argued by Cohen et. al. 2016 that more general classes of neural networks can be captured by considering tensor factorizations. However, in the tensor case, implicit regularization has only been rigorously established for gradient flow or in the lazy training regime. In this paper, we prove the first tensor result of its kind for gradient descent rather than gradient flow. We focus on the tubal tensor product and the associated notion of low tubal rank, encouraged by the relevance of this model for image data. We establish that gradient descent in an overparametrized tensor factorization model with a small random initialization exhibits an implicit bias towards solutions of low tubal rank. Our theoretical findings are illustrated in an extensive set of numerical simulations show-casing the dynamics predicted by our theory as well as the crucial role of using a small random initialization.

Estimating the test performance of a model, possibly under distribution shift, without having access to the ground-truth labels is a challenging, yet very important problem for the safe deployment of machine learning algorithms in the wild. Existing works mostly rely on information from either the outputs or the extracted features of neural networks to estimate a score that correlates with the ground-truth test accuracy. In this paper, we investigate -- both empirically and theoretically -- how the information provided by the gradients can be predictive of the ground-truth test accuracy even under distribution shifts. More specifically, we use the norm of classification-layer gradients, backpropagated from the cross-entropy loss after only one gradient step over test data. Our intuition is that these gradients should be of higher magnitude when the model generalizes poorly. We provide the theoretical insights behind our approach and the key ingredients that ensure its empirical success. Extensive experiments conducted with various architectures on diverse distribution shifts demonstrate that our method significantly outperforms current state-of-the-art approaches. The code is available at https://github.com/Renchunzi-Xie/GdScore

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.

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an equivalent number of gradient descent updates and show explicitly that stochastic gradient descent acts to regularize generalization error by decorrelating nearby updates. These calculations depends on the details of the model only through the mean and covariance of the gradient distribution, which may be readily measured for particular models of interest. We discuss further improvements to these calculations and comment on possible implications for stochastic optimization.

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.

Effective regularization techniques are highly desired in deep learning for alleviating overfitting and improving generalization. This work proposes a new regularization scheme, based on the understanding that the flat local minima of the empirical risk cause the model to generalize better. This scheme is referred to as adversarial model perturbation (AMP), where instead of directly minimizing the empirical risk, an alternative "AMP loss" is minimized via SGD. Specifically, the AMP loss is obtained from the empirical risk by applying the "worst" norm-bounded perturbation on each point in the parameter space. Comparing with most existing regularization schemes, AMP has strong theoretical justifications, in that minimizing the AMP loss can be shown theoretically to favour flat local minima of the empirical risk. Extensive experiments on various modern deep architectures establish AMP as a new state of the art among regularization schemes. Our code is available at https://github.com/hiyouga/AMP-Regularizer.

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.

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.

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.

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.

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

In natural language processing tasks, pure reinforcement learning (RL) fine-tuning methods often suffer from inefficient exploration and slow convergence; while supervised fine-tuning (SFT) methods, although efficient in training, have limited performance ceiling and less solid theoretical foundation compared to RL. To address efficiency-capability trade-off, we propose the Guess-Think-Answer (GTA) framework that combines the efficiency of SFT with the capability gains of RL in a unified training paradigm. GTA works by having the model first produce a provisional guess (optimized via cross-entropy loss), then reflect on this guess before generating the final answer, with RL rewards shaping both the final output and the format of the entire GTA structure. This hybrid approach achieves both faster convergence than pure RL and higher performance ceiling than pure SFT. To mitigate gradient conflicts between the two training signals, we employ loss masking and gradient constraints. Empirical results on four text classification benchmarks demonstrate that GTA substantially accelerates convergence while outperforming both standalone SFT and RL baselines.

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.

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.

The blooming of social media and face recognition (FR) systems has increased people's concern about privacy and security. A new type of adversarial privacy cloak (class-universal) can be applied to all the images of regular users, to prevent malicious FR systems from acquiring their identity information. In this work, we discover the optimization dilemma in the existing methods -- the local optima problem in large-batch optimization and the gradient information elimination problem in small-batch optimization. To solve these problems, we propose Gradient Accumulation (GA) to aggregate multiple small-batch gradients into a one-step iterative gradient to enhance the gradient stability and reduce the usage of quantization operations. Experiments show that our proposed method achieves high performance on the Privacy-Commons dataset against black-box face recognition models.

Unsupervised learning with generative adversarial networks (GANs) has proven hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss function for the discriminator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson χ^2 divergence. There are two benefits of LSGANs over regular GANs. First, LSGANs are able to generate higher quality images than regular GANs. Second, LSGANs perform more stable during the learning process. We evaluate LSGANs on five scene datasets and the experimental results show that the images generated by LSGANs are of better quality than the ones generated by regular GANs. We also conduct two comparison experiments between LSGANs and regular GANs to illustrate the stability of LSGANs.

