论文检索

Deep Learning · Theory

Jiahan Zhang, Yaoyu Zhang, Tao Luo

In this paper, we study the Karush-Kuhn-Tucker (KKT) points of the associated maximum-margin problem in homogeneous neural networks, including fully-connected and convolutional neural networks. In particular, We investigates the relationship between such KKT points across networks of different widths generated. We introduce and formalize the \textbf{KKT point embedding principle}, establishing that KKT points of a homogeneous network's max-margin problem ($P_{\Phi}$) can be embedded into the KKT points of a larger network's problem ($P_{\tilde{\Phi}}$) via specific linear isometric transformations. We rigorously prove this principle holds for neuron splitting in fully-connected networks and channel splitting in convolutional neural networks. Furthermore, we connect this static embedding to the dynamics of gradient flow training with smooth losses. We demonstrate that trajectories initiated from appropriately mapped points remain mapped throughout training and that the resulting $\omega$-limit sets of directions are correspondingly mapped , thereby preserving the alignment with KKT directions dynamically when directional convergence occurs. We conduct several experiments to justify that trajectories are preserved. Our findings offer insights into the effects of network width, parameter redundancy, and the structural connections between solutions found via optimization in homogeneous networks of varying sizes.

Social Aspects · Accountability, Transparency and Interpretability

Yazheng Liu, Xi Zhang, Sihong Xie, Hui Xiong

Explaining graph neural networks (GNNs) is a key approach to improve the trustworthiness of GNN in high-stakes applications, such as finance and healthcare. However, existing methods are vulnerable to perturbations, raising concerns about explanation reliability. Prior methods enhance explanation robustness using model retraining or explanation ensemble, with certain weaknesses. Retraining leads to models that are different from the original target model and misleading explanations, while ensemble can produce contradictory results due to different inputs or models. To improve explanation robustness without the above weaknesses, we take an unexplored route and exploit the two edge geometry properties curvature and resistance to enhance explanation robustness. We are the first to prove that these geometric notions can be used to bound explanation robustness. We design a general optimization algorithm to incorporate these geometric properties into a wide spectrum of base GNN explanation methods to enhance the robustness of base explanations. We empirically show that our method outperforms six base explanation methods in robustness across nine datasets spanning node classification, link prediction, and graph classification tasks, improving fidelity in 80\% of the cases and achieving up to a 10\% relative improvement in robust performance. The code is available at [https://github.com/yazhengliu/Robust_explanation_curvature](https://github.com/yazhengliu/Robust_explanation_curvature).

Applications · Physics

Chenhui Xu, Dancheng Liu, Amir Nassereldine, Jinjun Xiong

Physics‑Informed Neural Networks (PINNs) often exhibit “failure modes” in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep loss barriers. We challenge this understanding by demonstrate that the real culprit is insufficient arithmetic precision: with standard FP32, the L‑BFGS optimizer prematurely satisfies its convergence test, freezing the network in a spurious failure phase. Simply upgrading to FP64 rescues optimization, enabling vanilla PINNs to solve PDEs without any failure modes. These results reframe PINN failure modes as precision‑induced stalls rather than inescapable local minima and expose a three‑stage training dynamic—un‑converged, failure, success—whose boundaries shift with numerical precision. Our findings emphasize that rigorous arithmetic precision is the key to dependable PDE solving with neural networks. Our code is available at Supplementary Material.

Optimization · Neural Network Optimization

Xiao Han, ZIMO ZHAO, Wanyu Wang, Maolin Wang, Zitao Liu, Yi Chang, Xiangyu Zhao

Recent advancements in Large Language Models (LLMs) have emphasized the critical role of fine-tuning (FT) techniques in adapting LLMs to specific tasks, especially when retraining from scratch is computationally infeasible. Fine-tuning enables LLMs to leverage task- or domain-specific data, producing models that more effectively meet the requirements of targeted applications. However, con- ventional FT approaches often suffer from catastrophic forgetting and suboptimal data efficiency, limiting their real-world applicability. To address these challenges, this paper proposes DEAL, a novel framework that integrates Low-Rank Adapta- tion (LoRA) with a continuous fine-tuning strategy. By incorporating knowledge retention and adaptive parameter update modules, the framework mitigates the limitations of existing FT methods while maintaining efficiency. Experiments on 15 diverse datasets show that DEAL consistently outperforms baseline methods, yielding substantial gains in task accuracy and resource efficiency. These find- ings demonstrate the potential of our approach to advance continual adaptation in LLMs by enhancing task performance while improving resource efficiency. The source code is publicly available at https://github.com/Applied-Machine-Learning-Lab/DEAL.

