Daily Papers

This paper investigates the problem of forecasting multivariate aggregated human mobility while preserving the privacy of the individuals concerned. Differential privacy, a state-of-the-art formal notion, has been used as the privacy guarantee in two different and independent steps when training deep learning models. On one hand, we considered gradient perturbation, which uses the differentially private stochastic gradient descent algorithm to guarantee the privacy of each time series sample in the learning stage. On the other hand, we considered input perturbation, which adds differential privacy guarantees in each sample of the series before applying any learning. We compared four state-of-the-art recurrent neural networks: Long Short-Term Memory, Gated Recurrent Unit, and their Bidirectional architectures, i.e., Bidirectional-LSTM and Bidirectional-GRU. Extensive experiments were conducted with a real-world multivariate mobility dataset, which we published openly along with this paper. As shown in the results, differentially private deep learning models trained under gradient or input perturbation achieve nearly the same performance as non-private deep learning models, with loss in performance varying between 0.57% to 2.8%. The contribution of this paper is significant for those involved in urban planning and decision-making, providing a solution to the human mobility multivariate forecast problem through differentially private deep learning models.

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.

Deep Gradient Leakage (DGL) is a highly effective attack that recovers private training images from gradient vectors. This attack casts significant privacy challenges on distributed learning from clients with sensitive data, where clients are required to share gradients. Defending against such attacks requires but lacks an understanding of when and how privacy leakage happens, mostly because of the black-box nature of deep networks. In this paper, we propose a novel Inversion Influence Function (I^2F) that establishes a closed-form connection between the recovered images and the private gradients by implicitly solving the DGL problem. Compared to directly solving DGL, I^2F is scalable for analyzing deep networks, requiring only oracle access to gradients and Jacobian-vector products. We empirically demonstrate that I^2F effectively approximated the DGL generally on different model architectures, datasets, attack implementations, and noise-based defenses. With this novel tool, we provide insights into effective gradient perturbation directions, the unfairness of privacy protection, and privacy-preferred model initialization. Our codes are provided in https://github.com/illidanlab/inversion-influence-function.

To mitigate the privacy leakages and communication burdens of Federated Learning (FL), decentralized FL (DFL) discards the central server and each client only communicates with its neighbors in a decentralized communication network. However, existing DFL suffers from high inconsistency among local clients, which results in severe distribution shift and inferior performance compared with centralized FL (CFL), especially on heterogeneous data or sparse communication topology. To alleviate this issue, we propose two DFL algorithms named DFedSAM and DFedSAM-MGS to improve the performance of DFL. Specifically, DFedSAM leverages gradient perturbation to generate local flat models via Sharpness Aware Minimization (SAM), which searches for models with uniformly low loss values. DFedSAM-MGS further boosts DFedSAM by adopting Multiple Gossip Steps (MGS) for better model consistency, which accelerates the aggregation of local flat models and better balances communication complexity and generalization. Theoretically, we present improved convergence rates small Obig(1{KT}+1{T}+1{K^{1/2}T^{3/2}(1-lambda)^2}big) and small Obig(1{KT}+1{T}+lambda^Q+1{K^{1/2}T^{3/2}(1-lambda^Q)^2}big) in non-convex setting for DFedSAM and DFedSAM-MGS, respectively, where 1-lambda is the spectral gap of gossip matrix and Q is the number of MGS. Empirically, our methods can achieve competitive performance compared with CFL methods and outperform existing DFL methods.

In this paper, by introducing Generalized Bernstein condition, we propose the first Obig(sqrt{p}{nepsilon}big) high probability excess population risk bound for differentially private algorithms under the assumptions G-Lipschitz, L-smooth, and Polyak-{\L}ojasiewicz condition, based on gradient perturbation method. If we replace the properties G-Lipschitz and L-smooth by alpha-H{\"o}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to Obig(n^{-alpha{1+2alpha}}big) w.r.t n, which cannot achieve Oleft(1/nright) when alphain(0,1]. To solve this problem, we propose a variant of gradient perturbation method, max{1,g-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions alpha-H{\"o}lder smooth and Polyak-{\L}ojasiewicz condition can achieve Obig(sqrt{p}{nepsilon}big), which is the first Oleft(1/nright) high probability excess population risk bound w.r.t n for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.

Federated learning is an emerging distributed machine learning framework which jointly trains a global model via a large number of local devices with data privacy protections. Its performance suffers from the non-vanishing biases introduced by the local inconsistent optimal and the rugged client-drifts by the local over-fitting. In this paper, we propose a novel and practical method, FedSpeed, to alleviate the negative impacts posed by these problems. Concretely, FedSpeed applies the prox-correction term on the current local updates to efficiently reduce the biases introduced by the prox-term, a necessary regularizer to maintain the strong local consistency. Furthermore, FedSpeed merges the vanilla stochastic gradient with a perturbation computed from an extra gradient ascent step in the neighborhood, thereby alleviating the issue of local over-fitting. Our theoretical analysis indicates that the convergence rate is related to both the communication rounds T and local intervals K with a upper bound small O(1/T) if setting a proper local interval. Moreover, we conduct extensive experiments on the real-world dataset to demonstrate the efficiency of our proposed FedSpeed, which performs significantly faster and achieves the state-of-the-art (SOTA) performance on the general FL experimental settings than several baselines. Our code is available at https://github.com/woodenchild95/FL-Simulator.git.

Invisible image watermark removal has received growing attention. Despite substantial progress, existing attacks face a tension between practicality and specificity. Attacks exploiting detector outputs, decoder responses, or paired images can be tailored to the watermark decision boundary, but require information rarely available in realistic scenarios. Conversely, attacks based on compression, geometric distortion, or reconstruction are easily deployed from a single watermarked image, but remain largely open-loop: they apply generic transformations without knowing if the image is moving toward watermark failure. Thus, the key challenge in single-image blind watermark removal is not merely how to transform the image, but how to obtain a useful removal direction without accessing the hidden decoder. To bridge this gap, we propose ProxyEraseAgent, an agent-driven framework recovering attack specificity through proxy decoder responses. Publicly available watermarking schemes provide a natural knowledge base of candidate decoders, where some are informative for a given unknown image. Our insight is that a decoder producing a strong calibrated response to the query image likely shares a nearby decoding boundary with the hidden target mechanism. ProxyEraseAgent ranks these decoders by calibrated response strength and uses the top ones as proxy boundary estimators. Their responses then guide a progressive search over heterogeneous removal operations (e.g., geometric distortion, JPEG compression, image reconstruction, and gradient perturbation) under perceptual-quality constraints. Experiments across 11 watermarking systems show ProxyEraseAgent achieves a 94.8% attack success rate, demonstrating the effectiveness of response-guided proxy retrieval and feedback-driven sequential planning for blind watermark removal.

Large Language Models (LLMs) have achieved remarkable success in natural language processing, but their full fine-tuning remains resource-intensive. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have emerged as a practical solution by approximating parameter updates with low-rank matrices. However, LoRA often exhibits a "double descent" phenomenon during fine-tuning, where model performance degrades due to overfitting and limited expressiveness caused by low-rank constraints. To address this issue, we propose LoRA-GGPO (Gradient-Guided Perturbation Optimization), a novel method that leverages gradient and weight norms to generate targeted perturbations. By optimizing the sharpness of the loss landscape, LoRA-GGPO guides the model toward flatter minima, mitigating the double descent problem and improving generalization. Extensive experiments on natural language understanding (NLU) and generation (NLG) tasks demonstrate that LoRA-GGPO outperforms LoRA and its state-of-the-art variants. Furthermore, extended experiments specifically designed to analyze the double descent phenomenon confirm that LoRA-GGPO effectively alleviates this issue, producing more robust and generalizable models. Our work provides a robust and efficient solution for fine-tuning LLMs, with broad applicability in real-world scenarios. The code is available at https://github.com/llm172/LoRA-GGPO.

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM pretraining, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

Vision-enabled language models (VLMs) are now used to build autonomous multimodal agents capable of taking actions in real environments. In this paper, we show that multimodal agents raise new safety risks, even though attacking agents is more challenging than prior attacks due to limited access to and knowledge about the environment. Our attacks use adversarial text strings to guide gradient-based perturbation over one trigger image in the environment: (1) our captioner attack attacks white-box captioners if they are used to process images into captions as additional inputs to the VLM; (2) our CLIP attack attacks a set of CLIP models jointly, which can transfer to proprietary VLMs. To evaluate the attacks, we curated VisualWebArena-Adv, a set of adversarial tasks based on VisualWebArena, an environment for web-based multimodal agent tasks. Within an L-infinity norm of 16/256 on a single image, the captioner attack can make a captioner-augmented GPT-4V agent execute the adversarial goals with a 75% success rate. When we remove the captioner or use GPT-4V to generate its own captions, the CLIP attack can achieve success rates of 21% and 43%, respectively. Experiments on agents based on other VLMs, such as Gemini-1.5, Claude-3, and GPT-4o, show interesting differences in their robustness. Further analysis reveals several key factors contributing to the attack's success, and we also discuss the implications for defenses as well. Project page: https://chenwu.io/attack-agent Code and data: https://github.com/ChenWu98/agent-attack

In this paper we introduce a novel, unified, open-source model interpretability library for PyTorch [12]. The library contains generic implementations of a number of gradient and perturbation-based attribution algorithms, also known as feature, neuron and layer importance algorithms, as well as a set of evaluation metrics for these algorithms. It can be used for both classification and non-classification models including graph-structured models built on Neural Networks (NN). In this paper we give a high-level overview of supported attribution algorithms and show how to perform memory-efficient and scalable computations. We emphasize that the three main characteristics of the library are multimodality, extensibility and ease of use. Multimodality supports different modality of inputs such as image, text, audio or video. Extensibility allows adding new algorithms and features. The library is also designed for easy understanding and use. Besides, we also introduce an interactive visualization tool called Captum Insights that is built on top of Captum library and allows sample-based model debugging and visualization using feature importance metrics.

The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation (IMLE, Niepert, Minervini, and Franceschi 2021), a class of gradient estimators for discrete exponential family distributions, was proposed by combining implicit differentiation through perturbation with the path-wise gradient estimator. However, due to the finite difference approximation of the gradients, it is especially sensitive to the choice of the finite difference step size, which needs to be specified by the user. In this work, we present Adaptive IMLE (AIMLE), the first adaptive gradient estimator for complex discrete distributions: it adaptively identifies the target distribution for IMLE by trading off the density of gradient information with the degree of bias in the gradient estimates. We empirically evaluate our estimator on synthetic examples, as well as on Learning to Explain, Discrete Variational Auto-Encoders, and Neural Relational Inference tasks. In our experiments, we show that our adaptive gradient estimator can produce faithful estimates while requiring orders of magnitude fewer samples than other gradient estimators.

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.

Fractional gradient descent (FGD) incorporates long-range memory through Caputo-type operators and has been shown to improve stability in ill-conditioned and nonconvex optimization problems. Despite these advantages, its practical use remains limited, mainly due to the high computational cost of evaluating history-dependent convolutions, which scales quadratically with the number of iterations. In this paper, we focus on making Caputo-based optimization computationally viable without sacrificing its intrinsic memory structure. We begin by expressing the fractional descent direction as a discrete convolution over past gradients, which provides a unified view of the method. Based on this formulation, we introduce two complementary mechanisms to reduce the cost of the memory term. The first uses a sum-of-exponentials (SOE) approximation of the power-law kernel, leading to efficient recursive updates. The second approach, newly proposed in this paper as dyadic hierarchical discrete convolution (DHDC), compresses the gradient history through a multiscale aggregation strategy. Rather than treating these approximations as purely numerical accelerations, we interpret them as perturbations of the ideal Caputo operator. This viewpoint allows us to analyze how the compressed memory affects the optimization dynamics. Under standard μ-strong convexity and L-smoothness assumptions, we show that the resulting method still exhibits monotone descent and linear convergence, provided that the approximation error remains controlled.

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.

We develop a model-free policy gradient method for discrete-time mean-field control (MFC). In MFC, the policy affects the objective both through the controlled dynamics and through the population distribution. Standard REINFORCE estimators capture the first effect but not the second. We introduce Transport REINFORCE, a transport map-based approach that perturbs a suitable transformation of the population distribution to estimate this missing mean-field contribution. The method applies to both finite and continuous state spaces. In finite state spaces, we perturb the population distribution directly on the probability simplex through a convex combination of the current population weights and random weights. In continuous state spaces, we project the population distribution onto the manifold of Gaussian mixtures, and then randomize it via a transport map that ensures the perturbed law remains within this manifold. We prove consistency of the perturbed objective and gradient as the perturbation vanishes, and derive bias and mean-square error bounds for the resulting sample-based gradient estimator. Numerical experiments on several MFC benchmarks show that Transport REINFORCE improves over standard REINFORCE.