Modern generative adversarial networks (GANs) predominantly use piecewise linear activation functions in discriminators (or critics), including ReLU and LeakyReLU. Such models learn piecewise linear mappings, where each piece handles a subset of the input space, and the gradients per subset are piecewise constant. Under such a class of discriminator (or critic) functions, we present Gradient Normalization (GraN), a novel input-dependent normalization method, which guarantees a piecewise K-Lipschitz constraint in the input space. In contrast to spectral normalization, GraN does not constrain processing at the individual network layers, and, unlike gradient penalties, strictly enforces a piecewise Lipschitz constraint almost everywhere. Empirically, we demonstrate improved image generation performance across multiple datasets (incl. CIFAR-10/100, STL-10, LSUN bedrooms, and CelebA), GAN loss functions, and metrics. Further, we analyze altering the often untuned Lipschitz constant K in several standard GANs, not only attaining significant performance gains, but also finding connections between K and training dynamics, particularly in low-gradient loss plateaus, with the common Adam optimizer.

Large language model (LLM) unlearning has demonstrated its essential role in removing privacy and copyright-related responses, crucial for their legal and safe applications. However, the pursuit of complete unlearning often comes with substantial costs due to its compromises in their general functionality, leading to a notorious trade-off between unlearning and retention. It motivates this paper to explore enhanced unlearning schemes that can mitigate this trade-off. Specifically, we propose Gradient Rectified Unlearning (GRU), an improved framework that regulates the directions of gradient updates during the unlearning procedure such that their side impacts on other, unrelated responses can be minimized. GRU is easy and general to implement, demonstrating practical effectiveness across a variety of well-established unlearning benchmarks.

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for the ability of these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, and neural network theory, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new algorithm, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep neural network training, and provide preliminary numerical evidence for its superior performance.

The ability to remove features from the input of machine learning models is very important to understand and interpret model predictions. However, this is non-trivial for vision models since masking out parts of the input image typically causes large distribution shifts. This is because the baseline color used for masking (typically grey or black) is out of distribution. Furthermore, the shape of the mask itself can contain unwanted signals which can be used by the model for its predictions. Recently, there has been some progress in mitigating this issue (called missingness bias) in image masking for vision transformers. In this work, we propose a new masking method for CNNs we call layer masking in which the missingness bias caused by masking is reduced to a large extent. Intuitively, layer masking applies a mask to intermediate activation maps so that the model only processes the unmasked input. We show that our method (i) is able to eliminate or minimize the influence of the mask shape or color on the output of the model, and (ii) is much better than replacing the masked region by black or grey for input perturbation based interpretability techniques like LIME. Thus, layer masking is much less affected by missingness bias than other masking strategies. We also demonstrate how the shape of the mask may leak information about the class, thus affecting estimates of model reliance on class-relevant features derived from input masking. Furthermore, we discuss the role of data augmentation techniques for tackling this problem, and argue that they are not sufficient for preventing model reliance on mask shape. The code for this project is publicly available at https://github.com/SriramB-98/layer_masking

We introduce a new tool for interpreting neural net responses, namely full-gradients, which decomposes the neural net response into input sensitivity and per-neuron sensitivity components. This is the first proposed representation which satisfies two key properties: completeness and weak dependence, which provably cannot be satisfied by any saliency map-based interpretability method. For convolutional nets, we also propose an approximate saliency map representation, called FullGrad, obtained by aggregating the full-gradient components. We experimentally evaluate the usefulness of FullGrad in explaining model behaviour with two quantitative tests: pixel perturbation and remove-and-retrain. Our experiments reveal that our method explains model behaviour correctly, and more comprehensively than other methods in the literature. Visual inspection also reveals that our saliency maps are sharper and more tightly confined to object regions than other methods.

Training large language models (LLMs) relies almost exclusively on dense adaptive optimizers with increasingly sophisticated preconditioners. We challenge this by showing that randomly masking parameter updates can be highly effective, with a masked variant of RMSProp consistently outperforming recent state-of-the-art optimizers. Our analysis reveals that the random masking induces a curvature-dependent geometric regularization that smooths the optimization trajectory. Motivated by this finding, we introduce Momentum-aligned gradient masking (Magma), which modulates the masked updates using momentum-gradient alignment. Extensive LLM pre-training experiments show that Magma is a simple drop-in replacement for adaptive optimizers with consistent gains and negligible computational overhead. Notably, for the 1B model size, Magma reduces perplexity by over 19\% and 9\% compared to Adam and Muon, respectively.

