论文检索

Optimization · Zero-order and Black-box Optimization

Minhak Song, Liang Zhang, Bingcong Li, Niao He, Michael Muehlebach, Sewoong Oh

Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored. In this work, we provide an explicit step size condition that exactly captures the (mean-square) linear stability of a family of ZO methods based on the standard two-point estimator. Our characterization reveals a sharp contrast with first-order (FO) methods: whereas FO stability is governed solely by the largest Hessian eigenvalue, mean-square stability of ZO methods depends on the entire Hessian spectrum. Since computing the full Hessian spectrum is infeasible in practical neural network training, we further derive tractable stability bounds that depend only on the largest eigenvalue and the Hessian trace. Empirically, we find that full-batch ZO methods operate at the edge of stability: ZO-GD, ZO-GDM, and ZO-Adam consistently stabilize near the predicted stability boundary across CNNs, ResNets, and Transformers on vision tasks. Our results highlight an implicit regularization effect specific to ZO methods, where large step sizes primarily regularize the Hessian trace, whereas in FO methods they regularize the top eigenvalue.

Theory · Learning Theory

Guillaume Larue, Louis-Adrien Dufrène, Quentin Lampin, Hadi Ghauch, Ghaya Rekaya-Ben Othman

Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting, standard neural network architectures typically require exponential sample complexity, making gradient-based optimization intractable for large number of inputs $N$. We demonstrate that compact product-based neural architectures combined with stochastic data sparsity (Bernoulli inputs with $p_e \leq 1/N$) and appropriate hyperparameter choice enable efficient parity learning, with theoretical guarantees of convergence. Experiments validate our theory across dimensions up to $N = 10{,}000$, with empirical evidence showing optimal hyperparameter choices for $p_e$ and learning rate $\alpha$, as well as polynomial complexity scaling laws. This work establishes fundamental connections between architectural inductive bias and data sparsity, opening new possibilities for neural arithmetic, structured reasoning, binary neural networks, and machine learning applied to automated protocol discovery.

Deep Learning · Everything Else

Meng Bi, Hong Huang, Jinlong Song, Charles Wang, Chengming Hu, Xi Chen, Ting Yu, Xue Liu

Cross-device Federated Learning (FL) is frequently bottlenecked by the prohibitive computational and communication costs of training deep neural networks on resource-constrained edge hardware. While federated dynamic pruning aims to alleviate these costs by adjusting sparse topologies during training, existing methods rely on magnitude-based heuristics that are fundamentally ill-suited for the non-convergent, heterogeneous environments inherent to FL. To address this challenge, we propose Fedfit, a federated dynamic framework that replaces simple heuristics with optimization-centric criteria for topology adjustment. By leveraging a second-order approximation of the loss landscape via the Fisher Information Matrix, Fedfit enables precise and efficient topology adjustment without the overhead of explicit Hessian computation. Empirical evaluations across computer vision and natural language processing benchmarks demonstrate that Fedfit significantly narrows the sparse-to-dense accuracy gap, outperforming state-of-the-art methods while maintaining high communication efficiency.

Deep Learning · Graph Neural Networks

Junyi Yan, KE LIANG, Hao Yu, Meng Liu, Hao Tan, Tianrui Liu, Jun-Jie Huang, Xinwang Liu

Federated graph anomaly detection (GAD) aims to identify abnormal nodes in distributed subgraphs through collaborative learning. However, existing methods suffer from two limitations. 1) Their reliance on neighborhood aggregation assumes that anomalous information can be sufficiently captured, which often fails in federated learning with partitioned client subgraphs. 2) They overlook the detection bottleneck caused by weak attribute or structural anomalies. To tackle these challenges, we revisit federated GAD and reveal that weak anomalies exhibit harder-to-detect signals compared to strong anomalies. Specifically, we propose MV-FGAD, an efficient and effective federated GAD framework based on multi-view learning designed to mine anomalies of varying strengths. MV-FGAD introduces a federated knowledge learning module to aggregate and broadcast shared knowledge, which is further exploited to optimize local topological structures. Moreover, it designs a multi-view learning mechanism to capture diverse anomaly patterns, and adopts Mahalanobis distance–based scoring strategy to quantify node abnormality across views. Extensive experiments on real-world datasets of varying types and scales demonstrate MV-FGAD's efficiency and effectiveness.

