Spiking Neural Networks (SNNs) represent a promising paradigm for energy-efficient neuromorphic computing due to their bio-plausible and spike-driven characteristics. However, the robustness of SNNs in complex adversarial environments remains significantly constrained. In this study, we theoretically demonstrate that those threshold-neighboring spiking neurons are the key factors limiting the robustness of directly trained SNNs. We find that these neurons set the upper limits for the maximum potential strength of adversarial attacks and are prone to state-flipping under minor disturbances. To address this challenge, we propose a Threshold Guarding Optimization (TGO) method, which comprises two key aspects. First, we incorporate additional constraints into the loss function to move neurons' membrane potentials away from their thresholds. It increases SNNs' gradient sparsity, thereby reducing the theoretical upper bound of adversarial attacks. Second, we introduce noisy spiking neurons to transition the neuronal firing mechanism from deterministic to probabilistic, decreasing their state-flipping probability due to minor disturbances. Extensive experiments conducted in standard adversarial scenarios prove that our method significantly enhances the robustness of directly trained SNNs. These findings pave the way for advancing more reliable and secure neuromorphic computing in real-world applications.
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Deep Learning · Everything Else
Outlier detection (OD), distinguishing inliers and outliers in completely unlabeled datasets, plays a vital role in science and engineering. Although there have been many insightful OD methods, most of them require troublesome hyperparameter tuning (a challenge in unsupervised learning) and costly model training for every task or dataset. In this work, we propose UniOD, a universal OD framework that leverages labeled datasets to train a single model capable of detecting outliers of datasets with different feature dimensions and heterogeneous feature spaces from diverse domains. Specifically, UniOD extracts uniform and comparable features across different datasets by constructing and factorizing multi-scale point-wise similarity matrices. It then employs graph neural networks to capture comprehensive within-dataset and between-dataset information simultaneously, and formulates outlier detection tasks as node classification tasks. As a result, once the training is complete, UniOD can identify outliers in datasets from diverse domains without any further model/hyperparameter selection and parameter optimization, which greatly improves convenience and accuracy in real applications. More importantly, we provide theoretical guarantees for the effectiveness of UniOD, consistent with our numerical results. We evaluate UniOD on 30 benchmark OD datasets against 17 baselines, demonstrating its effectiveness and superiority.
Deep Learning · Graph Neural Networks
Counterfactual explanations offer an intuitive way to interpret graph neural networks (GNNs) by identifying minimal changes that alter a model’s prediction, thereby answering “what must differ for a different outcome?”. In this work, we propose a novel framework, ATEX-CF that unifies adversarial attack techniques with counterfactual explanation generation—a connection made feasible by theirshared goal of flipping a node’s prediction, yet differing in perturbation strategy:adversarial attacks often rely on edge additions, while counterfactual methods typically use deletions. Unlike traditional approaches that treat explanation and attack separately, our method efficiently integrates both edge additions and deletions, grounded in theory, leveraging adversarial insights to explore impactful counterfactuals. In addition, by jointly optimizing fidelity, sparsity, and plausibility under a constrained perturbation budget, our method produces instance-level explanations that are both informative and realistic. Experiments on synthetic and real-world node classification benchmarks demonstrate that ATEX-CF generates faithful, concise, and plausible explanations, highlighting the effectiveness of integrating adversarial insights into counterfactual reasoning for GNNs.
Deep Learning · Graph Neural Networks
This paper studies the problem of open-set graph anomaly detection, which aims to generalize a graph neural network (GNN) trained with a small number of both normal and abnormal nodes to detect unseen anomalies different from training anomalies during inference. This problem is highly challenging due to both the data scarcity of unseen anomalies and the label scarcity for training nodes. Towards this end, we propose a novel approach named Dynamic Multi-sample Mixup with Gradient Exploration (DEMO) for open-set graph anomaly detection. The core of our proposed DEMO is to leverage a dynamic framework to adapt the optimization procedure with high generalizability. In particular, our DEMO first adaptively fuses multiple seen nodes to simulate the unseen anomalies, which expands the decision boundary for the detection model with enhanced generalizability. Moreover, we dynamically adjust sample weights based on their energy gradients to prioritize uncertain and informative nodes, ensuring a robust optimization procedure. To further address both label scarcity and severe class imbalance, we maintain a memory bank of historical records to guide the pseudo-labeling process of unlabeled nodes. Extensive experiments on various benchmark datasets validate the superiority of the proposed DEMO in comparison to various baselines.