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.

Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. This paper suggests that, sometimes, increasing depth can speed up optimization. The effect of depth on optimization is decoupled from expressiveness by focusing on settings where additional layers amount to overparameterization - linear neural networks, a well-studied model. Theoretical analysis, as well as experiments, show that here depth acts as a preconditioner which may accelerate convergence. Even on simple convex problems such as linear regression with ell_p loss, p>2, gradient descent can benefit from transitioning to a non-convex overparameterized objective, more than it would from some common acceleration schemes. We also prove that it is mathematically impossible to obtain the acceleration effect of overparametrization via gradients of any regularizer.

Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and help steer these systems away from harmful behaviors. To that end, we suggest utilizing the circuit perspective brought forward by mechanistic interpretability. After laying out our intuition, we illustrate how it enables us to design a curriculum for efficient learning in a controlled setting. The code is available at https://github.com/facebookresearch/pal.

Advancing towards generalist agents necessitates the concurrent processing of multiple tasks using a unified model, thereby underscoring the growing significance of simultaneous model training on multiple downstream tasks. A common issue in multi-task learning is the occurrence of gradient conflict, which leads to potential competition among different tasks during joint training. This competition often results in improvements in one task at the expense of deterioration in another. Although several optimization methods have been developed to address this issue by manipulating task gradients for better task balancing, they cannot decrease the incidence of gradient conflict. In this paper, we systematically investigate the occurrence of gradient conflict across different methods and propose a strategy to reduce such conflicts through sparse training (ST), wherein only a portion of the model's parameters are updated during training while keeping the rest unchanged. Our extensive experiments demonstrate that ST effectively mitigates conflicting gradients and leads to superior performance. Furthermore, ST can be easily integrated with gradient manipulation techniques, thus enhancing their effectiveness.

Contrastive learning has been applied successfully to learn vector representations of text. Previous research demonstrated that learning high-quality representations benefits from batch-wise contrastive loss with a large number of negatives. In practice, the technique of in-batch negative is used, where for each example in a batch, other batch examples' positives will be taken as its negatives, avoiding encoding extra negatives. This, however, still conditions each example's loss on all batch examples and requires fitting the entire large batch into GPU memory. This paper introduces a gradient caching technique that decouples backpropagation between contrastive loss and the encoder, removing encoder backward pass data dependency along the batch dimension. As a result, gradients can be computed for one subset of the batch at a time, leading to almost constant memory usage.

Machine learning models often incorporate vast amounts of data, raising significant privacy concerns. Machine unlearning, the ability to remove the influence of specific data points from a trained model, addresses these concerns. This paper explores practical methods for implementing machine unlearning, focusing on a first-epoch gradient-ascent approach. Key findings include: 1. Single vs. Multi-Epoch Unlearning: First-epoch gradient unlearning is more effective than multi-epoch gradients. 2. Layer-Based Unlearning: The embedding layer in GPT-2 is crucial for effective unlearning. Gradients from the output layers (11 and 12) have no impact. Efficient unlearning can be achieved using only the embedding layer, halving space complexity. 3. Influence Functions & Scoring: Techniques like Hessian Vector Product and the dot product of activations and tensors are used for quantifying unlearning. 4. Gradient Ascent Considerations: Calibration is necessary to avoid overexposing the model to specific data points during unlearning, which could prematurely terminate the process. 5. Fuzzy Matching vs. Iterative Unlearning: Fuzzy matching techniques shift the model to a new optimum, while iterative unlearning provides a more complete modality. Our empirical evaluation confirms that first-epoch gradient ascent for machine unlearning is more effective than whole-model gradient ascent. These results highlight the potential of machine unlearning for enhancing data privacy and compliance with regulations such as GDPR and CCPA. The study underscores the importance of formal methods to comprehensively evaluate the unlearning process.

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions corresponding to noise, the kernel's near-zero eigenvalues trap residual error in a test-invisible reservoir. Within the signal channel, minibatch SGD ensures that coherent population signal accumulates via fast linear drift, while idiosyncratic memorization is suppressed into a slow, diffusive random walk. We prove generalization survives even when the kernel evolves O(1) in operator norm, the full feature-learning regime. This theory naturally explains disparate phenomena in deep learning theory, such as benign overfitting, double descent, implicit bias, and grokking. Lastly, we derive an exact population-risk objective from a single training run with no validation data, for any architecture, loss, or optimizer, and prove that it measures precisely the noise in the signal channel. This objective reduces in practice to an SNR preconditioner on top of Adam, adding one state vector at no extra cost; it accelerates grokking by 5 times, suppresses memorization in PINNs and implicit neural representations, and improves DPO fine-tuning under noisy preferences while staying 3 times closer to the reference policy.