Theory · Reinforcement Learning and Planning

Yike Zhao, Onno Eberhard, Malek khammassi, Ali Sayed, Michael Muehlebach

The family of linear recurrent neural networks has shown strong performance as recurrent memory units in partially observable reinforcement learning. We provide a theoretical justification for their empirical effectiveness by constructing and studying two linear filters: (i) the first exactly reproduces the pre–softmax logits of the belief vector in a hidden Markov model (HMM) under a deterministic transition matrix, thereby serving as a sufficient statistic for optimal policy learning, (ii) the second achieves vanishing state-decoding error under a nearly deterministic transition matrix, thus reducing state ambiguity to near zero. The results extend to action-controlled HMMs, where the corresponding linear filters become time-varying with action-dependent dynamics. We illustrate our main results through numerical experiments and further show that the constructed linear filter serves as a strong feature extractor in a small reinforcement learning game.

Deep Learning · Attention Mechanisms

Zhouzhiming Zhou, Yong He, Qiaoyun Wu, Chaoxu Mu, Ajmal Mian

The unordered nature of point cloud data poses significant challenges to conventional architectures primarily designed for structured data. Spiking neural networks (SNN), by virtue of their inherent sparsity and dynamics, are particularly well-suited for processing point clouds to effectively extract meaningful features. We propose SpikeNet, a novel spiking neural network architecture for energy-efficient and robust point cloud analysis. We introduce spiking-driven sparse attention mechanism coined the Spiking Vector Mask Transformer (SVMT). By dynamically aligning the sparsity of point cloud data through binary spiking masks, SVMT eliminates the need for softmax and multiplication operations, significantly improving computational efficiency. We also propose a Dynamic Sparse Spiking Residual (DSSR) structure and integrate it with SVMT to form the Spiking Neural Network (SpikeNet) for point cloud classification and segmentation. SpikeNet overcomes the trade-off between accuracy and efficiency in previous SNN methods, achieving collaborative optimization of performance and energy-efficiency. Experiments on benchmark datasets show that SpikeNet achieves state-of-the-art performance in shape classification and segmentation tasks, comparable to artificial neural network (ANN) based methods. Our source code is in supplementary material and will be made publicly available.

Deep Learning · Everything Else

Andries Rosseau, Robert Müller, Ann Nowe

Continual training of deep neural networks under non-stationarity often leads to a progressive loss of plasticity, eventually limiting further learning. We define plasticity loss as the network’s diminishing ability to make reliable progress under gradient descent updates in all output-space directions, and identify departures from dynamical isometry (i.e., drift of the layer-wise Jacobian singular values away from one) as a key mechanism driving this loss. We first revisit a class of networks that are isometric almost-everywhere while remaining universal Lipschitz function approximators, demonstrating that isometry is compatible with expressive nonlinear function classes. Turning to more general architectures, we study an efficient isometry-promoting regularization scheme for continual learning. We analyze its interaction with common activation functions, and reveal a mechanism by which it can reactivate dead ReLU units. To integrate this regularization with adaptive optimization, we propose AdamO, an Adam-style optimizer that decouples isometric regularization from gradient updates, analogous to AdamW. Finally, we evaluate our methods in supervised and reinforcement learning settings designed to induce plasticity loss and show that they effectively preserve plasticity while also yielding strong performance.

Deep Learning · Self-Supervised Learning

Maedeh Zarvandi, Michael Timothy, Theresa Wasserer, Debarghya Ghoshdastidar

Self-supervised learning (SSL) effectively learns representations from massive unlabeled data, yet the resulting models typically operate as black boxes, necessitating domain-specific post-hoc explanations. We introduce KREPES, a unified framework that learns inherently interpretable representations for arbitrary SSL objectives, including SimCLR, BYOL, VICReg. By bridging empirical neural tangent kernel approximations of neural networks with the Representer Theorem for kernels, we express the learned latent space directly via "Representer Landmarks", which are the representations of influential unlabeled training examples. We introduce two novel metrics, "Sample-Specific Influence Score" and "Conceptual Influence Profile", to quantify the transparency of the learned representations. KREPES enables direct audit of the latent space without supervision, for example, revealing an algorithmic bias in the Adult-1M dataset where SSL uses demographic proxies for income. Finally, to ensure scalability to SSL benchmarks with 1M+ samples (ImageNet-1K, Adult-1M), KREPES introduces a novel Nyström approximation-based optimization of any non-convex SSL objective.

