论文检索

Deep Learning · Graph Neural Networks

Tingyi Cai, Yunliang Jiang, Ming Li, Lu Bai, Changqin Huang, Yi Wang

With the growing adoption of Hypergraph Neural Networks (HNNs) to model higher-order relationships in complex data, concerns about their security and robustness have become increasingly important. However, current security research often overlooks the unique structural characteristics of hypergraph models when developing adversarial attack and defense strategies. To address this gap, we demonstrate that hypergraphs are particularly vulnerable to node injection attacks, which align closely with real-world applications. Through empirical analysis, we develop a relatively unnoticeable attack approach by monitoring changes in homophily and leveraging this self-regulating property to enhance stealth. Building on these insights, we introduce HyperNear, i.e., $\underline{N}$ode inj$\underline{E}$ction $\underline{A}$ttacks on hype$\underline{R}$graph neural networks, the first node injection attack framework specifically tailored for HNNs. HyperNear integrates homophily-preserving strategies to optimize both stealth and attack effectiveness. Extensive experiments show that HyperNear achieves excellent performance and generalization, marking the first comprehensive study of injection attacks on hypergraphs. Our code is available at https://github.com/ca1man-2022/HyperNear.

Deep Learning · Graph Neural Networks

Alessandro Manenti, Daniele Zambon, Cesare Alippi

Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data. Given their latent nature, no graph observations are available to provide a direct training signal to the learnable relations. Therefore, graph topologies are typically learned on the prediction task alongside the other graph neural network parameters.In this paper, we demonstrate that minimizing point-prediction losses does not guarantee proper learning of the latent relational information and its associated uncertainty. Conversely, we prove that suitable loss functions on the stochastic model outputs simultaneously grant solving two tasks: (i) learning the unknown distribution of the latent graph and (ii) achieving optimal predictions of the target variable. Finally, we propose a sampling-based method that solves this joint learning task. Empirical results validate our theoretical claims and demonstrate the effectiveness of the proposed approach.

General Machine Learning · Unsupervised and Semi-supervised Learning

Giovanni Catania, Aurélien Decelle, Cyril Furtlehner, Beatriz Seoane

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the eigenbasis of the coupling matrix, exploiting the independent evolution of eigenmodes and revealing that the learning timescales are tied to the spectral decomposition of the empirical covariance matrix. We see that optimal points for early stopping arise from the interplay between these timescales and the initial conditions of training. Moreover, we show that finite data corrections can be accurately modeled through asymptotic random matrix theory calculations and provide the counterpart of generalized cross-validation in the energy based model context. Our analytical framework extends to binary-variable maximum-entropy pairwise models with minimal variations.These findings offer strategies to control overfitting in discrete-variable models through empirical shrinkage corrections, improving the management of overfitting in energy-based generative models.Finally, we propose a generalization to arbitrary energy-based models by deriving the neural tangent kernel dynamics of the score function under the score-matching algorithm.

Theory · Learning Theory

Emanuele Troiani, Hugo Cui, Yatin Dandi, FLORENT KRZAKALA, Lenka Zdeborová

In this manuscript, we study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. We first establish a mapping of such models to sequence multi-index models, a generalization of the widely studied multi-index model to sequential covariates, for which we establish a number of general results. In the context of Bayes-optimal learning, in the limit of large dimension $D$ and proportionally large number of samples $N$, we derive a sharp asymptotic characterization of the optimal performance as well as the performance of the best-known polynomial-time algorithm for this setting --namely approximate message-passing--, and characterize sharp thresholds on the minimal sample complexity required for better-than-random prediction performance. Our analysis uncovers, in particular, how the different layers are learned sequentially. Finally, we discuss how this sequential learning can also be observed in a realistic setup.

Optimization

Yang Luo, Zangwei Zheng, Ziheng Qin, Zirui Zhu, Yong Liu, Yang You

Large-batch training has become a cornerstone in accelerating the training of deep neural networks, yet it poses challenges in optimization and generalization. Existing optimizers like AdamW present performance degradation during language models' large-batch training, due to the information bottleneck in attention layers caused by the sharp increase of max attention logit. While the LAMB optimizer partially addresses this issue, some attention layers still face this issue. The reason is that $l_2$-norm-based trust ratios in LAMB are less effective in directly influencing the max value of query/key weights. Furthermore, the weight-wise trust ratio in LAMB is error-prone as it overlooks relationships of weight values within rows or columns. Building on these observations, we propose a novel optimizer, MERIT, which leverages the max-norm to calculate the trust ratio to constrain the max attention logit more effectively. Moreover, we further construct element-wise trust ratios to provide more robust update scaling by focusing on local weight structures. Extensive experiments of large-batch training across various sizes of GPT-2 models demonstrate the superior performance of MERIT. Notably, during the training of GPT-2 Medium, MERIT enables a 6k batch size without any performance degradation compared to the standard batch size (480) with 48B training tokens.This work highlights the importance of considering the max attention logit and finer-granularity trust ratio in large-batch training. It successfully improves the training stability and paves the way for larger batch usage, enabling faster development and iteration of large language models. Code is available at https://github.com/NUS-HPC-AI-Lab/MERIT.