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalance such as oversampling.

When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of Transformer-based models that have achieved notable state-of-the-art results on various image tasks. However, deep learning-based methods often suffer from a lack of generalization ability. For example, deep models trained on Gaussian noise may perform poorly when tested on other noise distributions. To address this issue, we present a novel approach to enhance the generalization performance of denoising networks, known as masked training. Our method involves masking random pixels of the input image and reconstructing the missing information during training. We also mask out the features in the self-attention layers to avoid the impact of training-testing inconsistency. Our approach exhibits better generalization ability than other deep learning models and is directly applicable to real-world scenarios. Additionally, our interpretability analysis demonstrates the superiority of our method.

We present a submission to the SemEval 2025 shared task on unlearning sensitive content from LLMs. Our approach employs negative preference optimization using low-rank adaptation. We show that we can utilize this combination to efficiently compute additional regularization terms, which help with unlearning stabilization. The results of our approach significantly exceed the shared task baselines.

Diffusion models have shown remarkable performance in image synthesis, but they demand extensive computational and memory resources for training, fine-tuning and inference. Although advanced quantization techniques have successfully minimized memory usage for inference, training and fine-tuning these quantized models still require large memory possibly due to dequantization for accurate computation of gradients and/or backpropagation for gradient-based algorithms. However, memory-efficient fine-tuning is particularly desirable for applications such as personalization that often must be run on edge devices like mobile phones with private data. In this work, we address this challenge by quantizing a diffusion model with personalization via Textual Inversion and by leveraging a zeroth-order optimization on personalization tokens without dequantization so that it does not require gradient and activation storage for backpropagation that consumes considerable memory. Since a gradient estimation using zeroth-order optimization is quite noisy for a single or a few images in personalization, we propose to denoise the estimated gradient by projecting it onto a subspace that is constructed with the past history of the tokens, dubbed Subspace Gradient. In addition, we investigated the influence of text embedding in image generation, leading to our proposed time steps sampling, dubbed Partial Uniform Timestep Sampling for sampling with effective diffusion timesteps. Our method achieves comparable performance to prior methods in image and text alignment scores for personalizing Stable Diffusion with only forward passes while reducing training memory demand up to 8.2times.

Batch Normalization is a commonly used trick to improve the training of deep neural networks. These neural networks use L2 regularization, also called weight decay, ostensibly to prevent overfitting. However, we show that L2 regularization has no regularizing effect when combined with normalization. Instead, regularization has an influence on the scale of weights, and thereby on the effective learning rate. We investigate this dependence, both in theory, and experimentally. We show that popular optimization methods such as ADAM only partially eliminate the influence of normalization on the learning rate. This leads to a discussion on other ways to mitigate this issue.

Learning a policy with great generalization to unseen environments remains challenging but critical in visual reinforcement learning. Despite the success of augmentation combination in the supervised learning generalization, naively applying it to visual RL algorithms may damage the training efficiency, suffering from serve performance degradation. In this paper, we first conduct qualitative analysis and illuminate the main causes: (i) high-variance gradient magnitudes and (ii) gradient conflicts existed in various augmentation methods. To alleviate these issues, we propose a general policy gradient optimization framework, named Conflict-aware Gradient Agreement Augmentation (CG2A), and better integrate augmentation combination into visual RL algorithms to address the generalization bias. In particular, CG2A develops a Gradient Agreement Solver to adaptively balance the varying gradient magnitudes, and introduces a Soft Gradient Surgery strategy to alleviate the gradient conflicts. Extensive experiments demonstrate that CG2A significantly improves the generalization performance and sample efficiency of visual RL algorithms.

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared with SGD or even fail to converge due to unstable and extreme learning rates. Recent work has put forward some algorithms such as AMSGrad to tackle this issue but they failed to achieve considerable improvement over existing methods. In our paper, we demonstrate that extreme learning rates can lead to poor performance. We provide new variants of Adam and AMSGrad, called AdaBound and AMSBound respectively, which employ dynamic bounds on learning rates to achieve a gradual and smooth transition from adaptive methods to SGD and give a theoretical proof of convergence. We further conduct experiments on various popular tasks and models, which is often insufficient in previous work. Experimental results show that new variants can eliminate the generalization gap between adaptive methods and SGD and maintain higher learning speed early in training at the same time. Moreover, they can bring significant improvement over their prototypes, especially on complex deep networks. The implementation of the algorithm can be found at https://github.com/Luolc/AdaBound .

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

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.