Deep Learning · Self-Supervised Learning

Julie Mordacq, Vicky Kalogeiton, Steve Oudot

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning meaningful representations from unlabeled data. However, the standard protocol for evaluating these representations, linear probing, is computationally expensive, sensitive to hyperparameters, and provides limited insight into the geometric structure of the representation space. In this work, motivated by connections between neural network generalization and intrinsic dimensionality (ID) we propose IdEst, a method for estimating the ID of SSL representations via the Minimum Spanning Tree dimension estimator ($\mathrm{dim}_\mathrm{MST}$). Across diverse datasets, architectures, and SSL pretraining objectives, we show that IdEst strongly correlates withdownstream linear probe performances. Furthermore, we demonstrate that IdEst enables efficient hyperparameter selection, significantly reducing the computational cost compared to supervised alternatives. Our results highlight intrinsic dimensionality as a principled geometric proxy for assessing and optimizing SSL representations, complementing standard supervised probing protocols.

Deep Learning · Graph Neural Networks

Chunhui Zhang, Pengqi Li, Lizhong Ding, Peng Yang, Changsheng Li, Ye Yuan, Guoren Wang

Graph learning has been increasingly deployed in critical and sensitive domains, raising pressing demands for trustworthiness-robustness, fairness, and beyond. However, these properties are often undermined by various perturbations, which induce distributional uncertainty and compromise the trustworthiness of graph learning. To address this, we propose DICT, a novel framework that models distributional uncertainty to achieve trustworthy graph learning. Specifically, DICT formulates a unified optimization objective that captures perturbation-induced distributional shifts in graph topology, node features, and labels, and minimizes the worst-case risk over the uncertainty set. However, directly optimizing this objective in its primal form leads to an infinite-dimensional problem. To make this problem tractable, we integrate strong duality and local Lipschitz continuity of the loss, reformulating the objective as a finite-dimensional min-max problem. We focus on robustness and fairness as primary instantiations of DICT because they are not only critical in real-world applications, but also provide transferable modeling principles for broader trustworthiness objectives. By formulating fairness in the form of an uncertainty set, DICT pioneers unified robustness and fairness within a single optimization framework. Extensive experiments across diverse benchmarks and backbones demonstrate that DICT consistently improves both robustness and fairness, validating the effectiveness and adaptability of the DICT framework.

Deep Learning · Large Language Models

Shiguang Wu, Yaqing Wang, QUANMING YAO

The structural organization of language models plays a crucial role in the inference process of large language models (LLMs), occurring both iteratively within a single model for test-time scaling and interactively across multiple models for collaborative intelligence. While current systems primarily facilitate such interaction through natural language, this paper proposes constructing a high-level neural network, termed LMNet, by treating pre-trained LLMs as optimizable nodes connected via continuous dense vectors. Our approach eliminates the unnecessary embedding and de-embedding steps when one LLM connects to another, enabling more efficient information transfer, a fully differentiable optimization path, and exploration of capabilities beyond human heuristics. We place stripped LLMs as vertexes and optimizable seq2seq modules as edges to construct LMNet, a directed graph with a similar structure to MLPs, and perform end-to-end gradient-descent for efficient optimization. As two exemplar applications, we show the proposed architecture can effectively improve LLM’s general intelligence, and customize LLM with limited data. We also provide detailed discussion and analysis about the emergent behavior of this high-level network.

Deep Learning · Graph Neural Networks

Xinya Qin, Lu Bai, Lixin Cui, Ming Li, Hangyuan Du, Ziyu Lyu, Xin Jin

Graph Convolutional Networks (GCNs) are defined based on aggregating the node information of adjacent nodes, that are usually treated as equally important as each other, limiting the representational power of existing GCNs for graph classification. To address this shortcoming, we propose a novel Global Interacted Graph Convolutional Network (GI-GCN), that can leverage the solution vectors maintained during the iterative updates of the Dominant Set to adaptively characterize the global importance distribution of different nodes. Specifically, at each convolution layer, this distribution is adopted to adaptively modulate the importance weights of different node features before performing the local message passing. We show that this convolution strategy can effectively capture the highly correlated information between nonadjacent nodes through the Dominant Set algorithm, not only emphasizing the critical information at the graph level but also enhancing the discriminative power of graph representations. Furthermore, we optimize the spatial complexity of the framework, significantly reducing the memory overhead associated with the global interaction modeling. Experiments demonstrate the effectiveness of the proposed GI-GCN.