Applications · Physics

Ruoyan Li, Guancheng Wan, Zijie Huang, Zixiao Liu, Haixin Wang, Xiao Luo, Wei Wang, Yizhou Sun

Flow‐field reconstruction from sparse sensor measurements remains a central challenge in modern fluid dynamics, as the need for high‐fidelity data often conflicts with practical limits on sensor deployment. Existing deep learning–based methods have demonstrated promising results, but they typically depend on simplifying assumptions such as two‐dimensional domains, predefined governing equations, synthetic datasets derived from idealized flow physics, and unconstrained sensor placement. In this work, we address these limitations by studying flow reconstruction under realistic conditions and introducing a \emph{directional transport‐aware Graph Neural Network (GNN)} that explicitly encodes both flow directionality and information transport. We further show that conventional sensor placement strategies frequently yield suboptimal configurations. To overcome this, we propose a novel \emph{Two‐Step Constrained PPO} procedure for Proximal Policy Optimization (PPO), which jointly optimizes sensor layouts by incorporating flow variability and accounts for reconstruction model's performance disparity with respect to sensor placement. We conduct comprehensive experiments under realistic assumptions to benchmark the performance of our reconstruction model and sensor placement policy. Together, they achieve significant improvements over existing methods.

Deep Learning · Algorithms

Kangcong Li, Peng Ye, Chongjun Tu, Lin Zhang, Chunfeng Song, Jiamin Wu, Tao Yang, Qihao Zheng, Tao Chen

While Large Language Models (LLMs) demonstrate strong performance across domains, their long-context capabilities are limited by transient neural activations causing information decay and unstructured feed-forward network (FFN) weights leading to semantic fragmentation. Inspired by the brain’s working memory and cortical modularity, we propose PaceLLM, featuring two innovations: (1) a Persistent Activity (PA) Mechanism that mimics prefrontal cortex (PFC) neurons’ persistent firing by introducing an activation-level memory bank to dynamically retrieve, reuse, and update critical FFN states, addressing contextual decay; and (2) Cortical Expert (CE) Clustering that emulates task-adaptive neural specialization to reorganize FFN weights into semantic modules, establishing cross-token dependencies and mitigating fragmentation. Extensive evaluations show that PaceLLM achieves 6% improvement on LongBench’s Multi-document QA and 12.5–17.5% performance gains on $\infty$-Bench tasks, while extending measurable context length to 200K tokens in Needle-In-A-Haystack (NIAH) tests. This work pioneers brain-inspired LLM optimization and is complementary to other works. Besides, it can be generalized to any model and enhance their long-context performance and interpretability without structural overhauls.

Optimization · Stochastic & Convex Optimization

Aleksey Minabutdinov, Patrick Cheridito

We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory, physics and economics. While traditional numerical methods suffer from the curse of dimensionality and become computationally intractable in high dimensions, more recent neural network-based approaches scale better, but have mostly been studied with the aim of solving optimal transport problems and require the solution of complicated optimization or max-min problems. Using an implicit Fenchel formulation of convex conjugation, our approach facilitates an efficient gradient-based framework for the minimization of approximation errors and, as a byproduct, also provides a posteriori error estimates for the approximation quality. Numerical experiments demonstrate our method's ability to deliver accurate results across different high-dimensional examples. Moreover, by employing symbolic regression with Kolmogorov–Arnold networks, it is able to obtain the exact convex conjugates of specific convex functions.

Optimization · Neural Network Optimization

Kevin Frans, Sergey Levine, Pieter Abbeel

In this work, we take an experimentally grounded look at neural network optimization. Building on the Shampoo family of algorithms, we identify and alleviate three key issues, resulting in the proposed SPlus method. First, we find that naive Shampoo is prone to divergence when matrix-inverses are cached for long periods. We introduce an alternate bounded update combining a historical eigenbasis with instantaneous normalization, resulting in across-the-board stability and significantly lower computational requirements. Second, we adapt a shape-aware scaling to enable learning rate transfer across network width. Third, we find that high learning rates result in large parameter noise, and propose a simple iterate-averaging scheme which unblocks faster learning. To properly confirm these findings, we introduce a pointed Transformer training benchmark, considering three objectives (language modelling, image classification, and diffusion modelling) across different stages of training. On average, SPlus is able to reach the validation performance of Adam within 44-58% of the gradient steps and 62-83% of the wallclock time.