Adaptive optimization methods are widely recognized as among the most popular approaches for training Deep Neural Networks (DNNs). Techniques such as Adam, AdaGrad, and AdaHessian utilize a preconditioner that modifies the search direction by incorporating information about the curvature of the objective function. However, despite their adaptive characteristics, these methods still require manual fine-tuning of the step-size. This, in turn, impacts the time required to solve a particular problem. This paper presents an optimization framework named SANIA to tackle these challenges. Beyond eliminating the need for manual step-size hyperparameter settings, SANIA incorporates techniques to address poorly scaled or ill-conditioned problems. We also explore several preconditioning methods, including Hutchinson's method, which approximates the Hessian diagonal of the loss function. We conclude with an extensive empirical examination of the proposed techniques across classification tasks, covering both convex and non-convex contexts.

Binarization of neural networks is a dominant paradigm in neural networks compression. The pioneering work BinaryConnect uses Straight Through Estimator (STE) to mimic the gradients of the sign function, but it also causes the crucial inconsistency problem. Most of the previous methods design different estimators instead of STE to mitigate it. However, they ignore the fact that when reducing the estimating error, the gradient stability will decrease concomitantly. These highly divergent gradients will harm the model training and increase the risk of gradient vanishing and gradient exploding. To fully take the gradient stability into consideration, we present a new perspective to the BNNs training, regarding it as the equilibrium between the estimating error and the gradient stability. In this view, we firstly design two indicators to quantitatively demonstrate the equilibrium phenomenon. In addition, in order to balance the estimating error and the gradient stability well, we revise the original straight through estimator and propose a power function based estimator, Rectified Straight Through Estimator (ReSTE for short). Comparing to other estimators, ReSTE is rational and capable of flexibly balancing the estimating error with the gradient stability. Extensive experiments on CIFAR-10 and ImageNet datasets show that ReSTE has excellent performance and surpasses the state-of-the-art methods without any auxiliary modules or losses.

Deep neural networks are vulnerable to universal adversarial perturbation (UAP), an instance-agnostic perturbation capable of fooling the target model for most samples. Compared to instance-specific adversarial examples, UAP is more challenging as it needs to generalize across various samples and models. In this paper, we examine the serious dilemma of UAP generation methods from a generalization perspective -- the gradient vanishing problem using small-batch stochastic gradient optimization and the local optima problem using large-batch optimization. To address these problems, we propose a simple and effective method called Stochastic Gradient Aggregation (SGA), which alleviates the gradient vanishing and escapes from poor local optima at the same time. Specifically, SGA employs the small-batch training to perform multiple iterations of inner pre-search. Then, all the inner gradients are aggregated as a one-step gradient estimation to enhance the gradient stability and reduce quantization errors. Extensive experiments on the standard ImageNet dataset demonstrate that our method significantly enhances the generalization ability of UAP and outperforms other state-of-the-art methods. The code is available at https://github.com/liuxuannan/Stochastic-Gradient-Aggregation.

L_2 regularization and weight decay regularization are equivalent for standard stochastic gradient descent (when rescaled by the learning rate), but as we demonstrate this is not the case for adaptive gradient algorithms, such as Adam. While common implementations of these algorithms employ L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function. We provide empirical evidence that our proposed modification (i) decouples the optimal choice of weight decay factor from the setting of the learning rate for both standard SGD and Adam and (ii) substantially improves Adam's generalization performance, allowing it to compete with SGD with momentum on image classification datasets (on which it was previously typically outperformed by the latter). Our proposed decoupled weight decay has already been adopted by many researchers, and the community has implemented it in TensorFlow and PyTorch; the complete source code for our experiments is available at https://github.com/loshchil/AdamW-and-SGDW

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: "Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?" We answer this question in the affirmative by giving a particular construction of an Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded gradients at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.

Prompt tuning and adapter tuning have shown great potential in transferring pre-trained vision-language models (VLMs) to various downstream tasks. In this work, we design a new type of tuning method, termed as regularized mask tuning, which masks the network parameters through a learnable selection. Inspired by neural pathways, we argue that the knowledge required by a downstream task already exists in the pre-trained weights but just gets concealed in the upstream pre-training stage. To bring the useful knowledge back into light, we first identify a set of parameters that are important to a given downstream task, then attach a binary mask to each parameter, and finally optimize these masks on the downstream data with the parameters frozen. When updating the mask, we introduce a novel gradient dropout strategy to regularize the parameter selection, in order to prevent the model from forgetting old knowledge and overfitting the downstream data. Experimental results on 11 datasets demonstrate the consistent superiority of our method over previous alternatives. It is noteworthy that we manage to deliver 18.73% performance improvement compared to the zero-shot CLIP via masking an average of only 2.56% parameters. Furthermore, our method is synergistic with most existing parameter-efficient tuning methods and can boost the performance on top of them. Project page can be found here (https://wuw2019.github.io/R-AMT/).