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

Vision-Language-Action models (VLAs) have recently demonstrated remarkable progress in embodied environments, enabling robots to perceive, reason, and act through unified multimodal understanding. Despite their impressive capabilities, the adversarial robustness of these systems remains largely unexplored, especially under realistic multimodal and black-box conditions. Existing studies mainly focus on single-modality perturbations and overlook the cross-modal misalignment that fundamentally affects embodied reasoning and decision-making. In this paper, we introduce VLA-Fool, a comprehensive study of multimodal adversarial robustness in embodied VLA models under both white-box and black-box settings. VLA-Fool unifies three levels of multimodal adversarial attacks: (1) textual perturbations through gradient-based and prompt-based manipulations, (2) visual perturbations via patch and noise distortions, and (3) cross-modal misalignment attacks that intentionally disrupt the semantic correspondence between perception and instruction. We further incorporate a VLA-aware semantic space into linguistic prompts, developing the first automatically crafted and semantically guided prompting framework. Experiments on the LIBERO benchmark using a fine-tuned OpenVLA model reveal that even minor multimodal perturbations can cause significant behavioral deviations, demonstrating the fragility of embodied multimodal alignment.

Deep neural networks (DNN) have been widely applied in modern life, including critical domains like autonomous driving, making it essential to ensure the reliability and robustness of DNN-powered systems. As an analogy to code coverage metrics for testing conventional software, researchers have proposed neuron coverage metrics and coverage-driven methods to generate DNN test cases. However, Yan et al. doubt the usefulness of existing coverage criteria in DNN testing. They show that a coverage-driven method is less effective than a gradient-based method in terms of both uncovering defects and improving model robustness. In this paper, we conduct a replication study of the work by Yan et al. and extend the experiments for deeper analysis. A larger model and a dataset of higher resolution images are included to examine the generalizability of the results. We also extend the experiments with more test case generation techniques and adjust the process of improving model robustness to be closer to the practical life cycle of DNN development. Our experiment results confirm the conclusion from Yan et al. that coverage-driven methods are less effective than gradient-based methods. Yan et al. find that using gradient-based methods to retrain cannot repair defects uncovered by coverage-driven methods. They attribute this to the fact that the two types of methods use different perturbation strategies: gradient-based methods perform differentiable transformations while coverage-driven methods can perform additional non-differentiable transformations. We test several hypotheses and further show that even coverage-driven methods are constrained only to perform differentiable transformations, the uncovered defects still cannot be repaired by adversarial training with gradient-based methods. Thus, defensive strategies for coverage-driven methods should be further studied.

Language Generation Models produce words based on the previous context. Although existing methods offer input attributions as explanations for a model's prediction, it is still unclear how prior words affect the model's decision throughout the layers. In this work, we leverage recent advances in explainability of the Transformer and present a procedure to analyze models for language generation. Using contrastive examples, we compare the alignment of our explanations with evidence of the linguistic phenomena, and show that our method consistently aligns better than gradient-based and perturbation-based baselines. Then, we investigate the role of MLPs inside the Transformer and show that they learn features that help the model predict words that are grammatically acceptable. Lastly, we apply our method to Neural Machine Translation models, and demonstrate that they generate human-like source-target alignments for building predictions.

Federated Learning (FL) systems are gaining popularity as a solution to training Machine Learning (ML) models from large-scale user data collected on personal devices (e.g., smartphones) without their raw data leaving the device. At the core of FL is a network of anonymous user devices sharing training information (model parameter updates) computed locally on personal data. However, the type and degree to which user-specific information is encoded in the model updates is poorly understood. In this paper, we identify model updates encode subtle variations in which users capture and generate data. The variations provide a strong statistical signal, allowing an adversary to effectively deanonymize participating devices using a limited set of auxiliary data. We analyze resulting deanonymization attacks on diverse tasks on real-world (anonymized) user-generated data across a range of closed- and open-world scenarios. We study various strategies to mitigate the risks of deanonymization. As random perturbation methods do not offer convincing operating points, we propose data-augmentation strategies which introduces adversarial biases in device data and thereby, offer substantial protection against deanonymization threats with little effect on utility.

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

Objective perturbation adds a random linear term to a regularized empirical risk and releases the exact perturbed minimizer. We study the finite computation obtained by releasing the N-th iterate of deterministic gradient descent on wmapsto F(w;S)+langle z,wrangle, where zsimmathcal N(0,σ^2I_d) is drawn once before optimization. For strongly convex and smooth objectives with Lipschitz Hessian, we prove an explicit condition under which the map zmapsto w_N is a C^1-diffeomorphism on the bounded domains used in the privacy argument, with a quantitative lower bound on the smallest singular value of its Jacobian. This permits a direct change-of-variables analysis of the finite iterate. For generalized linear models, the resulting privacy-profile bound has no explicit ambient-dimension factor once the iteration condition holds, and its finite-iteration correction decreases geometrically. By letting the free truncation parameter grow slowly with N, we recover the corresponding exact-minimizer certificate in the limit. We also bound the expected excess empirical risk by dσ^2/(2μ) plus a geometrically decreasing optimization term, and transfer the result to population risk without an additional multiplicative condition-number factor in the leading statistical terms.

Post-training of language models is commonly framed as a sample-score-update loop implemented by gradient descent. A recent line of work, exemplified by RandOpt, relocates this loop to weight space, sampling Gaussian perturbations around a pretrained model and ensembling the top-K rewarded specialists at inference. While competitive with PPO and GRPO under matched training compute, this prediction-level ensemble incurs K forward passes per test example and does not extend cleanly to free-form generation. We ask whether the rewarded population can instead be folded into a single deployable model, replacing the inference-time ensemble with one consolidated update. A split-half analysis over 25 model-task pairs reveals reproducible low-rank structure in every case. We turn this geometry into CoRP (Consolidating Rewarded Perturbations), a gradient-free operator that combines reward-weighted aggregation, compatibility-aware reweighting, and a held-out validation gate, with no gradient flowing through the language model. Across five language models from 0.5B to 8B and five tasks covering math, code, and creative writing, CoRP improves the base model by 8.1 points on average. Using one tenth of RandOpt's perturbation budget, CoRP exceeds single-inference RandOpt by 6.5 points and recovers more than half of the gain of the 50-pass majority-vote ensemble, at one forward pass per test example.

An important and unresolved problem in the physical sciences is explaining the predictions made by neural networks. Several explainable artificial intelligence (XAI) methods have been proposed to address this problem, including gradient XAI, Integrated Gradients, and GradientSHAP. We evaluate the baseline XAI methods according to four scores: sensitivity (XAI patterns strongly affect predictions), attribution (XAI patterns reproduce the change in prediction relative to a baseline), robustness (XAI patterns remain stable for nearby inputs), and coherence (XAI patterns are spatially smooth). We also introduce a new method, average gradient outer product (AGOP) XAI, that uses global gradient information to identify an important direction for a specific input. We apply XAI to neural network predictions of the El Niño-Southern Oscillation (ENSO) based on data from the Zebiak-Cane model. AGOP XAI achieves the highest attribution, robustness, and coherence scores in the architecture and lead-time comparisons reported here. Its sensitivity is surpassed by gradient XAI, which is maximally sensitive by definition. Beyond diagnosing neural-network behavior, AGOP XAI can generate candidate hypotheses about physical mechanisms. The method highlights an equatorial thermocline-depth signal consistent with recharge oscillator physics, together with a southeastern-Pacific lobe that may be specific to the Zebiak-Cane model. Finally, we test the physical relevance of AGOP using optimized perturbations that move the Zebiak-Cane model along AGOP explanation coordinates. Such perturbations can suppress the selected extreme events or, from a near-neutral ensemble, generate strong El Niño or La Niña events 10 months later.

We propose an evolution strategies-based algorithm for estimating gradients in unrolled computation graphs, called ES-Single. Similarly to the recently-proposed Persistent Evolution Strategies (PES), ES-Single is unbiased, and overcomes chaos arising from recursive function applications by smoothing the meta-loss landscape. ES-Single samples a single perturbation per particle, that is kept fixed over the course of an inner problem (e.g., perturbations are not re-sampled for each partial unroll). Compared to PES, ES-Single is simpler to implement and has lower variance: the variance of ES-Single is constant with respect to the number of truncated unrolls, removing a key barrier in applying ES to long inner problems using short truncations. We show that ES-Single is unbiased for quadratic inner problems, and demonstrate empirically that its variance can be substantially lower than that of PES. ES-Single consistently outperforms PES on a variety of tasks, including a synthetic benchmark task, hyperparameter optimization, training recurrent neural networks, and training learned optimizers.

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While current efforts focus on improving uncertainty quantification accuracy and efficiency, there is a need to identify uncertainty sources and take actions to mitigate their effects on predictions. Therefore, we propose to develop explainable and actionable Bayesian deep learning methods to not only perform accurate uncertainty quantification but also explain the uncertainties, identify their sources, and propose strategies to mitigate the uncertainty impacts. Specifically, we introduce a gradient-based uncertainty attribution method to identify the most problematic regions of the input that contribute to the prediction uncertainty. Compared to existing methods, the proposed UA-Backprop has competitive accuracy, relaxed assumptions, and high efficiency. Moreover, we propose an uncertainty mitigation strategy that leverages the attribution results as attention to further improve the model performance. Both qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of our proposed methods.

We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under intermittent androgen suppression (IAS) to study a threshold-based policy for therapy design. IAS is currently one of the most widely used treatments for advanced prostate cancer. Patients undergoing IAS are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. One of the main challenges in IAS is to optimally design a therapy scheme, i.e., to determine when to discontinue and recommence androgen suppression. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. The threshold-based policy we propose is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. Using Infinitesimal Perturbation Analysis (IPA), we derive unbiased gradient estimators of this cost metric with respect to the controllable PSA threshold values based on actual data and show how these estimators can be used to adaptively adjust controllable parameters so as to improve therapy outcomes based on the cost metric defined.

Reinforcement learning (RL) post-training improves large language models (LLMs) on individual domains such as mathematical reasoning, code generation, question answering, and creative writing (CW), but training on one domain often degrades performance on others. Existing explanations based on catastrophic forgetting or global gradient conflict are incomplete: substantial interference can occur even when full-model gradients are nearly orthogonal. We show that single-domain RL produces sparse, small-magnitude parameter edits with weak overlap among top-changed neurons, while different domains still share substantial active computation routes on which update directions determine whether they act synergistically or conflict. Guided by this observation, we prove under a local perturbation model of multi-domain RL that later-domain training harms an earlier domain mainly through a second-order damage term, which under the observed sparse route structure concentrates in a low-dimensional shared conflict subspace. Moreover, a short domain refresh contracts the harmful component on this subspace, enabling selective recovery with limited collateral damage. Consistent with the theory, a brief Re-Math refresh after Code rightarrow Math rightarrow QA rightarrow CW recovers Math from 57.66 to 66.04 while largely preserving performance on the other domains, yielding the best average score of 66.39. Beyond refresh, a training-free rollback on a sparse proxy conflict coordinate set for the Math-QA pair partially restores Math, providing direct proxy-level evidence for localized damage. These results provide a localized mechanistic account of interference and recovery in multi-domain RL.

Speech deepfake detectors often lose accuracy when the distribution of the test data differs from that of the training data. Meta-learning for domain generalization (MLDG) shows promise by simulating domain shifts with episodic meta-train and meta-test splits. However, the MLDG meta-objective considers only a single clean adaptation trajectory and does not account for the local loss landscape around its endpoints. To address this limitation, we first propose an explicit worst-case MLDG variant, dubbed WC-MLDG-4P, which perturbs both the meta-train and meta-test states but requires four gradient evaluations per episode. We then introduce WC-MLDG-2P, a source-directed alternative to the explicit robust objective. It shifts the clean MLDG endpoint toward a locally higher source-loss state and evaluates the meta-test gradient there, retaining the two-evaluation cost of the first-order MLDG. A first-order expansion relates the resulting gradient change to meta-test directional curvature along the source gradient without explicitly computing a Hessian. Relative to MLDG, WC-MLDG-2P achieves relative mean-EER reductions of 23.4% with XLSR-AASIST and 7.6% with XLSR-Conformer-TCM, respectively.

Predicting cellular responses to perturbations supports the study of gene function, disease mechanisms, and therapeutic strategies. Despite advances in single-cell perturbation modeling, existing models typically optimize surrogate losses that do not directly reflect the biological criteria used for evaluation, so better data fitting need not yield better biological predictions. To address this mismatch, we introduce CellRFT, a reinforcement fine-tuning framework that uses biological evaluation as direct training feedback. CellRFT uses policy-gradient optimization to learn from non-differentiable evaluations of generated cell populations and integrates multiple biological rewards through hierarchical reward aggregation. Comprehensive experiments demonstrate CellRFT's applicability across different pretrained models and effectiveness in improving perturbation prediction, reveal that optimizing one biological criterion can help or hinder others, and show that complementary rewards can improve criteria beyond those directly optimized, offering a way to probe how biological metrics shape model behavior, with the potential to inform evaluation design. Code will be made available.