Applications · Neuroscience, Cognitive Science
Despite their impressive performance on computer vision benchmarks, Deep Neural Networks (DNNs) still fall short of adequately modeling human visual behavior, as measured by error consistency and shape bias. Recent work hypothesized that behavioral alignment can be drastically improved through generative - rather than discriminative - classifiers, with far-reaching implications for models of human vision. Here, we instead show that the increased alignment of generative models can be largely explained by a seemingly innocuous resizing operation in the generative model which effectively acts as a low-pass filter. In a series of controlled experiments, we show that removing high-frequency spatial information from discriminative models like CLIP drastically increases their behavioral alignment. Simply blurring images at test-time - rather than training on blurred images - achieves a new state-of-the-art score on the model-vs-human benchmark, halving the current alignment gap between DNNs and human observers. Furthermore, low-pass filters are likely optimal, which we demonstrate by directly optimizing filters for alignment. To contextualize the performance of optimal filters, we compute the frontier of all possible pareto-optimal solutions to the benchmark, which was formerly unknown. We explain our findings by observing that the frequency spectrum of optimal Gaussian filters roughly matches the spectrum of band-pass filters implemented by the human visual system. We show that the contrast sensitivity function, describing the inverse of the contrast threshold required for humans to detect a sinusoidal grating as a function of spatiotemporal frequency, is approximated well by Gaussian filters of a specific width.
AutoRegressive Visual Generation (ARVG) models retain an architecture compatible with language models, while achieving performance comparable to diffusion-based models. Quantization is commonly employed in neural networks to reduce model size and computational latency. However, applying quantization to ARVG remains largely underexplored, and existing quantization methods fail to generalize effectively to ARVG models. In this paper, we explore this issue and identify three key challenges: (1) severe outliers at channel-wise level, (2) highly dynamic activations at token-wise level, and (3) mismatched distribution information at sample-wise level. To these ends, we propose PTQ4ARVG, a training-free post-training quantization (PTQ) framework consisting of: (1) Gain-Projected Scaling (GPS) mitigates the channel-wise outliers, which expands the quantization loss via a Taylor series to quantify the gain of scaling for activation-weight quantization, and derives the optimal scaling factor through differentiation. (2) Static Token-Wise Quantization (STWQ) leverages the inherent properties of ARVG, fixed token length and position-invariant distribution across samples, to address token-wise variance without incurring dynamic calibration overhead. (3) Distribution-Guided Calibration (DGC) selects samples that contribute most to distributional entropy, eliminating the sample-wise distribution mismatch. Extensive experiments show that PTQ4ARVG can effectively quantize the ARVG family models to 8-bit and 6-bit while maintaining competitive performance.
Theory · Interpretability and Visualization
Deep learning has achieved remarkable success across many domains, but it has also created a growing demand for interpretability in model predictions. Although many explainable machine learning methods have been proposed, post-hoc explanations lack guaranteed fidelity and are sensitive to hyperparameter choices, highlighting the appeal of inherently interpretable models. For example, linear regression provides clear feature effects through its coefficients. However, such models are often outperformed by more complex neural networks (NNs) that usually lack inherent interpretability. To address this dilemma, we introduce NIMO, a framework that combines inherent interpretability with the expressive power of neural networks. Building on the simple linear regression, NIMO is able to provide flexible and intelligible feature effects. Relevantly, we develop an optimization method based on parameter elimination, that allows for optimizing the NN parameters and linear coefficients effectively and efficiently. By relying on adaptive ridge regression we can easily incorporate sparsity as well. We show empirically that our model can provide faithful and intelligible feature effects while maintaining good predictive performance.
Theory · Domain Adaptation and Transfer Learning
Test-time domain generalization (TTDG) methods enhance the performance of neural networks on target domains by transferring the feature distribution of target samples to approximate that of the source domain, while avoiding the computational cost associated with fine-tuning on the target domain. However, existing TTDG methods primarily rely on style transfer strategies operating at a coarse granularity, which prove ineffective for pixel-level prediction tasks such as image super-resolution (SR). To address this limitation, we propose a multi-codebook based test-time domain generalization framework (MC-TTDG). Our method leverages both domain-specific and domain-invariant codebooks to achieve fine-grained representation learning on source domains, and performs pixel-level nearest-neighbor feature matching and transfer to accurately adjust target domain features. Furthermore, we introduce a voting-based strategy for optimal domain-specific codebook selection, which improves the precision of feature transfer through multi-party consensus. Extensive experiments across diverse data distributions, and network architectures demonstrate that the proposed method effectively transfers feature distributions for SR networks. Our code is available at https://github.com/ZaizuoTang/MC-TTDG.