Domain adversarial training has been ubiquitous for achieving invariant representations and is used widely for various domain adaptation tasks. In recent times, methods converging to smooth optima have shown improved generalization for supervised learning tasks like classification. In this work, we analyze the effect of smoothness enhancing formulations on domain adversarial training, the objective of which is a combination of task loss (eg. classification, regression, etc.) and adversarial terms. We find that converging to a smooth minima with respect to (w.r.t.) task loss stabilizes the adversarial training leading to better performance on target domain. In contrast to task loss, our analysis shows that converging to smooth minima w.r.t. adversarial loss leads to sub-optimal generalization on the target domain. Based on the analysis, we introduce the Smooth Domain Adversarial Training (SDAT) procedure, which effectively enhances the performance of existing domain adversarial methods for both classification and object detection tasks. Our analysis also provides insight into the extensive usage of SGD over Adam in the community for domain adversarial training.

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.

ControlNet has enabled detailed spatial control in text-to-image diffusion models by incorporating additional visual conditions such as depth or edge maps. However, its effectiveness heavily depends on the availability of visual conditions that are precisely aligned with the generation goal specified by text prompt-a requirement that often fails in practice, especially for uncommon or imaginative scenes. For example, generating an image of a cat cooking in a specific pose may be infeasible due to the lack of suitable visual conditions. In contrast, structurally similar cues can often be found in more common settings-for instance, poses of humans cooking are widely available and can serve as rough visual guides. Unfortunately, existing ControlNet models struggle to use such loosely aligned visual conditions, often resulting in low text fidelity or visual artifacts. To address this limitation, we propose SemanticControl, a training-free method for effectively leveraging misaligned but semantically relevant visual conditions. Our approach adaptively suppresses the influence of the visual condition where it conflicts with the prompt, while strengthening guidance from the text. The key idea is to first run an auxiliary denoising process using a surrogate prompt aligned with the visual condition (e.g., "a human playing guitar" for a human pose condition) to extract informative attention masks, and then utilize these masks during the denoising of the actual target prompt (e.g., cat playing guitar). Experimental results demonstrate that our method improves performance under loosely aligned conditions across various conditions, including depth maps, edge maps, and human skeletons, outperforming existing baselines. Our code is available at https://mung3477.github.io/semantic-control.

We propose ScaledGD(\lambda), a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, ScaledGD(\lambda) starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, ScaledGD(\lambda) is remarkably robust to ill-conditioning compared to vanilla gradient descent (GD) even with overprameterization. Specifically, we show that, under the Gaussian design, ScaledGD(\lambda) converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla GD which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

Explaining the predictions of deep neural nets has been a topic of great interest in the computer vision literature. While several gradient-based interpretation schemes have been proposed to reveal the influential variables in a neural net's prediction, standard gradient-based interpretation frameworks have been commonly observed to lack robustness to input perturbations and flexibility for incorporating prior knowledge of sparsity and group-sparsity structures. In this work, we propose MoreauGrad as an interpretation scheme based on the classifier neural net's Moreau envelope. We demonstrate that MoreauGrad results in a smooth and robust interpretation of a multi-layer neural network and can be efficiently computed through first-order optimization methods. Furthermore, we show that MoreauGrad can be naturally combined with L_1-norm regularization techniques to output a sparse or group-sparse explanation which are prior conditions applicable to a wide range of deep learning applications. We empirically evaluate the proposed MoreauGrad scheme on standard computer vision datasets, showing the qualitative and quantitative success of the MoreauGrad approach in comparison to standard gradient-based interpretation methods.

Although there have been significant advances in the field of image restoration recently, the system complexity of the state-of-the-art (SOTA) methods is increasing as well, which may hinder the convenient analysis and comparison of methods. In this paper, we propose a simple baseline that exceeds the SOTA methods and is computationally efficient. To further simplify the baseline, we reveal that the nonlinear activation functions, e.g. Sigmoid, ReLU, GELU, Softmax, etc. are not necessary: they could be replaced by multiplication or removed. Thus, we derive a Nonlinear Activation Free Network, namely NAFNet, from the baseline. SOTA results are achieved on various challenging benchmarks, e.g. 33.69 dB PSNR on GoPro (for image deblurring), exceeding the previous SOTA 0.38 dB with only 8.4% of its computational costs; 40.30 dB PSNR on SIDD (for image denoising), exceeding the previous SOTA 0.28 dB with less than half of its computational costs. The code and the pre-trained models are released at https://github.com/megvii-research/NAFNet.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

Production deployments in complex systems require ML architectures to be highly efficient and usable against multiple tasks. Particularly demanding are classification problems in which data arrives in a streaming fashion and each class is presented separately. Recent methods with stochastic gradient learning have been shown to struggle in such setups or have limitations like memory buffers, and being restricted to specific domains that disable its usage in real-world scenarios. For this reason, we present a fully differentiable architecture based on the Mixture of Experts model, that enables the training of high-performance classifiers when examples from each class are presented separately. We conducted exhaustive experiments that proved its applicability in various domains and ability to learn online in production environments. The proposed technique achieves SOTA results without a memory buffer and clearly outperforms the reference methods.