Static subword tokenization algorithms have been an essential component of recent works on language modeling. However, their static nature results in important flaws that degrade the models' downstream performance and robustness. In this work, we propose MANTa, a Module for Adaptive Neural TokenizAtion. MANTa is a differentiable tokenizer trained end-to-end with the language model. The resulting system offers a trade-off between the expressiveness of byte-level models and the speed of models trained using subword tokenization. In addition, our tokenizer is highly explainable since it produces an explicit segmentation of sequences into blocks. We evaluate our pre-trained model on several English datasets from different domains as well as on synthetic noise. We find that MANTa improves robustness to character perturbations and out-of-domain data. We then show that MANTa performs comparably to other models on the general-domain GLUE benchmark. Finally, we show that it is considerably faster than strictly byte-level models.

As Large Language Models (LLMs) become integral software components in modern applications, unauthorized model derivations through fine-tuning, merging, and redistribution have emerged as critical software engineering challenges. Unlike traditional software where clone detection and license compliance are well-established, the LLM ecosystem lacks effective mechanisms to detect model lineage and enforce licensing agreements. This gap is particularly problematic when open-source model creators, such as Meta's LLaMA, require derivative works to maintain naming conventions for attribution, yet no technical means exist to verify compliance. To fill this gap, treating LLMs as software artifacts requiring provenance tracking, we present TensorGuard, a gradient-based fingerprinting framework for LLM similarity detection and family classification. Our approach extracts model-intrinsic behavioral signatures by analyzing gradient responses to random input perturbations across tensor layers, operating independently of training data, watermarks, or specific model formats. TensorGuard supports the widely-adopted safetensors format and constructs high-dimensional fingerprints through statistical analysis of gradient features. These fingerprints enable two complementary capabilities: direct pairwise similarity assessment between arbitrary models through distance computation, and systematic family classification of unknown models via the K-Means clustering algorithm with domain-informed centroid initialization using known base models. Experimental evaluation on 58 models comprising 8 base models and 50 derivatives across five model families (Llama, Qwen, Gemma, Phi, Mistral) demonstrates 94% classification accuracy under our centroid-initialized K-Means clustering.

Autoregressive video generation models generate videos sequentially, with each new block conditioned on previously generated blocks. By training on the model's own rollouts, Self Forcing and its follow-up methods substantially mitigate exposure bias caused by the mismatch between training- and inference-time history distributions. However, these models still suffer from error accumulation during long-horizon generation. We identify a key underlying limitation: the model remains highly sensitive to errors in its generated history, allowing small deviations to be amplified through subsequent generations. We refer to this underexplored problem as the local history robustness gap. To address this gap, we introduce Adversarial Gradient Forcing (AGF), a framework designed to improve the robustness of few-step autoregressive video models to perturbations and accumulated errors in their own generated histories. AGF uses distribution matching gradients from future block predictions to select adversarial perturbations of self-generated histories. It then jointly trains the generator on the original and perturbed histories to improve the robustness of future generation. Extensive experiments show that AGF achieves the highest VBench Total score on 60-second video generation and the best visual quality on four-minute video generation. Notably, AGF achieves such long-horizon robustness while requiring only 5-second rollouts for training.

Language model training in distributed settings is limited by the communication cost of gradient exchanges. In this short note, we extend recent work from Malladi et al. (2023), using shared randomness to perform distributed fine-tuning with low bandwidth. The method is a natural decentralized extension of memory-efficient Simultaneous Perturbation Stochastic Approximation (SPSA). Each iteration, each machine seeds a Random Number Generator (RNG) to perform local reproducible perturbations on model weights and calculate and exchange scalar projected gradients, which are then used to update each model. By using a (machine, sample) identifier as the random seed, each model can regenerate one another's perturbations. As machines only exchange single-byte projected gradients, this is highly communication efficient. There are also potential privacy benefits, as projected gradients may be calculated on different training data, and models never access the other's data. Our approach not only drastically reduces communication bandwidth requirements but also accommodates dynamic addition or removal of machines during the training process and retains the memory-efficient and inference-only advantages of recent work. We perform proof-of-concept experiments to demonstrate the potential usefulness of this method, building off of rich literature on distributed optimization and memory-efficient training.

Components of cyber physical systems, which affect real-world processes, are often exposed to the internet. Replacing conventional control methods with Deep Reinforcement Learning (DRL) in energy systems is an active area of research, as these systems become increasingly complex with the advent of renewable energy sources and the desire to improve their efficiency. Artificial Neural Networks (ANN) are vulnerable to specific perturbations of their inputs or features, called adversarial examples. These perturbations are difficult to detect when properly regularized, but have significant effects on the ANN's output. Because DRL uses ANN to map optimal actions to observations, they are similarly vulnerable to adversarial examples. This work proposes a novel attack technique for continuous control using Group Difference Logits loss with a bifurcation layer. By combining aspects of targeted and untargeted attacks, the attack significantly increases the impact compared to an untargeted attack, with drastically smaller distortions than an optimally targeted attack. We demonstrate the impacts of powerful gradient-based attacks in a realistic smart energy environment, show how the impacts change with different DRL agents and training procedures, and use statistical and time-series analysis to evaluate attacks' stealth. The results show that adversarial attacks can have significant impacts on DRL controllers, and constraining an attack's perturbations makes it difficult to detect. However, certain DRL architectures are far more robust, and robust training methods can further reduce the impact.

Out-of-distribution (OOD) detection is the task of identifying inputs that deviate from the training data distribution. This capability is essential for safely deploying deep computer vision models in open-world environments. In this work, we propose a post-hoc method, Perturbation-Rectified OOD detection (PRO), based on the insight that prediction confidence for OOD inputs is more susceptible to reduction under perturbation than in-distribution (IND) inputs. Based on the observation, we propose an adversarial score function that searches for the local minimum scores near the original inputs by applying gradient descent. This procedure enhances the separability between IND and OOD samples. Importantly, the approach improves OOD detection performance without complex modifications to the underlying model architectures. We conduct extensive experiments using the OpenOOD benchmark~yang2022openood. Our approach further pushes the limit of softmax-based OOD detection and is the leading post-hoc method for small-scale models. On a CIFAR-10 model with adversarial training, PRO effectively detects near-OOD inputs, achieving a reduction of more than 10\% on FPR@95 compared to state-of-the-art methods.

Large Vision-Language Models (VLMs) enable strong multimodal reasoning but incur heavy inference costs from redundant visual tokens. Token pruning alleviates this issue, yet existing approaches face limitations. Attention-based methods rely on raw attention scores, which are often unstable across layers and heads and can lead to redundant selections. Diversity-based methods improve robustness by selecting tokens far apart in feature space but risk dropping regions needed for accurate prediction. We propose \ours, a training-free framework built on a simple intuition: tokens with higher sensitivity are more likely to influence the model's output, and they should also capture complementary visual cues rather than overlapping information. To achieve this, we estimate token sensitivity using zeroth-order perturbations at the projection layer, a shallow and computationally light component of the model. This approach measures how small random perturbations affect the projection outputs, allowing us to approximate each token's influence through lightweight forward passes without backpropagation. Extensive experiments across multiple VLMs and benchmarks show that \ours consistently outperforms prior methods, pruning up to 94.4\% of tokens while maintaining accuracy and significantly improving efficiency, achieving up to 2.30x faster end-to-end inference over the baseline.

Cooperative MARL is commonly evaluated through cooperation discovery from random initialization, leaving open whether continued optimization can destabilize learned cooperation. Actor-critic comparisons can also conflate critic presence with value gradients entering shared actor representations. We study cooperation maintenance, defined as the survival of a behaviorally verified cooperative policy under continued training. We formulate maintenance as a right-censored event-time problem and compare matched warm starts: X0 allows value loss gradients to update shared actor features, X1 retains the critic while blocking those gradients, and X5 removes the learned critic as a critic-free reference. This isolates direct value-gradient access while controlling initialization, critic computation, and evaluation. Positive reward scaling preserves strategic preferences and equilibria while perturbing learning dynamics. Gradient audits confirm the intended routing pathways, and frozen-policy torso perturbations probe whether route-induced updates align with local cooperation boundaries. In confirmatory MinEx and CleanUp-lite experiments, higher scales selectively increase maintenance sensitivity in X0; X1 remains near the censoring ceiling, and X5 has no confirmed events in the tested settings. In CleanUp-lite, route-by-scale displacement is associated with reduced local cooperation margins; MinEx shows a weaker, optimizer-dependent effect. These results identify a conditional, scale-sensitive maintenance risk associated with direct value-gradient routing rather than a universal failure of critics.

Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in high-dimension spaces. Recently, the gradient of log probability density (a.k.a., score) w.r.t. the sample is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two samples under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we propose an EPS-based adversarial detection (EPS-AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. We also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Extensive experiments show the superior adversarial detection performance of our EPS-AD.

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.

Recently, flat minima are proven to be effective for improving generalization and sharpness-aware minimization (SAM) achieves state-of-the-art performance. Yet the current definition of flatness discussed in SAM and its follow-ups are limited to the zeroth-order flatness (i.e., the worst-case loss within a perturbation radius). We show that the zeroth-order flatness can be insufficient to discriminate minima with low generalization error from those with high generalization error both when there is a single minimum or multiple minima within the given perturbation radius. Thus we present first-order flatness, a stronger measure of flatness focusing on the maximal gradient norm within a perturbation radius which bounds both the maximal eigenvalue of Hessian at local minima and the regularization function of SAM. We also present a novel training procedure named Gradient norm Aware Minimization (GAM) to seek minima with uniformly small curvature across all directions. Experimental results show that GAM improves the generalization of models trained with current optimizers such as SGD and AdamW on various datasets and networks. Furthermore, we show that GAM can help SAM find flatter minima and achieve better generalization.

Lowering the memory requirement in full-parameter training on large models has become a hot research area. MeZO fine-tunes the large language models (LLMs) by just forward passes in a zeroth-order SGD optimizer (ZO-SGD), demonstrating excellent performance with the same GPU memory usage as inference. However, the simulated perturbation stochastic approximation for gradient estimate in MeZO leads to severe oscillations and incurs a substantial time overhead. Moreover, without momentum regularization, MeZO shows severe over-fitting problems. Lastly, the perturbation-irrelevant momentum on ZO-SGD does not improve the convergence rate. This study proposes ZO-AdaMU to resolve the above problems by adapting the simulated perturbation with momentum in its stochastic approximation. Unlike existing adaptive momentum methods, we relocate momentum on simulated perturbation in stochastic gradient approximation. Our convergence analysis and experiments prove this is a better way to improve convergence stability and rate in ZO-SGD. Extensive experiments demonstrate that ZO-AdaMU yields better generalization for LLMs fine-tuning across various NLP tasks than MeZO and its momentum variants.

Medical image segmentation is a critical component of clinical workflows, enabling accurate diagnosis, treatment planning, and disease monitoring. However, despite the superior performance of transformer-based models over convolutional architectures, their limited interpretability remains a major obstacle to clinical trust and deployment. Existing explainable artificial intelligence (XAI) techniques, including gradient-based saliency methods and perturbation-based approaches, are often computationally expensive, require numerous forward passes, and frequently produce noisy or anatomically irrelevant explanations. To address these limitations, we propose XAI-CLIP, an ROI-guided perturbation framework that leverages multimodal vision-language model embeddings to localize clinically meaningful anatomical regions and guide the explanation process. By integrating language-informed region localization with medical image segmentation and applying targeted, region-aware perturbations, the proposed method generates clearer, boundary-aware saliency maps while substantially reducing computational overhead. Experiments conducted on the FLARE22 and CHAOS datasets demonstrate that XAI-CLIP achieves up to a 60\% reduction in runtime, a 44.6\% improvement in dice score, and a 96.7\% increase in Intersection-over-Union for occlusion-based explanations compared to conventional perturbation methods. Qualitative results further confirm cleaner and more anatomically consistent attribution maps with fewer artifacts, highlighting that the incorporation of multimodal vision-language representations into perturbation-based XAI frameworks significantly enhances both interpretability and efficiency, thereby enabling transparent and clinically deployable medical image segmentation systems.