Deep Learning · Theory

Oskar Nordenfors, Fredrik Ohlsson, Axel Flinth

We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation. Our analysis reveals that the relative geometry of the admissible and the equivariant layers, respectively, plays a key role. Under natural assumptions on the data, network, loss, and group of symmetries, we show that compatibility of the spaces of admissible layers and equivariant layers, in the sense that the corresponding orthogonal projections commute, implies that the sets of equivariant stationary points are identical for the two strategies. If the linear layers of the network also are given a unitary parametrization, the set of equivariant layers is even invariant under the gradient flow for augmented models. Our analysis however also reveals that even in the latter situation, stationary points may be unstable for augmented training although they are stable for the manifestly equivariant models.

General Machine Learning · Unsupervised and Semi-supervised Learning

Kunling Li, Cunqing Hua, Hongyu Zhu, Tianjie Ju, Pengwenlong Gu

Radio Frequency Fingerprint Identification (RFFI) is a foundational pillar of physical-layer security, providing unclonable identity authentication and lightweight defense mechanisms for zero-trust wireless networks. Its practical deployment, however, often occurs in a source-free open-world (SF-OW) setting, characterized by a continuous influx of unregistered devices and privacy constraints that preclude the retention of historical data. In this paper, we formalize SF-OW RFFI task, which manifests a severe stability-plasticity dilemma: intrinsic signal similarity confuses new classes, while source absence precipitates catastrophic forgetting. To address this, we propose Incremental Orthogonal ETF (IO-ETF), a novel neural collapse-inspired framework utilizing output geometry to actively induce parameter separation and isolation. We further devise a Triple-Level Geometric Alignment (TLGA) strategy via semantic optimal transport, manifold progressive anchoring, and reliable subspace retention to stably align unlabeled streams to this geometric skeleton. Experiments on benchmarks demonstrate a superior trade-off between old-class retention and new-class discovery, offering a promising solution for secure access in dynamic networks.

Deep Learning · Algorithms

Tianren Zhang, Xiangxin Li, Minghao Xiao, Guanyu Chen, Feng Chen

Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce _polynomial representations_ as a distribution-aware, low-dimensional surrogate for neural functions: we approximate a network’s predictive behavior along data-dependent interpolation paths using orthogonal polynomial bases, yielding a compact functional representation. We show that the _effective degree_ of this representation serves as a practical simplicity metric that is predictive of generalization across tasks and architectures, and consistently outperforms existing generalization proxies such as sharpness. Finally, polynomial representations naturally yield a _differentiable_ simplicity regularizer, which consistently improves generalization in image and text classification, fine-tuning contrastive vision–language models, and reinforcement learning.

Probabilistic Methods · Monte Carlo and Sampling Methods

Emanuel Sommer, David Rügamer

The practical adoption of sampling-based inference (SAI) in Bayesian neural networks (BNNs) remains limited, partly due to persistent misconceptions about the feasibility and efficiency of sampling. This position paper argues that SAI has achieved computational parity with optimization-based methods and is at the verge of superseding such methods for effective and efficient inference in BNNs. This development should be in the interest of the whole community, promoting BNNs as a principled paradigm with its long-standing yet unfulfilled promise of providing principled uncertainty quantification for neural networks. SAI can even do more—yielding superior prediction performance through model averaging, serving as the foundation for a plethora of possible downstream tasks, and providing crucial insights into the landscape of BNNs. In order to make such a change happen and unfold the potential of sampling, overcoming current misconceptions is a necessary first step. The next step is to realign research efforts toward addressing remaining challenges in SAI. In particular, the community must focus on two core problems: sufficient exploration of the posterior landscape and high-fidelity distillation of posterior samples for efficient downstream inference. By addressing conceptual and practical obstacles, we can unlock the full potential of SAI and establish it as a central tool in Bayesian deep learning.