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and leverages its underlying structure making the gradients sequentially predictable. By exploiting the predictability and ideas from optimistic online learning, the proposed algorithm can accelerate the convergence and increase sample efficiency. After establishing a tighter upper bound under some convexity conditions on the regret, we offer a complimentary view of our algorithm which generalizes the offline and stochastic version of nonconvex optimization. In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization. We illustrate the practical speedup on several deep learning models via numerical experiments.

Recent studies have demonstrated the effectiveness of directly aligning diffusion models with human preferences using differentiable reward. However, they exhibit two primary challenges: (1) they rely on multistep denoising with gradient computation for reward scoring, which is computationally expensive, thus restricting optimization to only a few diffusion steps; (2) they often need continuous offline adaptation of reward models in order to achieve desired aesthetic quality, such as photorealism or precise lighting effects. To address the limitation of multistep denoising, we propose Direct-Align, a method that predefines a noise prior to effectively recover original images from any time steps via interpolation, leveraging the equation that diffusion states are interpolations between noise and target images, which effectively avoids over-optimization in late timesteps. Furthermore, we introduce Semantic Relative Preference Optimization (SRPO), in which rewards are formulated as text-conditioned signals. This approach enables online adjustment of rewards in response to positive and negative prompt augmentation, thereby reducing the reliance on offline reward fine-tuning. By fine-tuning the FLUX.1.dev model with optimized denoising and online reward adjustment, we improve its human-evaluated realism and aesthetic quality by over 3x.

The deep learning recipe of casting real-world problems as mathematical optimisation and tackling the optimisation by training deep neural networks using gradient-based optimisation has undoubtedly proven to be a fruitful one. The understanding behind why deep learning works, however, has lagged behind its practical significance. We aim to make steps towards an improved understanding of deep learning with a focus on optimisation and model regularisation. We start by investigating gradient descent (GD), a discrete-time algorithm at the basis of most popular deep learning optimisation algorithms. Understanding the dynamics of GD has been hindered by the presence of discretisation drift, the numerical integration error between GD and its often studied continuous-time counterpart, the negative gradient flow (NGF). To add to the toolkit available to study GD, we derive novel continuous-time flows that account for discretisation drift. Unlike the NGF, these new flows can be used to describe learning rate specific behaviours of GD, such as training instabilities observed in supervised learning and two-player games. We then translate insights from continuous time into mitigation strategies for unstable GD dynamics, by constructing novel learning rate schedules and regularisers that do not require additional hyperparameters. Like optimisation, smoothness regularisation is another pillar of deep learning's success with wide use in supervised learning and generative modelling. Despite their individual significance, the interactions between smoothness regularisation and optimisation have yet to be explored. We find that smoothness regularisation affects optimisation across multiple deep learning domains, and that incorporating smoothness regularisation in reinforcement learning leads to a performance boost that can be recovered using adaptions to optimisation methods.

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and a lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms other optimizers. Also, we show that diffGrad performs uniformly well for training CNN using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

Classifier-Free Guidance (CFG) enhances the quality and condition adherence of text-to-image diffusion models. It operates by combining the conditional and unconditional predictions using a fixed weight. However, recent works vary the weights throughout the diffusion process, reporting superior results but without providing any rationale or analysis. By conducting comprehensive experiments, this paper provides insights into CFG weight schedulers. Our findings suggest that simple, monotonically increasing weight schedulers consistently lead to improved performances, requiring merely a single line of code. In addition, more complex parametrized schedulers can be optimized for further improvement, but do not generalize across different models and tasks.

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.