Wasserstein gradient flow extends gradient descent to probability measures. Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems. We investigate when its approximation by finitely many interacting particles remains accurate over growing time horizons. Our analysis retains the curvature accumulated along the population-driven reference path: negative curvature can amplify approximation errors, while subsequent positive curvature can damp their influence. This captures favorable scenarios in which temporary instability is compatible with accurate tracking over growing horizons. Under regularity assumptions and a prescribed common perturbation schedule, we prove particle and objective-value tracking bounds on a high-probability event for reference paths satisfying explicit conditions on accumulated curvature. To handle state-dependent Gaussian jumps, we construct a population-first coupling that preserves the reference particles' conditional independence and reduces jump errors to covariance comparison. We verify the conditions in a variance-plus-cosine model, where curvature recovery yields a growing-horizon tracking guarantee. We also establish local attraction, transverse descent, and positive second variation in two regions of a regularized matrix-factorization model, motivating a positive-negative-positive curvature pattern.

Geometric alignment scores based on Gram determinants provide a compact way to model higher-order consistency among modalities, yet how such scores respond to modality degradation is poorly understood. This paper asks whether the response of a multimodal geometric score is determined primarily by the magnitude of the perturbation-induced displacement. Using frozen cohorts from MSR-VTT (N=878) and DiDeMo (N=980), we apply controlled video blur and audio noise and analyze the response in the relational geometry on which the score is defined. Displacement magnitude explains at most 15% of the out-of-sample variance in the absolute response, and magnitude-matched pairs respond systematically differently, so scalar magnitude does not organize the response. The closed-form first-order expansion of the Gramian volume yields the Directional Geometric Response (DGR): the projection of the displacement onto the local volume gradient, which jointly captures the clean operating point, displacement magnitude, and displacement direction. The absolute first-order DGR term explains the observed response with out-of-sample R^2 of 0.838-0.969, matched-magnitude ranking accuracies of 0.864-0.963, and response-sign accuracies of 0.909-0.989, whereas the tested direction-free alternatives remain weak or unstable under the corresponding evaluation protocols. A pre-specified gain-normalization candidate, V/(g_V+eps), fails its predictability and clean-order gates. DGR uses the observed degraded-state displacement and is therefore an explanatory quantity, not a deployment-time predictor: geometric response depends on where the representation operates, how far degradation moves the relational geometry, and in which direction it moves.

Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

Most existing works focus on improving robustness against adversarial attacks bounded by a single l_p norm using adversarial training (AT). However, these AT models' multiple-norm robustness (union accuracy) is still low, which is crucial since in the real-world an adversary is not necessarily bounded by a single norm. The tradeoffs among robustness against multiple l_p perturbations and accuracy/robustness make obtaining good union and clean accuracy challenging. We design a logit pairing loss to improve the union accuracy by analyzing the tradeoffs from the lens of distribution shifts. We connect natural training (NT) with AT via gradient projection, to incorporate useful information from NT into AT, where we empirically and theoretically show it moderates the accuracy/robustness tradeoff. We propose a novel training framework RAMP, to boost the robustness against multiple l_p perturbations. RAMP can be easily adapted for robust fine-tuning and full AT. For robust fine-tuning, RAMP obtains a union accuracy up to 53.3% on CIFAR-10, and 29.1% on ImageNet. For training from scratch, RAMP achieves a union accuracy of 44.6% and good clean accuracy of 81.2% on ResNet-18 against AutoAttack on CIFAR-10. Beyond multi-norm robustness RAMP-trained models achieve superior universal robustness, effectively generalizing against a range of unseen adversaries and natural corruptions.

Density peak clustering (DPC) connects each observation to its nearest neighbor of higher density and identifies cluster centers as high-density observations with unusually large nearest neighbor uphill shifts. The resulting uphill paths from observations to cluster centers, however, can be irregular and unstable in low-density regions, making the clustering assignments sensitive to local perturbations and obscuring the population geometry of the DPC graph. In this paper, we introduce gradient-guided density peak clustering (GGDPC), which performs a gradient ascent step before each nearest neighbor uphill search. We develop a stability theory that relates the GGDPC graph to the gradient ascent flow of the population density. In particular, we establish consistency of GGDPC under five complementary criteria: recovery of local modes, adjusted Rand index, dendrogram (cluster tree), path length, and waterfall measure. Together, these results provide new statistical, geometric, and topological interpretations of DPC-type clustering algorithms.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Multi-task learning (MTL) enables a joint model to capture commonalities across multiple tasks, reducing computation costs and improving data efficiency. However, a major challenge in MTL optimization is task conflicts, where the task gradients differ in direction or magnitude, limiting model performance compared to single-task counterparts. Sharpness-aware minimization (SAM) minimizes task loss while simultaneously reducing the sharpness of the loss landscape. Our empirical observations show that SAM effectively mitigates task conflicts in MTL. Motivated by these findings, we explore integrating SAM into MTL but face two key challenges. While both the average loss gradient and individual task gradients-referred to as global and local information-contribute to SAM, how to combine them remains unclear. Moreover, directly computing each task gradient introduces significant computational and memory overheads. To address these challenges, we propose SAMO, a lightweight Sharpness-Aware Multi-task Optimization approach, that leverages a joint global-local perturbation. The local perturbations are approximated using only forward passes and are layerwise normalized to improve efficiency. Extensive experiments on a suite of multi-task benchmarks demonstrate both the effectiveness and efficiency of our method. Code is available at https://github.com/OptMN-Lab/SAMO.

Although attention mechanisms have been applied to a variety of deep learning models and have been shown to improve the prediction performance, it has been reported to be vulnerable to perturbations to the mechanism. To overcome the vulnerability to perturbations in the mechanism, we are inspired by adversarial training (AT), which is a powerful regularization technique for enhancing the robustness of the models. In this paper, we propose a general training technique for natural language processing tasks, including AT for attention (Attention AT) and more interpretable AT for attention (Attention iAT). The proposed techniques improved the prediction performance and the model interpretability by exploiting the mechanisms with AT. In particular, Attention iAT boosts those advantages by introducing adversarial perturbation, which enhances the difference in the attention of the sentences. Evaluation experiments with ten open datasets revealed that AT for attention mechanisms, especially Attention iAT, demonstrated (1) the best performance in nine out of ten tasks and (2) more interpretable attention (i.e., the resulting attention correlated more strongly with gradient-based word importance) for all tasks. Additionally, the proposed techniques are (3) much less dependent on perturbation size in AT. Our code is available at https://github.com/shunk031/attention-meets-perturbation

Large language models (LLMs) are increasingly trained with classical optimization techniques like AdamW to improve convergence and generalization. However, the mechanisms by which quantum-inspired methods enhance classical training remain underexplored. We introduce Superpositional Gradient Descent (SGD), a novel optimizer linking gradient updates with quantum superposition by injecting quantum circuit perturbations. We present a mathematical framework and implement hybrid quantum-classical circuits in PyTorch and Qiskit. On synthetic sequence classification and large-scale LLM fine-tuning, SGD converges faster and yields lower final loss than AdamW. Despite promising results, scalability and hardware constraints limit adoption. Overall, this work provides new insights into the intersection of quantum computing and deep learning, suggesting practical pathways for leveraging quantum principles to control and enhance model behavior.

Jailbreak attacks on audio language models (ALMs) optimize audio perturbations to elicit unsafe generations, and they typically update the entire waveform densely throughout optimization. In this work, we investigate the necessity of such dense optimization by analyzing the structure of token-aligned gradients in ALMs. We find that gradient energy is highly non-uniform across audio tokens, indicating that only a small subset of token-aligned audio regions dominates the optimization signal. Motivated by this observation, we propose Token-Aware Gradient Optimization (TAGO), which enables sparse jailbreak optimization by retaining only waveform gradients aligned with audio tokens that have high gradient energy, while masking the remaining gradients at each iteration. Across three ALMs, TAGO outperforms baselines, and substantial sparsification preserves strong attack success rates (e.g. on Qwen3-Omni, ASR_{l} remains at 86% with a token retention ratio of 0.25, compared to 87% with full token retention). These results demonstrate that dense waveform updates are largely redundant, and we advocate that future audio jailbreak and safety alignment research should further leverage this heterogeneous token-level gradient structure.

This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.

Modern training on a new task often starts from a previously trained model rather than from scratch, raising the question of how this initialization affects the subsequent training trajectory. Classical implicit-bias results characterize the direction selected by prolonged training, but this direction alone does not provide information regarding the intermediate behavior. We address this question through a geometric approximation of full-batch logistic gradient descent (GD) trajectories on strictly linearly separable data, with large initialization of scale R motivated by prior training. From any limiting normalized initial position, we use minimum-norm projection rules to construct a unique continuous ideal path consisting of finitely many linear segments. The path has two stages: negative-margin correction followed by minimum-margin growth. We prove that, after an explicit two-stage time reparameterization, the fixed-step GD trajectory divided by R converges uniformly to this path on every fixed parameter interval as Rtoinfty. Further, our quantitative error bounds account for initialization perturbations and the transition between stages. This approximation provides asymptotic formulas for peak evaluation loss and cumulative training loss. In particular, peak evaluation loss can grow linearly in R even when both endpoint losses tend to zero. The cumulative losses in the correction and margin-growth stages, normalized by R^2 and R, respectively, converge to explicit limits. Experiments on controlled geometries and fixed image features complement our theoretical results.

Planning effective interventions in biological systems requires treatment-effect models that adapt to unseen biological contexts by identifying their specific underlying mechanisms. Yet single-cell perturbation datasets span only a handful of biological contexts, and existing methods cannot leverage new interventional evidence at inference time to adapt beyond their training data. To meta-learn a perturbation effect estimator, we present MapPFN, a prior-data fitted network (PFN) pretrained on synthetic data generated from a prior over causal perturbations. Given a set of experiments, MapPFN uses in-context learning to predict post-perturbation distributions, without gradient-based optimization. Despite being pretrained on in silico gene knockouts alone, MapPFN identifies differentially expressed genes, matching the performance of models trained on real single-cell data. Our code and data are available at https://github.com/marvinsxtr/MapPFN.

Feature attribution (FA) methods are common post-hoc approaches that explain how Large Language Models (LLMs) make predictions. Accordingly, generating faithful attributions that reflect the actual inner behavior of the model is crucial. In this paper, we introduce Noiser, a perturbation-based FA method that imposes bounded noise on each input embedding and measures the robustness of the model against partially noised input to obtain the input attributions. Additionally, we propose an answerability metric that employs an instructed judge model to assess the extent to which highly scored tokens suffice to recover the predicted output. Through a comprehensive evaluation across six LLMs and three tasks, we demonstrate that Noiser consistently outperforms existing gradient-based, attention-based, and perturbation-based FA methods in terms of both faithfulness and answerability, making it a robust and effective approach for explaining language model predictions.

Video large language models (Video LLMs) often generate responses unsupported by the input video. Contrastive decoding (CD) can mitigate these hallucinations, but its effectiveness depends on how the negative branch weakens visual evidence. Existing methods rely on predefined perturbations or masking guided by question reconstruction, offering limited control over the model's visual reliance during answer generation. We introduce Attention-guided Representation Perturbation for Contrastive Decoding (ARP-CD), a training-free framework for constructing contrastive negatives directly in representation space. ARP-CD uses the attention mass assigned to visual tokens at the answer-prediction position to guide bounded gradient updates of the language model's input visual hidden states. These updates reduce visual attention and produce a negative input, whose predictions are contrasted with those of the original branch throughout generation. Experiments across four Video LLMs and four benchmarks show that ARP-CD outperforms representative training-free baselines in most model--benchmark settings, reducing hallucinations while improving general video understanding. Further analyses show that attention-guided perturbation directions improve negative quality and that the resulting negatives provide effective contrastive references for correcting the original predictions.

Large Language Models (LLMs) have proven their exceptional capabilities in performing language-related tasks. However, their deployment poses significant challenges due to their considerable memory and storage requirements. In response to this issue, weight-only quantization, particularly 3 and 4-bit weight-only quantization, has emerged as one of the most viable solutions. As the number of bits decreases, the quantization grid broadens, thus emphasizing the importance of up and down rounding. While previous studies have demonstrated that fine-tuning up and down rounding with the addition of perturbations can enhance accuracy in some scenarios, our study is driven by the precise and limited boundary of these perturbations, where only the threshold for altering the rounding value is of significance. Consequently, we propose a concise and highly effective approach for optimizing the weight rounding task. Our method, named SignRound, involves lightweight block-wise tuning using signed gradient descent, enabling us to achieve outstanding results within 400 steps. SignRound outperforms the established baseline of rounding-to-nearest (RTN) and competes impressively against recent methods, without introducing additional inference overhead. The source code will be publicly available at https://github.com/intel/neural-compressor soon.

Interpretability is an emerging area of research in trustworthy machine learning. Safe deployment of machine learning system mandates that the prediction and its explanation be reliable and robust. Recently, it has been shown that the explanations could be manipulated easily by adding visually imperceptible perturbations to the input while keeping the model's prediction intact. In this work, we study the problem of attributional robustness (i.e. models having robust explanations) by showing an upper bound for attributional vulnerability in terms of spatial correlation between the input image and its explanation map. We propose a training methodology that learns robust features by minimizing this upper bound using soft-margin triplet loss. Our methodology of robust attribution training (ART) achieves the new state-of-the-art attributional robustness measure by a margin of approx 6-18 % on several standard datasets, ie. SVHN, CIFAR-10 and GTSRB. We further show the utility of the proposed robust training technique (ART) in the downstream task of weakly supervised object localization by achieving the new state-of-the-art performance on CUB-200 dataset.