Optimization · Stochastic

Vassilis Apidopoulos, Iosif Lytras, Panayotis Mertikopoulos

Many optimization problems in machine learning and data science—from deep neural networks to Bayesian inference and beyond—fall outside the standard Lipschitz smoothness framework that underpins the convergence theory of stochastic gradient descent (SGD). Motivated by this theory-practice disconnect, we examine the almost sure convergence of the trajectories of SGD in non-convex landscapes under a generalized $(L_0,L)1)$-smoothness condition which allows for gradients with superlinear growth (even exponential). We begin by proposing a taming scheme for SGD that achieves almost sure convergence under a generalized ABC-type condition on the gradient noise. Subsequently, to relax this requirement, we introduce a more flexible, dissipative taming scheme which converges almost surely under less restrictive moment bound conditions for the stochastic gradients entering the process. For both taming schemes, we show that the generated trajectories avoid strict saddle points (and/or manifolds thereof) with probability 1 so, generically, both methods only converge to local minimizers.

Deep Learning · Theory

Zhiwei Bai, Zhangchen Zhou, Jiajie Zhao, Xiaolong Li, Zhiyu li, Feiyu Xiong, Hongkang Yang, Yaoyu Zhang, Zhi-Qin John Xu

Loss spikes commonly emerge during neural network training with the Adam optimizer across diverse architectures and scales, yet their underlying mechanism remains elusive. While previous explanations attribute these phenomena to sharper loss landscapes at lower loss, we show that landscape geometry alone is insufficient to explain the phenomenon. In this work, we pinpoint the root cause in the internal dynamics of Adam's second moment estimator. We identify a critical ``decoupling'' mechanism where the adaptive preconditioner $v_t$ fails to track the instantaneous squared gradients $g_t^2$, causing the adaptive mechanism to effectively fail. This decoupling allows the preconditioner to decay autonomously despite rising gradients, which pushes the maximum eigenvalue of the preconditioned Hessian beyond the stability threshold $2/\eta$ for sustained periods, manifesting as dramatic loss spikes. Through a quadratic approximation analysis, we theoretically and experimentally characterize five distinct stages of spike evolution and propose a predictor for anticipating spikes based on gradient-directional curvature. We empirically find that the proposed loss spike mechanism, although derived from simplified models, generalizes well to practical scenarios ranging from small neural networks to large-scale Transformers.

Optimization · Everything Else

Arghya Sinha, Aditya Banerjee, Trishit Mukherjee, Kunal Narayan Chaudhury

Trainable denoisers with Lipschitz control have become central to convergent image reconstruction. However, training neural networks that simultaneously offer strong denoising performance and global Lipschitz guarantees is challenging. Existing approaches enforce Lipschitz control only empirically, providing no guarantees beyond the training data. In this work, we show that by exploiting the action of permutations on the image lattice, we can constrain a neural architecture that is globally nonexpansive (Lipschitz bound $\leqslant 1$). We integrate the proposed denoiser with forward imaging operators to develop a reconstruction mechanism that is provably contractive and therefore globally convergent. Experiments on standard inverse problems, such as superresolution and deblurring, demonstrate that our reconstruction performance is competitive with softly constrained baselines while providing Lipschitz guarantees.

General Machine Learning · Representation Learning

Di Hong, Dazhong Rong, Yueming Wang

Recent work has shown that brain-aligned visual representations can emerge even in randomly initialized, high-dimensional neural networks, suggesting that cortical representations may be discovered rather than fully learned through task optimization. However, how such latent brain-relevant representations are stabilized and refined during development remains unclear. Motivated by this perspective and by neuroscientific evidence of activity-dependent synaptic pruning, we study how brain-aligned representations can emerge and be refined from high-dimensional unsupervised spiking systems. We propose a biologically grounded deep spiking neural network (SNN) that integrates unsupervised learning with developmental pruning dynamics. Starting from an overcomplete spiking architecture, the model self-organizes through sensory-driven activity while selectively eliminating weak or redundant synapses, progressively yielding compact and informative representations. Without using labels, the resulting network forms hierarchical visual representations that strongly align with neural responses across multiple areas of the mouse and macaque visual cortex, outperforming supervised and unsupervised ANN and SNN baselines. Synaptic pruning consistently enhances this alignment and further improves robustness under noisy and few-shot recognition settings. By unifying high-dimensional unsupervised spiking representations with activity-dependent synaptic pruning, this work provides a computational account of developmental refinement in visual cortex and bridges recent findings on emergent brain alignment in random networks with biologically grounded models of representation learning and structure formation.