Tingting Dan, Zhihao Fan, Guorong Wu

Alzheimer’s disease (AD) is marked by cognitive decline along with the widespread of tau aggregates across the brain cortex. Due to the challenges of imaging pathology spreading flows *in vivo*, however, quantitative analysis on the cortical pathways of tau propagation and its interaction with the cascade of amyloid-beta (A$\beta$) plaques lags behind the experimental insights of underlying pathophysiological mechanisms. To address this challenge, we present a physics-informed neural network, empowered by mean-field theory, to uncover the biologically meaningful spreading pathways of tau aggregates between two longitudinal snapshots. Following the notion of `prion-like' mechanism in AD, we first formulate the dynamics of tau propagation as a mean-field game (MFG), where the spread of tau aggregate at each location (aka. agent) depends on the collective behavior of the surrounding agents as well as the potential field formed by amyloid burden. Given the governing equation of propagation dynamics, MFG reaches an equilibrium that allows us to model the evolution of tau aggregates as an optimal transport with the lowest cost in *Wasserstein* space. By leveraging the variational primal-dual structure in MFG, we propose a *Wasserstein*-1 Lagrangian generative adversarial network (GAN), in which a Lipschitz critic seeks the appropriate transport cost at the population level and a generator parameterizes the flow fields of optimal transport across individuals. Additionally, we incorporate a symbolic regression module to derive an explicit formulation capturing the A$\beta$-tau crosstalk. Experimental results on public neuroimaging datasets demonstrate that our explainable deep model not only yields precise and reliable predictions of future tau progression for unseen new subjects but also provides a new window to uncover new understanding of pathology propagation in AD through learning-based approaches.

Theory · Learning Theory

Hongrui Chen, Jihao Long, Lei Wu

"We consider the problem of learning functions within the $\mathcal{F}_{p,\pi}$ and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks, as well as kernel methods. Leveraging tools from information-based complexity (IBC), we establish a dual equivalence between approximation and estimation, and then apply it to study the learning of the preceding function spaces. The duality allows us to focus on the more tractable problem between approximation and estimation. To showcase the efficacy of our duality framework, we delve into two important but under-explored problems: \begin{itemize} \item \textbf{Random feature learning beyond kernel regime:} We derive sharp bounds for learning $\cF_{p,\pi}$ using RFMs. Notably, the learning is efficient without the curse of dimensionality for $p>1$. This underscores the extended applicability of RFMs beyond the traditional kernel regime, since $\mathcal{F}_{p,\pi}$ with $p<2$ is strictly larger than the corresponding reproducing kernel Hilbert space (RKHS) where $p=2$. \item \textbf{The $L^\infty$ learning of RKHS:} We establish sharp, spectrum-dependent characterizations for the convergence of $L^\infty$ learning error in both noiseless and noisy settings. Surprisingly, we show that popular kernel ridge regression can achieve near-optimal performance in $L^\infty$ learning, despite it primarily minimizing square loss. \end{itemize} To establish the aforementioned duality, we introduce a type of IBC, termed $I$-complexity, to measure the size of a function class. Notably, $I$-complexity offers a tight characterization of learning in noiseless settings, yields lower bounds comparable to Le Cam's in noisy settings, and is versatile in deriving upper bounds. We believe that our duality framework holds potential for broad application in learning analysis across more scenarios."

Theory · Learning Theory

Maria-Florina Balcan, Anh Nguyen, Dravyansh Sharma

Modern machine learning algorithms, especially deep learning-based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search-based approaches to automating this laborious and compute-intensive task, the fundamental learning-theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data-driven setting. We assume that we have a series of learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile, and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts, including tools from algebraic geometry, differential geometry, and constrained optimization. We use this to show that the learning-theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications—tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

Nicolas Zucchet, Francesco D&#x27;Angelo, Andrew Lampinen, Stephanie Chan

Emergence is a fascinating property of large language models and neural networks more broadly: as models scale and train for longer, they sometimes develop new abilities in sudden ways. Despite initial studies, we still lack a comprehensive understanding of how and when these abilities emerge. To address this gap, we study the emergence over training of sparse attention, a critical and frequently observed attention pattern in Transformers. By combining theoretical analysis of a toy model with empirical observations on small Transformers trained on a linear regression variant, we uncover the mechanics driving sparse attention emergence and reveal that emergence timing follows power laws based on task structure, architecture, and optimizer choice. We additionally find that repetition can greatly speed up emergence. Finally, we confirm these results on a well-studied in-context associative recall task. Our findings provide a simple, theoretically grounded framework for understanding how data distributions and model design influence the learning dynamics behind one form of emergence.