We analyse the boundary behaviour of the gradient of the torsion function w_Om in convex domains OmsubsetR^d. We prove that its L^infty-norm is attained at a boundary point and establish the stability of this norm under general (convex) perturbations. For problems of the form $sup{|nabla w_{Om}|_infty: Om subset R^d,open, bounded and convex, G(Om)=m}, where G is either volume or perimeter, we show the existence of maximisers which are C^1-smooth, rotationally symmetric about an axis and contain a (d-1)$- dimensional ball (of estimated size) in their boundary. Other constraints, whether geometric (such as diameter or circumradius) or variational (such as torsion or first Dirichlet eigenvalue), are also briefly discussed, and some of their characteristic behaviours are highlighted.

Spacetime singularities displayed by classical black hole solutions are expected to be cured by high-energy effects, beyond the regime of validity of General Relativity. On the other hand, there are well-known examples of classical theories allowing for nonsingular black hole solutions. The most prominent is obtained by complementing the gravitational sector of General Relativity with a minimally coupled nonlinear-electrodynamics sector. It has recently been shown that purely electric/purely magnetic nonsingular black holes in an Einstein-nonlinear-electrodynamics setup are always plagued by a gradient instability. In this work, we derive the quadratic action for linear perturbations of static, spherically symmetric dyonic solutions of Einstein-nonlinear-electrodynamics theories with a general dependence on both invariants. We show that regularity of the center, absence of ghosts and angular gradient stability cannot hold simultaneously: arbitrarily close to a regular center, at least one photon polarization has a negative squared angular propagation speed. We further show that regularity drives one electromagnetic kinetic eigenvalue to zero at the center, which may limit perturbative control near the core. Evading the obstruction requires extending the theory, for example by introducing additional degrees of freedom.

Visual deep reinforcement learning (RL) enables robots to acquire skills from visual input for unstructured tasks. However, current algorithms suffer from low sample efficiency, limiting their practical applicability. In this work, we present MENTOR, a method that improves both the architecture and optimization of RL agents. Specifically, MENTOR replaces the standard multi-layer perceptron (MLP) with a mixture-of-experts (MoE) backbone, enhancing the agent's ability to handle complex tasks by leveraging modular expert learning to avoid gradient conflicts. Furthermore, MENTOR introduces a task-oriented perturbation mechanism, which heuristically samples perturbation candidates containing task-relevant information, leading to more targeted and effective optimization. MENTOR outperforms state-of-the-art methods across three simulation domains -- DeepMind Control Suite, Meta-World, and Adroit. Additionally, MENTOR achieves an average of 83% success rate on three challenging real-world robotic manipulation tasks including peg insertion, cable routing, and tabletop golf, which significantly surpasses the success rate of 32% from the current strongest model-free visual RL algorithm. These results underscore the importance of sample efficiency in advancing visual RL for real-world robotics. Experimental videos are available at https://suninghuang19.github.io/mentor_page.

Adversarial optimization under a shared ell_1 budget requires deciding not only how much perturbation to use, but also where that limited budget should be spent. This allocation problem becomes particularly important when individual input coordinates are subject to local magnitude constraints, which restrict the extent to which perturbation can be concentrated on a small number of locations. We introduce an importance-guided allocation mechanism that uses a fixed clean-gradient prior to steer perturbation toward model-sensitive regions while leaving the feasible perturbation set unchanged. A centered allocation objective encourages perturbation at above-average importance locations and discourages unnecessary expenditure elsewhere, thereby redistributing rather than enlarging the available budget. Across ten robust model--dataset configurations under a common capacity-limited threat setting, the proposed method improves attack success over matched APGD- and PMA-based baselines by 2.52 to 17.70 percentage points. Allocation analysis shows that these gains are accompanied by substantially greater perturbation mass in high-importance regions without increased global ell_1 consumption. Mechanism ablations further show that centered non-uniform redistribution provides part of the benefit, while model-derived importance yields an additional improvement. These results identify perturbation allocation as a distinct and practically relevant dimension of adversarial optimization under shared-budget, locally constrained threat models.

This paper presents a JAX-Python implementation of the galaxy power spectrum up to one-loop order in the effective field theory of large-scale structure, based on both the Eulerian and Lagrangian perturbation theories. The code uses JAX to enable automatic differentiation with respect to parameters such as cosmology, galaxy bias, or counterterm coefficients. This facilitates applications such as parameter inference using the gradient of the posterior, e.g., Hamiltonian Monte Carlo sampling. The code can compute both the EPT and LPT power spectra in a few milliseconds on a GPU, after just-in-time compilation. We also identify the various sources of numerical errors associated with discretization, and design the numerical implementation to minimize them, achieving relative errors of order 0.01% at scales k lesssim 1, h, Mpc^{-1}, compared with brute-force numerical integration. Notably, this is the first auto-differentiable implementation of the one-loop galaxy power spectrum based on LPT. The natural resummation of the long-wavelength displacements in LPT further makes the code well suited for applications involving features in the power spectrum beyond the standard BAO feature, including primordial features. Our code, elf, is publicly available.

While open-weight models have enjoyed steady progress in capabilities and wide adoption across multiple domains, their safety remains an important concern. One key feature is the ability to refuse or deflect harmful, malicious, or insensitive prompts. In this paper, we expose safety vulnerabilities across six common open-weight LLMs of various sizes that consistently lead to harmful or unsafe responses on the JailbreakBench benchmark dataset. Our proposed attack, Perturbed Embedding Vector (PEV), is a simple and fast "jailbreaking" technique that is cheaper than prior approaches, which typically require gradient computations, per-prompt optimizations, or altering internal weights of the models. PEV just adds independent Gaussian noise in the embedding vector representations of the prompt, with no need for further manipulations. To generate unsafe responses, we repeatedly sample additive noise from this distribution. In our experiments, we observe that the average compute cost to get the first successful attack is up to an order of magnitude less than previous attacks. The first successful jailbreak on a new prompt typically arrives within one minute on every tested model, and PEV generates unsafe responses across all models for all prompts in JailbreakBench. No other tested method achieves such results, despite them taking longer to run. More broadly, we believe that understanding the behavior of LLMs under perturbations in the embedding vectors is an important research direction: while perturbations constitute a major security risk, they can also serve as a valuable tool for exploring the dynamical behavior of such models.

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

Predicting cellular responses to unseen chemical perturbations is challenging due to unknown targets and mechanisms, high-dimensional expression responses, and limited experimental coverage of the large small-molecule design space. We propose PerturbPFN, a PFN-style amortized model for unknown-target perturbation prediction under a hierarchical synthetic structural prior. Instead of directly regressing high-dimensional expression responses, PerturbPFN infers a latent system graph, sparse atomic intervention targets, and intervention strengths, then propagates their effects through an SCM decoder. The model is trained entirely on prior-predictive synthetic episodes generated from biologically motivated graph and expression simulators, enabling structured in-context learning without test-time gradient updates. We evaluate PerturbPFN on both real single-cell perturbation data and synthetic benchmarks, covering effect prediction, target identification, and regulatory structure discovery. Our results show that PerturbPFN offers a complementary trade-off to specialized baselines, achieving competitive perturbation prediction with low inference cost while exposing interpretable intermediate estimates of targets, strengths, and system structure.

Several published comparisons of variational quantum optimizers time only runs that reach a target loss, or read the verdict at a single target. Either convention could decide whether an optimizer's costlier steps pay off. We measure how much each convention changes verdicts among Adam, simultaneous perturbation stochastic approximation (SPSA) and quantum natural gradient (QNG), on initializations held out from the selection of settings. We compute the exact metric that preconditions QNG, price every step in circuit evaluations and give every method the same budget. In a median pooled over circuit widths, cost families and a sweep of settings with common misses, SPSA needs more than twice Adam's evaluations to reach a loose target. Dropping the censored runs that miss the target hides this gap. On the global-cost family we hold fixed the settings selected for a strict target. QNG then usually reaches the loose target after Adam but the strict target first. QNG's strict-target lead disappears when the metric's simulator price, linear in the number of parameters, is replaced by an assumed hardware count quadratic in that number. We recommend charging every miss the budget and reporting verdicts across targets.

Training Data Attribution (TDA) seeks to trace a model's predictions back to its training data. The gold standard for TDA relies on causal interventions, observing how a model changes when data is added or removed, but repeated retraining is computationally challenging for Large Language Models (LLMs). Consequently, most approaches approximate this effect in the parameter space using gradients. However, tracking gradients across billions of parameters is not only prohibitively expensive but relies on local approximations. In this work, we propose a shift: rather than estimating parameter changes, we model the functional effect of training data in the activation space. We introduce STRIDE (Steering-based Training Data Influence Decomposition), a framework that formulates TDA as a sparse recovery problem in the spirit of compressive sensing. STRIDE learns lightweight "steering operators" that mimic the behavioral shift caused by training on data subsets. By measuring how these operators perturb test predictions, we recover individual training example influences via sparse linear decomposition. STRIDE achieves state-of-the-art for LLM pre-training attribution while being an order of magnitude (13times) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative analysis.

Discovering stable neuron behavior across entire domains remains a challenge in mechanistic interpretability. Existing methods often rely on instance-level point estimates or computationally expensive procedures, which either obscure population-level variability or limit scalable domain-wide analysis. We present RACE (Residual Alignment for Consistency Estimation), a forward-pass statistical framework that evaluates the domain-wide functional consistency of Transformer neurons. Perturbation experiments demonstrate that RACE achieves superior domain specificity compared to gradient-based point estimates. Meanwhile, token-distribution-level results verify the association between the selected neurons and the target domain. Furthermore, its computational overhead is two orders of magnitude lower than that of gradient-based methods.

Variational Quantum Algorithms (VQAs) rely heavily on classical optimization routines to navigate high-dimensional, noisy parameter landscapes. However, the evaluation of analytical gradients via the parameter-shift rule requires O(p) circuit executions, rendering this approach computationally prohibitive for deep circuits. While simultaneous perturbation methods provide an O(1) alternative, their gradient estimates suffer from severe O(p) spatial variance, which impedes convergence. To resolve this tension, we introduce the Cached Recycled Variance-Reduced Gradient (CRVG) by leveraging variance reduction techniques. We formulate two variants: a 3-Circuit (1-Sided) Non-Recursive CRVG and a Recursive CRVG. By introducing a center-point caching mechanism, the 3-Circuit CRVG mathematically recycles quantum measurements to reduce the inner-loop circuit complexity by 25\% across both variants. We establish a theoretical separation between the two routing paths to achieve an ε^2-stationary point: the non-recursive variant reaches a sample complexity of O(max{p/ε^2, p^{2/3}/ε^{10/3}}), while the recursive variant achieves an improved complexity of O(max{p/ε^2, p/ε^3}). Empirically, extensive evaluations on MaxCut and Maximum Independent Set (MIS) benchmarks validate these findings. While standard simultaneous perturbation remains a robust baseline across varying depths, CRVG demonstrates targeted advantages in specific amortizable regimes, such as the non-recursive variant on EfficientSU2 circuits and both variants on depth-three QAOA, yielding superior energy minimums and tighter output variances. Ultimately, CRVG establishes a principled bias-throughput trade-off for scaling near-term quantum optimization.

We study the Cauchy problem for the one-dimensional isothermal compressible Navier--Stokes system with the van der Waals equation of state, and analyze the well-posedness and asymptotic stability of steady-state phase-transition solutions at subcritical temperatures. Working in Lagrangian coordinates, we use variational techniques to construct piecewise smooth steady-state solutions corresponding to two-phase equilibrium states under finite-mass perturbations. Introducing artificial-viscosity regularization, we first establish existence of the global minimizer of the regularized variational problem, unique within each fixed symmetry class; passing to the vanishing artificial-viscosity limit then yields a physically admissible steady-state solution with two phase interfaces. For initial perturbations that are small with respect to energy, piecewise-gradient, total-variation, and integral norms but may exhibit large pointwise jumps across phase boundaries, we derive uniform a priori bounds for weak solutions near the two-phase equilibrium profile. We further prove that these global weak solutions converge to the steady-state two-phase equilibrium in L^infty(R) as ttoinfty, thereby characterizing their large-time asymptotic behavior. Physically, finite mass perturbations break the uniqueness of the uniform steady state and generate infinitely many piecewise constant two-phase equilibria satisfying the Maxwell equal-area rule. Artificial viscosity acts as a selection principle that singles out the physically relevant two-interface steady-state configuration, and this two-phase equilibrium is asymptotically stable under small integral perturbations that allow large-amplitude discontinuities at phase interfaces.