General Machine Learning · Representation Learning
High-resolution imagery is often hindered by limitations in sensor technology, atmospheric conditions, and costs. Such challenges occur in satellite remote sensing, but also with handheld cameras, such as our smartphones. Hence, super-resolution aims to enhance the image resolution algorithmically. Since single-image super-resolution requires to solve an inverse problem, such methods must exploit strong priors, e.g. learned from high-resolution training data, or be constrained by auxiliary data, e.g. by a high-resolution guide from another modality. While qualitatively pleasing, such approaches often lead to "hallucinated" structures that do not match reality. In contrast, multi-image super-resolution (MISR) aims to improve the (optical) resolution by constraining the super-resolution process with multiple views taken with sub-pixel shifts. Here, we propose SuperF, a test-time optimization approach for MISR that leverages coordinate-based neural networks, also called neural fields. Their ability to represent continuous signals with an implicit neural representation (INR) makes them an ideal fit for the MISR task. The key characteristic of our approach is to share an INR for multiple shifted low-resolution frames and to jointly optimize the frame alignment with the INR. Our approach advances related INR baselines, adopted from burst fusion for layer separation, by directly parameterizing the sub-pixel alignment as optimizable affine transformation parameters and by optimizing via a super-sampled coordinate grid that corresponds to the output resolution. Our experiments yield compelling results on simulated bursts of satellite imagery and ground-level images from handheld cameras, with upsampling factors of up to 8. A key advantage of SuperF is that this approach does not rely on any high-resolution training data.
Deep Learning · Graph Neural Networks
Graph Neural Networks (GNNs) have advanced graph classification, yet they remain vulnerable to graph-level imbalance, encompassing class imbalance and topological imbalance. To address both types of imbalance in a unified manner, we propose UniImb, a Unified framework for Imbalanced graph classification. Specifically, UniImb first captures multi-scale topological features and enhances data diversity via learnable personalized graph perturbations. It then employs a dynamic balanced prototype module to learn representative prototypes from graph instances, improving the quality of graph representations. Concurrently, a prototype load-balancing optimization term mitigates dominance by majority samples to equalize sample influence during training. We justify these design choices theoretically using the Information Bottleneck principle. Extensive experiments on 19 datasets-including a large-scale imbalanced air pollution graph dataset AirGraph released by us and 23 baselines demonstrate that UniImb has achieved dominant performance across various imbalanced scenarios. Our code is available at GitHub.
Applications · Neuroscience, Cognitive Science
The efficiency of Logic Optimization (LO) has become one of the key bottlenecks in chip design. To prompt efficient LO, many graph-based machine learning (ML) methods, such as graph neural networks (GNNs), have been proposed to predict and prune a large number of ineffective subgraphs of the LO heuristics. However, the high inference cost and limited interpretability of these approaches severely limit their wide application to modern LO tools. To address this challenge, we propose a novel **H**ierarchical C**i**rcuit **S**ymbolic Discovery Framework, namely HIS, to learn a *lightweight* and *interpretable* symbolic function that can *accurately* identify ineffective subgraphs for efficient LO. Specifically, HIS proposes a hierarchical tree structure to represent the circuit symbolic function, where every layer of the symbolic tree performs an efficient and interpretable message passing to capture the structural information of the circuit graph. To learn the hierarchical tree, we propose a circuit symbolic generation framework that leverages reinforcement learning to optimize a structure-aware Transformer model for symbolic token generation. To the best of our knowledge, HIS is *the first* approach to discover an efficient, interpretable, and high-performance symbolic function from the circuit graph for efficient LO. Experiments on two widely used circuit benchmarks show that the learned graph symbolic functions outperform previous state-of-the-art approaches in terms of efficiency and optimization performance. Moreover, we integrate HIS with the Mfs2 heuristic, one of the most time-consuming LO heuristics. Results show that HIS significantly enhances both its efficiency and optimization performance on a CPU-based machine, achieving an average runtime improvement of 27.22% and a 6.95% reduction in circuit size.