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.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

We show that diffusion models can achieve image sample quality superior to the current state-of-the-art generative models. We achieve this on unconditional image synthesis by finding a better architecture through a series of ablations. For conditional image synthesis, we further improve sample quality with classifier guidance: a simple, compute-efficient method for trading off diversity for fidelity using gradients from a classifier. We achieve an FID of 2.97 on ImageNet 128times128, 4.59 on ImageNet 256times256, and 7.72 on ImageNet 512times512, and we match BigGAN-deep even with as few as 25 forward passes per sample, all while maintaining better coverage of the distribution. Finally, we find that classifier guidance combines well with upsampling diffusion models, further improving FID to 3.94 on ImageNet 256times256 and 3.85 on ImageNet 512times512. We release our code at https://github.com/openai/guided-diffusion

Diffusion models have recently been extended to language generation through Masked Diffusion Language Models (MDLMs), which achieve performance competitive with strong autoregressive models. However, MDLMs tend to degrade in the few-step regime and cannot directly adopt existing few-step distillation methods designed for continuous diffusion models, as they lack the intrinsic property of mapping from noise to data. Recent Uniform-state Diffusion Models (USDMs), initialized from a uniform prior, alleviate some limitations but still suffer from complex loss formulations that hinder scalability. In this work, we propose a simplified denoising-based loss for USDMs that optimizes only noise-replaced tokens, stabilizing training and matching ELBO-level performance. Furthermore, by framing denoising as self-supervised learning, we introduce a simple modification to our denoising loss with contrastive-inspired negative gradients, which is practical and yield additional improvements in generation quality.

Night images suffer not only from low light, but also from uneven distributions of light. Most existing night visibility enhancement methods focus mainly on enhancing low-light regions. This inevitably leads to over enhancement and saturation in bright regions, such as those regions affected by light effects (glare, floodlight, etc). To address this problem, we need to suppress the light effects in bright regions while, at the same time, boosting the intensity of dark regions. With this idea in mind, we introduce an unsupervised method that integrates a layer decomposition network and a light-effects suppression network. Given a single night image as input, our decomposition network learns to decompose shading, reflectance and light-effects layers, guided by unsupervised layer-specific prior losses. Our light-effects suppression network further suppresses the light effects and, at the same time, enhances the illumination in dark regions. This light-effects suppression network exploits the estimated light-effects layer as the guidance to focus on the light-effects regions. To recover the background details and reduce hallucination/artefacts, we propose structure and high-frequency consistency losses. Our quantitative and qualitative evaluations on real images show that our method outperforms state-of-the-art methods in suppressing night light effects and boosting the intensity of dark regions.

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.

This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a given function. A neural network can also be seen as an additive expansion where the scalar product of the responses of the last hidden layer and its weights provide the final output of the network. Instead of training the network as a whole, the proposed algorithm trains the network sequentially in T steps. First, the bias term of the network is initialized with a constant approximation that minimizes the average loss of the data. Then, at each step, a portion of the network, composed of J neurons, is trained to approximate the pseudo-residuals on the training data computed from the previous iterations. Finally, the T partial models and bias are integrated as a single NN with T times J neurons in the hidden layer. Extensive experiments in classification and regression tasks, as well as in combination with deep neural networks, are carried out showing a competitive generalization performance with respect to neural networks trained with different standard solvers, such as Adam, L-BFGS, SGD and deep models. Furthermore, we show that the proposed method design permits to switch off a number of hidden units during test (the units that were last trained) without a significant reduction of its generalization ability. This permits the adaptation of the model to different classification speed requirements on the fly.

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

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.

Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Activation Gradient Pruning (AGP) strategy. The strategy leverages the heterogeneity of gradients by pruning less informative gradients and enhancing the numerical precision of remaining gradients to mitigate gradient variance. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13x compared to full precision training.

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.

Denoising diffusion models have been a mainstream approach for image generation, however, training these models often suffers from slow convergence. In this paper, we discovered that the slow convergence is partly due to conflicting optimization directions between timesteps. To address this issue, we treat the diffusion training as a multi-task learning problem, and introduce a simple yet effective approach referred to as Min-SNR-gamma. This method adapts loss weights of timesteps based on clamped signal-to-noise ratios, which effectively balances the conflicts among timesteps. Our results demonstrate a significant improvement in converging speed, 3.4times faster than previous weighting strategies. It is also more effective, achieving a new record FID score of 2.06 on the ImageNet 256times256 benchmark using smaller architectures than that employed in previous state-of-the-art. The code is available at https://github.com/TiankaiHang/Min-SNR-Diffusion-Training.

Large language models memorize sensitive data from their pretraining corpora. In this work, we propose CE-U (Cross Entropy Unlearning), a loss function for unlearning. CE-U addresses fundamental limitations of gradient ascent approaches that suffer from vanishing gradients when model confidence is high and exploding gradients when confidence is low. We also unify standard cross entropy learning and unlearning into a single framework. On the TOFU benchmark for unlearning, CE-U achieves state-of-the-art results on LLaMA2-7B models without using an extra oracle model or additional positive samples. Our analysis reveals that the problematic gradient ascent component also exists in reinforcement learning algorithms like DPO and GRPO. This suggests that applying CE-U approach to reinforcement learning could be promising to improve stability and convergence.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.