Traditional white-box methods for creating adversarial perturbations against LLMs typically rely only on gradient computation from the targeted model, ignoring the internal mechanisms responsible for attack success or failure. Conversely, interpretability studies that analyze these internal mechanisms lack practical applications beyond runtime interventions. We bridge this gap by introducing a novel white-box approach that leverages mechanistic interpretability techniques to craft practical adversarial inputs. Specifically, we first identify acceptance subspaces - sets of feature vectors that do not trigger the model's refusal mechanisms - then use gradient-based optimization to reroute embeddings from refusal subspaces to acceptance subspaces, effectively achieving jailbreaks. This targeted approach significantly reduces computation cost, achieving attack success rates of 80-95\% on state-of-the-art models including Gemma2, Llama3.2, and Qwen2.5 within minutes or even seconds, compared to existing techniques that often fail or require hours of computation. We believe this approach opens a new direction for both attack research and defense development. Furthermore, it showcases a practical application of mechanistic interpretability where other methods are less efficient, which highlights its utility. The code and generated datasets are available at https://github.com/Sckathach/subspace-rerouting.

Analysis of 3D segmentation models, especially in the context of medical imaging, is often limited to segmentation performance metrics that overlook the crucial aspect of explainability and bias. Currently, effectively explaining these models with saliency maps is challenging due to the high dimensions of input images multiplied by the ever-growing number of segmented class labels. To this end, we introduce Agg^2Exp, a methodology for aggregating fine-grained voxel attributions of the segmentation model's predictions. Unlike classical explanation methods that primarily focus on the local feature attribution, Agg^2Exp enables a more comprehensive global view on the importance of predicted segments in 3D images. Our benchmarking experiments show that gradient-based voxel attributions are more faithful to the model's predictions than perturbation-based explanations. As a concrete use-case, we apply Agg^2Exp to discover knowledge acquired by the Swin UNEt TRansformer model trained on the TotalSegmentator v2 dataset for segmenting anatomical structures in computed tomography medical images. Agg^2Exp facilitates the explanatory analysis of large segmentation models beyond their predictive performance.

Adversarial text attacks remain a persistent threat to transformer models, yet existing defenses are typically attack-specific or require costly model retraining. We introduce Representation Stability (RS), a model-agnostic detection framework that identifies adversarial examples by measuring how embedding representations change when important words are masked. RS first ranks words using importance heuristics, then measures embedding sensitivity to masking top-k critical words, and processes the resulting patterns with a BiLSTM detector. Experiments show that adversarially perturbed words exhibit disproportionately high masking sensitivity compared to naturally important words. Across three datasets, three attack types, and two victim models, RS achieves over 88% detection accuracy and demonstrates competitive performance compared to existing state-of-the-art methods, often at lower computational cost. Using Normalized Discounted Cumulative Gain (NDCG) to measure perturbation identification quality, we reveal that gradient-based ranking outperforms attention and random selection approaches, with identification quality correlating with detection performance for word-level attacks. RS also generalizes well to unseen datasets, attacks, and models without retraining, providing a practical solution for adversarial text detection.

Intermittent Androgen Suppression (IAS) is a treatment strategy for delaying or even preventing time to relapse of advanced prostate cancer. IAS consists of alternating cycles of therapy (in the form of androgen suppression) and off-treatment periods. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. In spite of extensive recent clinical experience with IAS, the design of an ideal protocol for any given patient remains one of the main challenges associated with effectively implementing this therapy. We use a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We apply Infinitesimal Perturbation Analysis (IPA) to a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and derive unbiased estimators of the cost metric gradient with respect to various model and therapy parameters. These estimators are subsequently used for system analysis. By evaluating sensitivity estimates with respect to several model parameters, we identify critical parameters and demonstrate that relaxing the optimality condition in favor of increased robustness to modeling errors provides an alternative objective to therapy design for at least some patients.

Hardware-aware training (HAT) is widely used to improve the robustness of neural networks on non-ideal AI accelerators, such as analog in-memory computing (IMC) systems. However, not all hardware-induced distortions are equally compensable by training. This paper presents a diagnostic framework that models hardware non-idealities as structured perturbations of the forward operator and evaluates their compatibility with gradient-based optimization. We analyze six representative perturbation classes--read noise, variability, drift, stuck-at faults, IR-drop, and ADC discretization--and identify three key diagnostics: gradient expectation consistency, bounded gradient variance, and non-degenerate sensitivity. Our results show a clear separation between perturbations that can be compensated by HAT and those that consistently break optimization. This provides practical guidance for hardware-software co-design, clarifying which non-idealities can be addressed at the training level and which require circuit-, architecture-, or calibration-level mitigation. This study should be interpreted as a controlled empirical analysis under vanilla forward-perturbation HAT, rather than as a universal theory of hardware-aware training.

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.

Vision Language Models (VLMs) have recently emerged as a critical component of multimodal AI systems, enabling joint reasoning over visual and textual inputs in real-world and safety-critical applications. Despite their growing deployment, the robustness of VLMs against adversarial threats remains insufficiently explored, particularly in the context of evasion attacks targeting multimodal alignment. In this work, we investigate the vulnerability of VLMs to adversarial perturbations applied to visual inputs and study two attack settings: untargeted attacks, where the goal is to disrupt the model's interpretation of the original image, and targeted attacks, where the adversary aims to force the model to generate a specific semantic description unrelated to the original image. To efficiently generate adversarial examples, we propose a gradient-based attack method that performs optimization exclusively on the vision encoder of the VLM rather than on the entire multimodal architecture. This design significantly reduces the computational cost and resource requirements of the attack while maintaining strong effectiveness. We evaluate our approach on several open-source VLMs, including Qwen2.5-VL, Granite-Vision, FastVLM, and Phi-3.5-Vision, and show that small, human-imperceptible perturbations can substantially alter the textual interpretation produced by the models. Our findings highlight the vulnerability of modern VLMs to adversarial manipulation and emphasize the need for improved robustness and security mechanisms in multimodal AI systems.

Fine-tuning large language models (LLMs) remains resource-intensive due to their sheer scale. While zeroth-order (ZO) optimization provides a memory-efficient alternative by eliminating backward passes, its application to multi-hundred-billion-parameter models is constrained by GPU memory and compute throughput. The ZO2 framework addresses the memory bottleneck by offloading model parameters to CPU memory and overlapping transformer block transfer with dual forward computation on a single GPU. However, ZO2 remains limited by its single-device execution and achieves modest throughput. In this work, we present DistZO2, a high-throughput, memory-efficient framework for distributed zeroth-order fine-tuning of LLMs. DistZO2 introduces three parallel strategies: (1) Perturbation Parallelism (PertP), which parallelizes the two perturbed forward passes across devices; (2) Distributed Data Parallelism (DDP), adapted to the scalar-gradient nature of ZO training; and (3) a unified 2D Parallelism design that combines PertP and DDP. To further mitigate communication bottlenecks introduced by parameter offloading, we propose a hardware-aware communication strategy that slices parameter blocks and redistributes them across GPUs via high-speed interconnects such as NVLink. DistZO2 scales zeroth-order fine-tuning to modern multi-GPU systems, preserving ZO2's memory efficiency while substantially improving training throughput. In our experiments on OPT-175B, DistZO2 achieves a 3x speedup over ZO2 with distributed computing. DistZO2's code has been open-sourced in https://github.com/liangyuwang/zo2.

Modern video generative models produce visually impressive results, yet frequently violate basic physical principles. We propose Proprio, a training-free framework that enables a frozen video generator to assess and improve the physical plausibility of its own outputs. Inspired by proprioception, the biological sense of one's own movement, Proprio treats the model's flow residual under controlled latent perturbations as a self-scoring signal. Samples that are better explained by the generator's learned dynamics induce smaller and more stable residuals. We aggregate this signal across timesteps and perturbations, focus it on motion-relevant regions with a dynamic spatiotemporal mask, and use it for best-of-N search, gradient-based self-refinement, or both. Across text-to-video and image-to-video benchmarks, Proprio consistently improves physical plausibility, outperforming VLM-based scoring, and external world-model baselines in several settings. With TurboWan2.2, Proprio improves Physics-IQ from 32.2 to 37.5 (+16.5%) and VideoPhy2-hard physical commonsense from 45.6 to 55.0 (+20.6%). Human evaluation further shows that raters prefer Proprio-selected or refined videos for physical plausibility in roughly two-thirds of comparisons. These results suggest that frozen video generators contain actionable internal signals for evaluating and improving the physical plausibility of their own outputs.

Recent advances in Audio-Language Models (ALMs) have significantly improved multimodal understanding capabilities. However, the introduction of the audio modality also brings new and unique vulnerability vectors. Previous studies have proposed jailbreak attacks that specifically target ALMs, revealing that defenses directly transferred from traditional audio adversarial attacks or text-based Large Language Model (LLM) jailbreaks are largely ineffective against these ALM-specific threats. To address this issue, we propose ALMGuard, the first defense framework tailored to ALMs. Based on the assumption that safety-aligned shortcuts naturally exist in ALMs, we design a method to identify universal Shortcut Activation Perturbations (SAPs) that serve as triggers that activate the safety shortcuts to safeguard ALMs at inference time. To better sift out effective triggers while preserving the model's utility on benign tasks, we further propose Mel-Gradient Sparse Mask (M-GSM), which restricts perturbations to Mel-frequency bins that are sensitive to jailbreaks but insensitive to speech understanding. Both theoretical analyses and empirical results demonstrate the robustness of our method against both seen and unseen attacks. Overall, \MethodName reduces the average success rate of advanced ALM-specific jailbreak attacks to 4.6% across four models, while maintaining comparable utility on benign benchmarks, establishing it as the new state of the art. Our code and data are available at https://github.com/WeifeiJin/ALMGuard.

Projector-based adversarial attack aims to project carefully designed light patterns (i.e., adversarial projections) onto scenes to deceive deep image classifiers. It has potential applications in privacy protection and the development of more robust classifiers. However, existing approaches primarily focus on individual classifiers and fixed camera poses, often neglecting the complexities of multi-classifier systems and scenarios with varying camera poses. This limitation reduces their effectiveness when introducing new classifiers or camera poses. In this paper, we introduce Classifier-Agnostic Projector-Based Adversarial Attack (CAPAA) to address these issues. First, we develop a novel classifier-agnostic adversarial loss and optimization framework that aggregates adversarial and stealthiness loss gradients from multiple classifiers. Then, we propose an attention-based gradient weighting mechanism that concentrates perturbations on regions of high classification activation, thereby improving the robustness of adversarial projections when applied to scenes with varying camera poses. Our extensive experimental evaluations demonstrate that CAPAA achieves both a higher attack success rate and greater stealthiness compared to existing baselines. Codes are available at: https://github.com/ZhanLiQxQ/CAPAA.

Contrastive learning and Siamese embedding models have become the foundation of modern verification systems, where decisions are governed not by discrete classification boundaries, but by relational geometry in embedding space. However, existing adversarial attacks remain fundamentally classification-centric, overlooking the vulnerability of relational geometry. In this paper, we introduce a geometry-aware adversarial attack framework that reformulates attacks on contrastive systems as manifold-level relational corruption. Instead of targeting individual predictions, the proposed framework systematically distorts similarity organization within the embedding manifold by pushing positive pairs apart while simultaneously pulling negative pairs closer, ultimately collapsing and inverting pairwise similarity structure. To enable scalable deployment, we shift iterative online optimization into an offline adversarial geometry deformation prior learning stage and train a lightweight feed-forward generator that learns generalized geometry deformation patterns from the victim model. Once trained, the generator produces adversarial perturbations through a single forward pass without requiring online gradient computation, enabling real-time online attacks against similarity-based verification systems. Experimental results across multiple verification architectures demonstrate substantial degradation of verification performance together with severe manifold-level relational corruption. On the Markmatch verification system, the proposed attack reduces accuracy from 95.4% to 38.6% while completely reversing the positive-negative similarity structure.

A cumulative variational framework for solid deformation is proposed. Its central organizing principle is the recursive combination of three structural components of one material body: a compatible Cosserat component, a distributed-incompatibility component, and a defect-source component. At any prescribed external condition these components constitute a combined material state. They are governed under common physical boundary and initial conditions and are coupled through one cumulative energy and the associated field equations. They are not separate boundary-value problems and need not appear in a prescribed temporal sequence. The cumulative character of the framework concerns the response of the combined state to variation of externally prescribed conditions. For the special case of an initially perfect body, loss of stability may produce successive branches with defect and then source participation. Such a sequence is a bifurcation property of the selected initial state and constitutive energy, rather than a defining hierarchy of the framework. A one-dimensional specialization illustrates structural bifurcation, residual deformation and residual stress produced by retained structure, dependence on the initial combined state, directional memory under reverse loading, parametric cumulative hysteresis, and changes of observable tangent stiffness associated with structural stabilization. A spatial extension introduces defect and source gradient terms and yields a size-dependent structural stability operator. For the stable quartic energy considered, the gradient terms regularize nonuniform perturbations but do not by themselves generate a finite-wavelength localization instability on an already stable three-component branch. The examples thereby distinguish consequences of the cumulative structure and energy from phenomena requiring additional constitutive evolution laws.