Computer Vision · Image and Video Generation
Diffusion Transformers (DiTs) excel at visual generation yet remain hampered by slow sampling. Existing training-free accelerators—step reduction, feature caching, and sparse attention—enhance inference speed but typically rely on a uniform heuristic or manually designed adaptive strategy for all images, leaving quality on the table. Alternatively, dynamic neural networks offer per-image adaptive acceleration, but their high fine-tuning costs limit broader applicability. To address these limitations, we introduce RAPID^3: Tri-Level Reinforced Acceleration Policies for Diffusion Transformer framework that delivers image-wise acceleration with zero updates to the base generator. Specifically, three lightweight policy heads—Step-Skip, Cache-Reuse, and Sparse-Attention—observe the current denoising state and independently decide their corresponding speed-up at each timestep. All policy parameters are trained online via Group Relative Policy Optimization (GRPO) while the generator remains frozen. Meanwhile, an adversarially learned discriminator augments the reward signal, discouraging reward hacking by boosting returns only when generated samples stay close to the original model’s distribution. Across state-of-the-art DiT backbones including Stable Diffusion 3 and FLUX, RAPID^3 achieves nearly 3$\times$ faster sampling with competitive generation quality.
Continual learning aims to acquire new knowledge incrementally while retaining prior information, with catastrophic forgetting (CF) being a central challenge. Existing methods can mitigate CF to some extent but are constrained by limited capacity, which often requires dynamic expansion for long task sequences and makes performance sensitive to task order. Inspired by the richness and plasticity of synaptic connections in biological nervous systems, we propose the Multi-Synaptic Cooperative Network (MSCN), a generalized framework that models cooperative interactions among multiple synapses through multi-synaptic connections modulated by local synaptic activity. This design enhances model representational capacity and enables task-adaptive plasticity by means of multi-synaptic cooperation, providing a new avenue for expanding model capacity while improving robustness to task order. During learning, our MSCN dynamically activates task-relevant synapses while suppressing irrelevant ones, enabling targeted retrieval and minimizing interference. Extensive experiments across four benchmark datasets, involving both spiking and non-spiking neural networks, demonstrate that our method consistently outperforms state-of-the-art continual learning methods with significantly improved robustness to task-order variation. Furthermore, our analysis reveals an optimal trade-off between synaptic richness and learning efficiency, where excessive connectivity can impair circuit performance. These findings highlight the importance of the multi-synaptic cooperation mechanism for achieving efficient continual learning and provide new insights into biologically inspired, robust, and scalable continual learning.
Computer Vision · Image and Video Generation
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS) based on random projections, all of which rely on axis- or subspace-aligned statistical characterization of the signal source. However, many naturally occurring signals, including photographic images, contain richer statistical structure. To exploit such structure, we introduce a general method for obtaining an optimized set of linear measurements for efficient image reconstruction, where the signal statistics are expressed by the prior implicit in a neural network trained to perform denoising (known as a ``diffusion model''). We demonstrate that the optimal measurements derived for two natural image datasets differ from those of PCA, ICA, or CS, and result in substantially lower mean squared reconstruction error. Interestingly, the marginal distributions of the measurement values are asymmetrical (skewed), substantially more so than those of previous methods. We also find that optimizing with respect to perceptual loss, as quantified by structural similarity (SSIM), leads to measurements different from those obtained when optimizing for MSE. Our results highlight the importance of incorporating the specific statistical regularities of natural signals when designing effective linear measurements.
Optimization · Large Scale, Parallel and Distributed
Scaling neural network training increasingly depends on synchronous data-parallelism, yet full-precision gradient all-reduce imposes a severe communication bottleneck. We propose Decoupled Momentum Optimization, a drop-in replacement for any momentum-based optimizers that significantly reduces the communication bandwidth while maintaining convergence. DeMo (i) decouples local momentum updates, (ii) applies a fast orthonormal transform (e.g., DCT) followed by top-$k$ sparsification, and (iii) reuses the momentum buffer for error feedback via momentum subtraction. This design reduces per-step communication by up to two orders of magnitude with minimal computational overhead. Experiments on 300M- and 1B-parameter DeMo language models show DeMo transmits up to 85× less data per GPU than AdamW-DDP while achieving comparable loss and accuracy. DeMo is topology-agnostic and enables training across multi-datacenter or Ethernet-based setups.
Optimization · Global Optimization
Modern neural networks exhibit a striking property: basins of attraction in the loss landscape are often connected by low-loss paths, yet optimization dynamics generally remain confined to a single convex basin and rarely explore intermediate points. We resolve this paradox by identifying entropic barriers arising from the interplay between curvature variations along these paths and noise in optimization dynamics. Empirically, we find that curvature systematically rises away from minima, producing effective forces that bias noisy dynamics back toward the endpoints — even when the loss remains nearly flat. These barriers persist longer than energetic barriers, shaping the late-time localization of solutions in parameter space. Our results highlight the role of curvature-induced entropic forces in governing both connectivity and confinement in deep learning landscapes.