Applications · Robotics

Korneel Van den Berghe, Stein Stroobants, Vijay Janapa Reddi, Guido de Croon

Neuromorphic computing systems are set to revolutionize energy-constrained robotics by achieving orders-of-magnitude efficiency gains, while enabling native temporal processing. Spiking Neural Networks (SNNs) represent a promising algorithmic approach for these systems, yet their application to complex control tasks faces two critical challenges: (1) the non-differentiable nature of spiking neurons necessitates surrogate gradients with unclear optimization properties, and (2) the stateful dynamics of SNNs require training on sequences, which in reinforcement learning (RL) is hindered by limited sequence lengths during early training, preventing the network from bridging its warm-up period. We address these challenges by systematically analyzing surrogate gradient slope settings, showing that shallower slopes increase gradient magnitude in deeper layers but reduce alignment with true gradients. In supervised learning, we find no clear preference for fixed or scheduled slopes. The effect is much more pronounced in RL settings, where shallower slopes or scheduled slopes lead to a $\times2.1$ improvement in both training and final deployed performance. Next, we propose a novel training approach that leverages a privileged guiding policy to bootstrap the learning process, while still exploiting online environment interactions with the spiking policy. Combining our method with an adaptive slope schedule for a real-world drone position control task, we achieve an average return of 400 points, substantially outperforming prior techniques, including Behavioral Cloning and TD3BC, which achieve at most –200 points under the same conditions. This work advances both the theoretical understanding of surrogate gradient learning in SNNs and practical training methodologies for neuromorphic controllers demonstrated in real-world robotic systems.

Optimization · Neural Network Optimization

Thomas Pethick, Wanyun Xie, Mete Erdogan, Kimon Antonakopoulos, Antonio Silveti-Falls, Volkan Cevher

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of ($L_0$,$L_1$)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal $O(n^{-1/4})$ convergence rate by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning, which we dub Clipped Scion, and demonstrate their properties on image classification and language modeling. The code is available at https://github.com/LIONS-EPFL/ClippedScion.

Applications · Neuroscience, Cognitive Science

Yangxuan Zhou, Sha Zhao, Jiquan Wang, Haiteng Jiang, Shijian Li, Tao Li, Gang Pan

Human brain achieves dynamic stability-plasticity balance through synaptic homeostasis, a self-regulatory mechanism that stabilizes critical memory traces while preserving optimal learning capacities. Inspired by this biological principle, we propose SPICED: a neuromorphic framework that integrates the synaptic homeostasis mechanism for unsupervised continual EEG decoding, particularly addressing practical scenarios where new individuals with inter-individual variability emerge continually. SPICED comprises a novel synaptic network that enables dynamic expansion during continual adaptation through three bio-inspired neural mechanisms: (1) critical memory reactivation, which mimics brain functional specificity, selectively activates task-relevant memories to facilitate adaptation; (2) synaptic consolidation, which strengthens these reactivated critical memory traces and enhances their replay prioritizations for further adaptations and (3) synaptic renormalization, which are periodically triggered to weaken global memory traces to preserve learning capacities. The interplay within synaptic homeostasis dynamically strengthens task-discriminative memory traces and weakens detrimental memories. By integrating these mechanisms with continual learning system, SPICED preferentially replays task-discriminative memory traces that exhibit strong associations with newly emerging individuals, thereby achieving robust adaptations. Meanwhile, SPICED effectively mitigates catastrophic forgetting by suppressing the replay prioritization of detrimental memories during long-term continual learning. Validated on three EEG datasets, SPICED show its effectiveness. More importantly, SPICED bridges biological neural mechanisms and artificial intelligence through synaptic homeostasis, providing insights into the broader applicability of bio-inspired principles.

General Machine Learning · Transfer, Multitask and Meta-learning

Tim Genewein, Kevin Li, Jordi Grau-Moya, Anian Ruoss, Laurent Orseau, Marcus Hutter

Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.