With the surge of large-scale pre-trained models (PTMs), fine-tuning these models to numerous downstream tasks becomes a crucial problem. Consequently, parameter efficient transfer learning (PETL) of large models has grasped huge attention. While recent PETL methods showcase impressive performance, they rely on optimistic assumptions: 1) the entire parameter set of a PTM is available, and 2) a sufficiently large memory capacity for the fine-tuning is equipped. However, in most real-world applications, PTMs are served as a black-box API or proprietary software without explicit parameter accessibility. Besides, it is hard to meet a large memory requirement for modern PTMs. In this work, we propose black-box visual prompting (BlackVIP), which efficiently adapts the PTMs without knowledge about model architectures and parameters. BlackVIP has two components; 1) Coordinator and 2) simultaneous perturbation stochastic approximation with gradient correction (SPSA-GC). The Coordinator designs input-dependent image-shaped visual prompts, which improves few-shot adaptation and robustness on distribution/location shift. SPSA-GC efficiently estimates the gradient of a target model to update Coordinator. Extensive experiments on 16 datasets demonstrate that BlackVIP enables robust adaptation to diverse domains without accessing PTMs' parameters, with minimal memory requirements. Code: https://github.com/changdaeoh/BlackVIP

Advances in multimodal pre-training have propelled object-level foundation models, such as Grounding DINO and Florence-2, in tasks like visual grounding and object detection. However, interpreting these models\' decisions has grown increasingly challenging. Existing interpretable attribution methods for object-level task interpretation have notable limitations: (1) gradient-based methods lack precise localization due to visual-textual fusion in foundation models, and (2) perturbation-based methods produce noisy saliency maps, limiting fine-grained interpretability. To address these, we propose a Visual Precision Search method that generates accurate attribution maps with fewer regions. Our method bypasses internal model parameters to overcome attribution issues from multimodal fusion, dividing inputs into sparse sub-regions and using consistency and collaboration scores to accurately identify critical decision-making regions. We also conducted a theoretical analysis of the boundary guarantees and scope of applicability of our method. Experiments on RefCOCO, MS COCO, and LVIS show our approach enhances object-level task interpretability over SOTA for Grounding DINO and Florence-2 across various evaluation metrics, with faithfulness gains of 23.7\%, 31.6\%, and 20.1\% on MS COCO, LVIS, and RefCOCO for Grounding DINO, and 102.9\% and 66.9\% on MS COCO and RefCOCO for Florence-2. Additionally, our method can interpret failures in visual grounding and object detection tasks, surpassing existing methods across multiple evaluation metrics. The code will be released at https://github.com/RuoyuChen10/VPS.

Previous work has shown that well-crafted adversarial perturbations can threaten the security of video recognition systems. Attackers can invade such models with a low query budget when the perturbations are semantic-invariant, such as StyleFool. Despite the query efficiency, the naturalness of the minutia areas still requires amelioration, since StyleFool leverages style transfer to all pixels in each frame. To close the gap, we propose LocalStyleFool, an improved black-box video adversarial attack that superimposes regional style-transfer-based perturbations on videos. Benefiting from the popularity and scalably usability of Segment Anything Model (SAM), we first extract different regions according to semantic information and then track them through the video stream to maintain the temporal consistency. Then, we add style-transfer-based perturbations to several regions selected based on the associative criterion of transfer-based gradient information and regional area. Perturbation fine adjustment is followed to make stylized videos adversarial. We demonstrate that LocalStyleFool can improve both intra-frame and inter-frame naturalness through a human-assessed survey, while maintaining competitive fooling rate and query efficiency. Successful experiments on the high-resolution dataset also showcase that scrupulous segmentation of SAM helps to improve the scalability of adversarial attacks under high-resolution data.

Current LLM unlearning methods face a critical security vulnerability that undermines their fundamental purpose: while they appear to successfully remove sensitive or harmful knowledge, this ``forgotten" information remains precariously recoverable through relearning attacks. We identify that the root cause is that conventional methods optimizing the forgetting loss at individual data points will drive model parameters toward sharp minima in the loss landscape. In these unstable regions, even minimal parameter perturbations can drastically alter the model's behaviors. Consequently, relearning attacks exploit this vulnerability by using just a few fine-tuning samples to navigate the steep gradients surrounding these unstable regions, thereby rapidly recovering knowledge that was supposedly erased. This exposes a critical robustness gap between apparent unlearning and actual knowledge removal. To address this issue, we propose StableUN, a bi-level feedback-guided optimization framework that explicitly seeks more stable parameter regions via neighborhood-aware optimization. It integrates forgetting feedback, which uses adversarial perturbations to probe parameter neighborhoods, with remembering feedback to preserve model utility, aligning the two objectives through gradient projection. Experiments on WMDP and MUSE benchmarks demonstrate that our method is significantly more robust against both relearning and jailbreaking attacks while maintaining competitive utility performance.

Three important criteria of existing convolutional neural networks (CNNs) are (1) test-set accuracy; (2) out-of-distribution accuracy; and (3) explainability. While these criteria have been studied independently, their relationship is unknown. For example, do CNNs that have a stronger out-of-distribution performance have also stronger explainability? Furthermore, most prior feature-importance studies only evaluate methods on 2-3 common vanilla ImageNet-trained CNNs, leaving it unknown how these methods generalize to CNNs of other architectures and training algorithms. Here, we perform the first, large-scale evaluation of the relations of the three criteria using 9 feature-importance methods and 12 ImageNet-trained CNNs that are of 3 training algorithms and 5 CNN architectures. We find several important insights and recommendations for ML practitioners. First, adversarially robust CNNs have a higher explainability score on gradient-based attribution methods (but not CAM-based or perturbation-based methods). Second, AdvProp models, despite being highly accurate more than both vanilla and robust models alone, are not superior in explainability. Third, among 9 feature attribution methods tested, GradCAM and RISE are consistently the best methods. Fourth, Insertion and Deletion are biased towards vanilla and robust models respectively, due to their strong correlation with the confidence score distributions of a CNN. Fifth, we did not find a single CNN to be the best in all three criteria, which interestingly suggests that CNNs are harder to interpret as they become more accurate.

Adapting vision-language-action (VLA) models to deployment-time distribution shifts is important for reliable robotic operation, but conventional first-order adaptation can exceed the memory budget of inference-oriented deployment platforms. Zeroth-order (ZO) optimization offers a forward-only alternative with inference-level memory, but accurate gradient estimation requires many perturbation queries, making naive ZO prohibitively slow for large VLA models. We present VLA-ZO, a framework for fast ZO adaptation that exploits the structure of VLA computation. By confining adaptation to the action side, VLA-ZO keeps the expensive vision-language prefix frozen and reuses its conditioning states across perturbation queries and optimizer steps, while schedule-aware prefetching hides state-transfer overhead. On LIBERO camera-viewpoint shifts, VLA-ZO reduces end-to-end adaptation time by 25.59times at q=16 and 32.54times at q=64 relative to baseline ZO, while improving average task success from 48.27% without adaptation to 58.17% and 63.58%, respectively. These results show that making ZO faster can make larger query budgets practical, providing a promising path toward resource-efficient VLA adaptation on deployment platforms.

Reinforcement learning for flow-matching text-to-speech is complicated by deterministic ODE sampling: trajectory-level policy-gradient methods typically convert the ODE into an SDE and track per-step likelihood ratios, introducing stochastic perturbations and substantial overhead. We propose GROW, a group-relative advantage-weighted on-policy RL method that acts directly on the standard flow-matching objective. For each prompt, GROW samples a group of on-policy utterances, separately standardizes intelligibility and speaker-similarity rewards within the group, and combines them to reweight flow-matching regression. A Wasserstein-2 velocity penalty anchors the updated model to a frozen pretrained reference. A group-mean reward baseline is introduced to convert reward weighting into advantage weighting. For strong pretrained TTS models with concentrated rewards, positive exponential weighting is dominated by reward-agnostic self-imitation, whereas a zero-mean signed advantage preserves effective within-group credit assignment. Instantiated on DiTAR and evaluated on LibriSpeech and Seed-TTS EN/ZH, GROW reduces average WER from 2.016 to 1.558 and raises speaker similarity from 0.676 to 0.715 while keeping UTMOS. With 10-NFE training rollouts and 32-NFE evaluation, GROW retains comparable performance while training 2.9x faster than 32-NFE DiTAR-GRPO. We will open-source complete GROW codes, faithful DiTAR reproduction, and all model checkpoints.

Sparse-view computed tomography (CT) reduces radiation dose and acquisition time and may mitigate motion artifacts. However, angular undersampling provides insufficient information to determine the image uniquely and stably. Limited-angle CT, arising from restricted angular coverage, produces strongly directional information loss associated with the missing angular range. In both settings, image directions may be strongly observed, weakly constrained, or unobservable, leading to severe ill-posedness and reconstruction ambiguity. Existing diffusion-based approaches incorporate measurement information through likelihood guidance, data-consistency operations, or range-null-space corrections. However, they do not generally use the continuously varying measurement sensitivity of the acquisition to jointly shape both reconstruction updates and stochastic exploration. We propose a geometry-aware diffusion-guided stochastic reconstruction framework for sparse-view and limited-angle CT. Its central component is a regularized noise-weighted pullback metric constructed from the CT forward operator and measurement-noise covariance. This metric continuously adapts both the measurement-aware update and stochastic exploration according to directional measurement sensitivity, suppressing changes along strongly constrained directions while permitting greater exploration along weakly constrained and unobservable directions. We complement this geometry-aware update with a regularized data-consistency correction and approximately null-space-restricted stochastic perturbations, implemented matrix-free using forward and backprojection operations together with conjugate-gradient solves. Experiments on sparse-view, noisy, and limited-angle CT demonstrate competitive reconstruction quality, strong measurement consistency, and spatially resolved empirical uncertainty estimates.

Knowledge distillation with multiple teachers is increasingly used to improve robustness, efficiency, and safety, yet existing approaches rely largely on heuristic or implementation-specific weighting schemes. This paper develops an operator-agnostic axiomatic framework for adaptive weighting in multi-teacher knowledge distillation across three complementary scales: token, task, and context. We formalize structural conditions under which adaptive weighting operators are well-defined, admit multiple non-equivalent implementations, and can be hierarchically composed via product-structure normalization. Within this framework, we establish existence and non-uniqueness of conforming operators, characterize convergence of gradient-based optimization under standard assumptions, analyze stability and perturbation robustness, and provide an abstract formulation of safety-constrained distillation. The results decouple theoretical guarantees from specific weighting formulas, enabling principled analysis of adaptive distillation methods under heterogeneity, distribution shift, and safety constraints.

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce a surrogate model that not only sheds new light on the design of Muon, but more importantly leads to a new optimizer. In the same spirit as the derivation of Newton's method, the surrogate approximates the loss as a quadratic function of the perturbation to a weight matrix W using only three matrices: the gradient G, an output-space curvature matrix H, and the data matrix Z that stacks the layer inputs. By minimizing this surrogate in one step and adopting a certain isotropic assumption on the weights, we obtain the closed-form update rule (up to momentum and weight decay) W leftarrow W - ηcdot msgn(G(ZZ^top)^{-1}), where η is the learning rate and msgn(X)=UV^top if X=USV^top is a compact singular value decomposition. This new optimization method, which we refer to as Newton-Muon, shows that standard Muon can be interpreted as an implicit Newton-type method that neglects the right preconditioning induced by the input second moment. Empirically, on a reproduction of the earliest publicly released Modded-NanoGPT speedrun configuration using Muon for GPT-2 pretraining, Newton-Muon reaches the target validation loss in 6\% fewer iteration steps and reduces wall-clock training time by about 4\%.

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce memory pressure. This introduces a rollout-training mismatch that biases the policy gradient and can cause training to collapse outright on reasoning benchmarks. We show that the mismatch is non-stationary and acts as a double-edged sword: early in training it provides a stochastic exploration bonus, exposing the gradient to trajectories the trainer would otherwise under-sample, but the same perturbation transitions into a destabilizing source of bias as the policy concentrates. To solve this, we propose Adaptive Importance Sampling (AIS), a correction framework that adjusts the strength of its intervention on a per-batch basis. AIS combines three real-time diagnostics, namely weight reliability, divergence severity, and variance amplification, into a single mixing coefficient that interpolates between the uncorrected and fully importance-weighted gradients, suppressing the destabilizing component of the mismatch while preserving its exploratory benefit. We integrate AIS into GRPO and evaluate it on the diffusion-based LLaDA-8B-Instruct and the autoregressive Qwen3-8B and Qwen3.5-9B across mathematical reasoning and planning benchmarks. AIS matches the BF16 baseline on most tasks while retaining the 1.5 to 2.76x rollout speedup of FP8.