Fast Convergence of Natural Gradient Descent for Over-parameterized Physics-Informed Neural Networks
Applications · Physics
In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss function. However, the convergence rate of GD for training two-layer neural networks exhibits poor dependence on the sample size and the Gram matrix, leading to a slow training process. In this paper, we show that for training two-layer $\text{ReLU}^3$ Physics-Informed Neural Networks (PINNs), the learning rate can be improved from the smallest eigenvalue of the limiting Gram matrix to the reciprocal of the largest eigenvalue, implying that GD actually enjoys a faster convergence rate. Despite such improvements, the convergence rate is still tied to the least eigenvalue of the Gram matrix, leading to slow convergence. We then develop the positive definiteness of Gram matrices with general smooth activation functions and provide the convergence analysis of natural gradient descent (NGD) in training two-layer PINNs, demonstrating that the maximal learning rate can be $\mathcal{O}(1)$ and at this rate, the convergence rate is independent of the Gram matrix. In particular, for smooth activation functions, the convergence rate of NGD is quadratic. Numerical experiments are conducted to verify our theoretical results.
Theory · Learning Theory
This paper introduces the first globally optimal algorithm for the empirical risk minimization problem of two-layer maxout and ReLU networks, i.e., minimizing the number of misclassifications. The algorithm has a worst-case time complexity of $O\left(N^{DK+1}\right)$, where $K$ denotes the number of hidden neurons and $D$ represents the number of features. It can be can be generalized to accommodate arbitrary computable loss functions without affecting its computational complexity. Our experiments demonstrate that the proposed algorithm provides provably exact solutions for small-scale datasets. To handle larger datasets, we introduce a heuristic method that reduces the data size to a manageable scale, making it feasible for our algorithm. This extension enables efficient processing of large-scale datasets and achieves significantly improved performance in both training and prediction, compared to state-of-the-art approaches (neural networks trained using gradient descent and support vector machines), when applied to the same models (two-layer networks with fixed hidden nodes and linear models).
Social Aspects · Privacy-preserving Statistics and Machine Learning
Differentially-Private SGD (DP-SGD) and its adaptive variant DP-Adam are powerful techniques to protect user privacy when using sensitive data to train neural networks. During training, converting model weights and activations into low-precision formats, i.e., quantization, can drastically reduce training times, energy consumption, and cost, and is thus a widely used technique. In this work, we demonstrate for the first time that quantization causes significantly higher accuracy degradation in DP training compared to regular SGD. We observe that this is caused by noise injection, which amplifies quantization variance, leading to disproportionately large accuracy degradation. To address this challenge, we present DPQuant, a dynamic quantization framework that adaptively selects a changing subset of layers to quantize at each epoch. Our method combines two key ideas that effectively reduce quantization variance: (i) probabilistic sampling that rotates which layers are quantized every epoch, and (ii) loss-aware layer prioritization, which uses a differentially private loss sensitivity estimator to identify layers that can be quantized with minimal impact on model quality. This estimator consumes a negligible fraction of the overall privacy budget, preserving DP guarantees. Empirical evaluations on ResNet18, ResNet50, and DenseNet121 across a range of datasets demonstrate that DPQuant consistently outperforms static quantization baselines, achieving near Pareto-optimal accuracy-compute trade-offs and up to $2.21\times$ theoretical throughput improvements on low‑precision hardware, with less than 2% drop in validation accuracy. We further show that our framework extends to DP-Adam with similar gains.
Theory · Learning Theory
In this paper, we uniquely study the adversarial robustness of deep neural networks (NN) for classification tasks against that of optimal classifiers. We look at the smallest magnitude of possible additive perturbations that can change a classifier's output. We provide a matrix-theoretic explanation of the adversarial fragility of deep neural networks for classification. In particular, our theoretical results show that a neural network's adversarial robustness can degrade as the input dimension $d$ increases. Analytically, we show that neural networks' adversarial robustness can be only $1/\sqrt{d}$ of the best possible adversarial robustness of optimal classifiers. Our theories match remarkably well with numerical experiments of practically trained NN, including NN for ImageNet images. The matrix-theoretic explanation is consistent with an earlier information-theoretic feature-compression-based explanation for the adversarial fragility of neural networks.