Optimization

Xijun Li, Jiexiang Yang, Jinghao Wang, Bo Peng, Jianguo Yao, Haibing Guan

Combinatorial optimization (CO) problems, central to operation research and theoretical computer science, present significant computational challenges due to their $\mathcal{NP}$-hard nature. While large language models (LLMs) have emerged as promising tools for CO—either by directly generating solutions or synthesizing solver-specific codes—existing approaches often $\textit{neglect critical structural priors inherent to CO problems}$, leading to suboptimality and iterative inefficiency. Inspired by human experts’ success in leveraging CO structures for algorithm design, we propose $\texttt{STRCMP}$, a novel structure-aware LLM-based algorithm discovery framework that systematically integrates structure priors to enhance solution quality and solving efficiency. Our framework combines a graph neural network (GNN) for extracting structural embeddings from CO instances with an LLM conditioned on these embeddings to identify high-performed algorithms in the form of solver-specific codes. This composite architecture ensures syntactic correctness, preserves problem topology, and aligns with natural language objectives, while an evolutionary refinement process iteratively optimizes generated algorithm. Extensive evaluations across Mixed Integer Linear Programming and Boolean Satisfiability problems, using nine benchmark datasets, demonstrate that our proposed $\texttt{STRCMP}$ outperforms five strong neural and LLM-based methods by a large margin, in terms of both solution optimality and computational efficiency. The code is publicly available in the repository: https://github.com/Y-Palver/L2O-STRCMP.

Social Aspects · Accountability, Transparency and Interpretability

Dilyara Bareeva, Marina Höhne, Alexander Warnecke, Lukas Pirch, Klaus-Robert Müller, Konrad Rieck, Sebastian Lapuschkin, Kirill Bykov

Feature Visualization (FV) is a widely used technique for interpreting concepts learned by Deep Neural Networks (DNNs), which synthesizes input patterns that maximally activate a given feature. Despite its popularity, the trustworthiness of FV explanations has received limited attention. We introduce Gradient Slingshots, a novel method that enables FV manipulation without modifying model architecture or significantly degrading performance. By shaping new trajectories in off-distribution regions of a feature's activation landscape, we coerce the optimization process to converge to a predefined visualization. We evaluate our approach on several DNN architectures, demonstrating its ability to replace faithful FVs with arbitrary targets. These results expose a critical vulnerability: auditors relying solely on FV may accept entirely fabricated explanations. To mitigate this risk, we propose a straightforward defense and quantitatively demonstrate its effectiveness.

Deep Learning · Robustness

Zenghui Yang, Xingquan Zuo, Hai Huang, Gang Chen, Xinchao Zhao, Tianle Zhang

Deep neural networks have become foundational in various applications but remain vulnerable to adversarial patch attacks. Crafting effective adversarial patches is inherently challenging due to the combinatorial complexity involved in jointly optimizing critical factors such as patch shape, location, number, and content. Existing approaches often simplify this optimization by addressing each factor independently, which limits their effectiveness. To tackle this significant challenge, we introduce a novel and flexible adversarial attack framework termed IMPACT (Irregular Multi-Patch Adversarial Composition based on Two-phase optimization). IMPACT uniquely enables comprehensive optimization of all essential patch factors using gradient-free methods. Specifically, we propose a novel dimensionality reduction encoding scheme that substantially lowers computational complexity while preserving expressive power. Leveraging this encoding, we further develop a two-phase optimization framework: phase 1 employs differential evolution for joint optimization of patch mask and content, while phase 2 refines patch content using an evolutionary strategy for enhanced precision. Additionally, we introduce a new aggregation algorithm explicitly designed to produce contiguous, irregular patches by merging localized regions, ensuring physical applicability. Extensive experiments demonstrate that our method significantly outperforms several state-of-the-art approaches, highlighting the critical benefit of jointly optimizing all patch factors in adversarial patch attacks.

Deep Learning · Graph Neural Networks

Yisen Gao, Xingcheng Fu, Qingyun Sun, Jianxin Li, Xianxian LI

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified latent space, modeling prediction tasks including classification and regression as a form of conditional generation. However, due to the non-Euclidean nature of graph data, features of different curvatures are entangled in the same latent space without releasing their geometric potential. To address this issue, we aim to construt an ideal Riemannian diffusion model to capture distinct manifold signatures of complex graph data and learn their distribution. This goal faces two challenges: numerical instability caused by exponential mapping during the encoding proces and manifold deviation during diffusion generation. To address these challenges, we propose **GeoMancer**: a novel Riemannian graph diffusion framework for both generation and prediction tasks. To mitigate numerical instability, we replace exponential mapping with an isometric-invariant Riemannian gyrokernel approach and decouple multi-level features onto their respective task-specific manifolds to learn optimal representations. To address manifold deviation, we introduce a manifold-constrained diffusion method and a self-guided strategy for unconditional generation, ensuring that the generated data remains aligned with the manifold signature. Extensive experiments validate the effectiveness of our approach, demonstrating superior performance across a variety of tasks.