Radio maps and channel knowledge maps provide reusable propagation knowledge, but a stored map can become locally outdated after persistent changes to doors, partitions, furniture, large equipment, or infrastructure. Motivated by digital-twin state synchronization, we develop an electromagnetic twin that recurrently converts sparse channel measurements into a persistent wireless state, exposes that state to communication queries, and uses its uncertainty to request subsequent measurements. The twin tracks persistent or semi-persistent propagation changes rather than transient human motion or fast fading. Each update is a constrained inverse problem that combines the previous map, a scene graph, and an imperfect physics prior. Measurement consistency with a confidence-calibrated radius and physical gain bounds enforce feasibility, while scene-aware spatial regularization and selective temporal memory preserve propagation boundaries and unchanged regions. Successive convex approximation (SCA), majorization--minimization alternating direction method of multipliers (MM-ADMM), and a low-complexity primal--dual hybrid gradient (LC-PDHG) mode realize the framework at different computational scales, and a local perturbation analysis gives an explicit multi-update tracking recursion. The updated state supports access-point association and codebook beam selection, while change-weighted A-optimal design closes the measurement--update--query loop. Over 500 realizations, the recurrent update remains stable through eight persistent scene events and raises best-beam accuracy from 76.64% to 90.83% as measured-location density grows from 2% to 16%.

We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.

Data selection is already a central bottleneck in large-language-model training, where web-scale corpora are noisy and token budgets are finite. In continual pre-training (CPT), it becomes a forgetting-control problem: a poorly chosen target-domain corpus can overwrite capabilities encoded in the pretrained checkpoint. Existing CPT practice either scores candidates with parameter-agnostic scalars such as perplexity, or mitigates forgetting by spending many extra general-domain replay tokens. Neither strategy directly asks how training on a candidate will move the model parameters. We show that loss-based selection causes the post-CPT Fisher diagonal to drift downward on exactly the high-Fisher coordinates the pretrained model had committed to, while leaving low-Fisher coordinates largely untouched. This asymmetry exposes a parameter-space mechanism for catastrophic forgetting. Motivated by this observation, we propose a Fisher-aware CPT selector that decomposes each candidate's gradient into an anchor component, which measures perturbation along committed parameter directions, and a frontier component, which measures update capacity in unconstrained low-Fisher subspaces. We aggregate these signals with a log-determinant submodular objective and optimize it in a single pass using a scalable streaming data selection pipeline. On TinyLlama-1.1B and Llama-3.1-8B CPT over medical data, our selector improves target-domain quality while bounding forgetting on held-out pretraining benchmarks. Most importantly, it is substantially more token-efficient than forgetting-aware replay. 1B selected tokens already outperform the replay strategy trained with 10B tokens on both adaptation and forgetting, giving a 10x token-efficiency advantage.

Outer-learning algorithms use infinitesimal sensitivities to propose finite changes to initialization or training parameters. For hard-ReLU training, the derivative of the finite program and the derivative of its flow limit do not by themselves specify the response at a chosen radius. We characterize the intervening regime in which the perturbation radius is proportional to the GD step. Integer event rounding then survives at leading order: smooth Euler bias shifts each discrete phase, and upstream rounding moves downstream branch boundaries. We derive the crossing indices and a uniform endpoint expansion for finitely many separated transverse events in piecewise-C^2 dynamics, away from recursive phase boundaries. In contractive affine regions, an explicit remainder and complete branch verification certify finite candidate comparisons. Scalar phase frequencies and a coupled feedback ablation test the mechanism; frozen nonlinear-network experiments show radius-dependent prediction accuracy, including incomplete branch matches and failed-word tails. Together with local AD and uniform flow consistency, the result identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

The eight-component relativistic wave equation for spin-1{2} particles of Robson and Staudte (FV1{2}), a Feshbach--Villars linearization of the Feynman--Gell-Mann equation, reproduces the Dirac hydrogenic spectrum with a doubled solution space and an indefinite inner product. Its exact Stark shifts must equal the Dirac ones; whether its indefinite-metric perturbation theory delivers them is not guaranteed. We compute the first- and second-order Stark shifts of the n=1--3 levels of hydrogenic ions from H to U^{91+} in the Schrödinger, Dirac and FV1{2} theories, evaluating all spectral sums, continuum included, by the Dalgarno--Lewis method. The FV1{2} and Dirac shifts coincide level by level, to working precision at first order (closed-form roots) and to 45 significant figures at second order. Both ingredients are needed: without the explicit spin--field coupling the first-order roots become complex, and without the negative-norm states the (Zα)^2 coefficient is wrong. Norm sign and parity are locked in the doubled space: a potential lifting the 2s_{1/2}--2p_{1/2} degeneracy needs its own spin--gradient term, and shifts placed by hand on the κ-labeled states give a spurious imaginary linear Stark shift. The relativistic linear Stark effect is smaller by finite factors, but a second-moment sum rule shows the non-relativistic linear Stark strength is conserved, the missing part reappearing in singular (Zα)^{-2} second-order terms. For levels with a fine-structure partner, an exact intra-shell/regular split of the second-order shift gives the (Zα)^0 coefficients analytically and relates the π^2 terms of the (Zα)^2 coefficients to the singular ones. The Dirac weak/strong-field crossover for n=2 of hydrogen lies near 2.8~kV cm^{-1}, and the perturbative window set by the fine structure grows as Z^5.

As large language models become increasingly integrated into daily life, audio has emerged as a key interface for human-AI interaction. However, this convenience also introduces new vulnerabilities, making audio a potential attack surface for adversaries. Our research introduces WhisperInject, a two-stage adversarial audio attack framework that can manipulate state-of-the-art audio language models to generate harmful content. Our method uses imperceptible perturbations in audio inputs that remain benign to human listeners. The first stage uses a novel reward-based optimization method, Reinforcement Learning with Projected Gradient Descent (RL-PGD), to guide the target model to circumvent its own safety protocols and generate harmful native responses. This native harmful response then serves as the target for Stage 2, Payload Injection, where we use Projected Gradient Descent (PGD) to optimize subtle perturbations that are embedded into benign audio carriers, such as weather queries or greeting messages. Validated under the rigorous StrongREJECT, LlamaGuard, as well as Human Evaluation safety evaluation framework, our experiments demonstrate a success rate exceeding 86% across Qwen2.5-Omni-3B, Qwen2.5-Omni-7B, and Phi-4-Multimodal. Our work demonstrates a new class of practical, audio-native threats, moving beyond theoretical exploits to reveal a feasible and covert method for manipulating AI behavior.

Reinforcement learning (RL) has become a powerful tool for propelling Large Language Models (LLMs) beyond imitation-based training towards more robust reasoning capabilities. Among existing approaches, RL with Verifiable Rewards (RLVR) has emerged as a pivotal paradigm for advancing LLM reasoning. Despite its empirical success, recent studies have offered different insights. One line of inquiry advocates prioritizing high-entropy token positions during training, while another perspective cautions against allowing low-probability tokens to dominate gradient updates. Notably, although high-entropy tokens are usually correlated with low probability, both paradigms empirically yield substantial performance gains. In this work, we argue that evaluating sampled-token probability or entropy in isolation is insufficient to capture the policy optimization dynamics. To resolve this tension, we introduce the Relative Surprisal Index (RSI), a principled, information-theoretic metric that naturally couples the token's entropy with the probability of the selected token. We show that, under mild conditions, RSI is related to the local ratio between the first-order variations of the logit-gradient norm and predictive entropy under a selected-logit perturbation. Building on RSI, we propose RSI Selection (RSI-S), an entropy-adaptive token filtering method that retains tokens within a stable RSI interval. RSI-S successfully reconciles previous contradictory paradigms and filters out both redundant low-surprisal tokens and unstable high-surprisal tail tokens. Empirical evaluations show that RSI-S achieves higher avg@32 accuracy across different model scales (Qwen2.5-1.5B, 3B, and 7B) on AIME and AMC benchmarks: RSI-S improves avg@32 accuracy by 2--3 percentage points over GRPO. Overall, RSI offers a promising perspective for RLVR improvement.

Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse candidate solutions. Unfortunately, the standard approach to post-training LLMs through Reinforcement Learning (RL) may limit pass@k: the model's output distribution narrows around high-reward outputs, causing the solution coverage to collapse. The alternative is to use Evolution Strategies (ES), a population-based, gradient-free post-training method that optimizes directly in weight space through random perturbations. As this paper shows, ES achieves consistently higher pass@k than RL and produces a broader output distribution with greater solution coverage. This coverage in turn makes it possible to achieve better results in e.g. standard math benchmarks. Thus, ES provides a better foundation for post-training in discovery problems and other domains where diverse solution coverage is critical.

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.

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.

Overfitting widely exists in adversarial robust training of deep networks. An effective remedy is adversarial weight perturbation, which injects the worst-case weight perturbation during network training by maximizing the classification loss on adversarial examples. Adversarial weight perturbation helps reduce the robust generalization gap; however, it also undermines the robustness improvement. A criterion that regulates the weight perturbation is therefore crucial for adversarial training. In this paper, we propose such a criterion, namely Loss Stationary Condition (LSC) for constrained perturbation. With LSC, we find that it is essential to conduct weight perturbation on adversarial data with small classification loss to eliminate robust overfitting. Weight perturbation on adversarial data with large classification loss is not necessary and may even lead to poor robustness. Based on these observations, we propose a robust perturbation strategy to constrain the extent of weight perturbation. The perturbation strategy prevents deep networks from overfitting while avoiding the side effect of excessive weight perturbation, significantly improving the robustness of adversarial training. Extensive experiments demonstrate the superiority of the proposed method over the state-of-the-art adversarial training methods.

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.

The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In this paper, we discuss some of the shortcomings of existing approaches to perturbation analysis and address them by introducing the concept of extremal perturbations, which are theoretically grounded and interpretable. We also introduce a number of technical innovations to compute extremal perturbations, including a new area constraint and a parametric family of smooth perturbations, which allow us to remove all tunable hyper-parameters from the optimization problem. We analyze the effect of perturbations as a function of their area, demonstrating excellent sensitivity to the spatial properties of the deep neural network under stimulation. We also extend perturbation analysis to the intermediate layers of a network. This application allows us to identify the salient channels necessary for classification, which, when visualized using feature inversion, can be used to elucidate model behavior. Lastly, we introduce TorchRay, an interpretability library built on PyTorch.

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

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.

Diffusion models have achieved remarkable success in generative modeling, with their sampling procedures routinely modified to control generation and improve efficiency. These modifications introduce perturbations along the sampling trajectory, raising a central question: how do such perturbations affect generated output? To address this question, we develop a theoretical framework to investigate perturbation propagation, combining dynamical analysis of the sampling process with an information-theoretic characterization of output responses. Within this framework, we quantify perturbation strength using the Kullback--Leibler (KL) divergence between perturbed and reference trajectory distributions, termed as path cost, which is shown to bound, but do not determine, changes in the output distribution. Building on this analysis, we derive a response identity that connects the propagation and accumulation of local perturbations with the information captured by a selected feature mean, explaining why changes in the output distribution can remain undetected by its first-order response. We test our theoretical analysis through controlled interventions at equal path cost in pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. To assess whether our framework can diagnose perturbations arising from practical approximations, we apply it to cache-based acceleration and show that our propagation analysis reliably identifies sampling intervals where caching causes larger image errors.

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.

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i.e., the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.

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

Sharpness Aware Minimization (SAM) enhances performance across various neural architectures and datasets. As models are continually scaled up to improve performance, a rigorous understanding of SAM's scaling behaviour is paramount. To this end, we study the infinite-width limit of neural networks trained with SAM, using the Tensor Programs framework. Our findings reveal that the dynamics of standard SAM effectively reduce to applying SAM solely in the last layer in wide neural networks, even with optimal hyperparameters. In contrast, we identify a stable parameterization with layerwise perturbation scaling, which we call Maximal Update and Perturbation Parameterization (μP^2), that ensures all layers are both feature learning and effectively perturbed in the limit. Through experiments with MLPs, ResNets and Vision Transformers, we empirically demonstrate that μP^2 achieves hyperparameter transfer of the joint optimum of learning rate and perturbation radius across model scales. Moreover, we provide an intuitive condition to derive μP^2 for other perturbation rules like Adaptive SAM and SAM-ON, also ensuring balanced perturbation effects across all layers.

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

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.