Optimization

Tomoharu Iwata, Shinsaku Sakaue

We propose a data-driven method for reducing the dimensionality of linear programming problems (LPs) by generating instance-specific projection matrices using a neural network-based model. Once the model is trained using multiple LPs by maximizing the expected objective value, we can efficiently find high-quality feasible solutions of newly given LPs. Our method can shorten the computational time of any LP solvers due to its solver-agnostic nature, it can provide feasible solutions by relying on projection that reduces the number of variables, and it can handle LPs of different sizes using neural networks with permutation equivariance and invariance. We also provide a theoretical analysis of the generalization bound for learning a neural network to generate projection matrices that reduce the size of LPs. Our experimental results demonstrate that our method can obtain solutions with higher quality than the existing methods, while its computational time is significantly shorter than solving the original LPs.

Optimization

Yuyang Hu, Albert Peng, Weijie Gan, Peyman Milanfar, Mauricio Delbracio, Ulugbek Kamilov

Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. We introduce Stochastic deep Restoration Priors (ShaRP), a novel framework that stochastically leverages an ensemble of deep restoration models beyond denoisers to regularize inverse problems. By using generalized restoration models trained on a broad range of degradations beyond simple Gaussian noise, ShaRP effectively addresses structured artifacts and enables self-supervised training without fully sampled data. We prove that ShaRP minimizes an objective function involving a regularizer derived from the score functions of minimum mean square error (MMSE) restoration operators. We also provide theoretical guarantees for learning restoration operators from incomplete measurements. ShaRP achieves state-of-the-art performance on tasks such as magnetic resonance imaging reconstruction and single-image super-resolution, surpassing both denoiser- and diffusion-model-based methods without requiring retraining.

Probabilistic Methods · Bayesian Models and Methods

Parikshit Pareek, Abhijith Jayakumar, Kaarthik Sundar, Sidhant Misra, Deepjyoti Deka

Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods.

Deep Learning · Foundation Models

Na Lee, Konstantinos Barmpas, Yannis Panagakis, Dimitrios Adamos, Nikolaos Laskaris, Stefanos Zafeiriou

Foundation Models have demonstrated significant success across various domains in Artificial Intelligence (AI), yet their capabilities for brainwave modeling remain unclear. In this paper, we comprehensively evaluate current Large Brainwave Foundation Models (LBMs) through systematic fine-tuning experiments across multiple Brain-Computer Interface (BCI) benchmark tasks, including memory tasks and sleep stage classification. Our extensive analysis shows that state-of-the-art LBMs achieve only marginal improvements (0.5\%) over traditional deep architectures while requiring significantly more parameters (millions vs thousands), raising important questions about their efficiency and applicability in BCI contexts. Moreover, through detailed ablation studies and Low-Rank Adaptation (LoRA), we significantly reduce trainable parameters without performance degradation, while demonstrating that architectural and training inefficiencies limit LBMs' current capabilities. Our experiments span both full model fine-tuning and parameter-efficient adaptation techniques, providing insights into optimal training strategies for BCI applications. We pioneer the application of LoRA to LBMs, revealing that performance benefits generally emerge when adapting multiple neural network components simultaneously. These findings highlight the critical need for domain-specific development strategies to advance LBMs, suggesting that current architectures may require redesign to fully leverage the potential of foundation models in brainwave analysis.

Theory · Deep Learning

Pascal Jr Tikeng Notsawo, Guillaume Dumas, Guillaume Rabusseau

Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or implicit. More precisely, we show that when there exists a model with a property $P$ (e.g., sparse or low-rank weights) that generalizes on the problem of interest, gradient descent with a small but non-zero regularization of $P$ (e.g., $\ell_1$ or nuclear norm regularization) results in grokking. This extends previous work showing that small non-zero weight decay induces grokking. Moreover, our analysis shows that over-parameterization by adding depth makes it possible to grok or ungrok without explicitly using regularization, which is impossible in shallow cases. We further show that the $\ell_2$ norm is not a reliable proxy for generalization when the model is regularized toward a different property $P$, as the $\ell_2$ norm grows in many cases where no weight decay is used, but the model generalizes anyway. We also show that grokking can be amplified solely through data selection, with any other hyperparameter fixed.

Applications · Energy

Ankit Bhardwaj, Amar Phanishayee, Deepak Narayanan, Ryan Stutsman

In this paper, we investigate how to push the performance limits of serving Deep Neural Network (DNN) models on CPU-based servers. Specifically, we observe that while intra-operator parallelism across multiple threads is an effective way to reduce inference latency, it provides diminishing returns. Our primary insight is that instead of running a single instance of a model with all available threads on a server, running multiple instances each with smaller batch sizes and fewer threads for intra-op parallelism can provide lower inference latency. However, the right configuration is hard to determine manually since it is workload- (DNN model and batch size used by the serving system) and deployment-dependent (number of CPU cores on server). We present Packrat, a new serving system for online inference that given a model and batch size (𝐵) algorithmically picks the optimal number of instances (𝑖), the number of threads each should be allocated (𝑡), and the batch sizes each should operate on (𝑏) that minimizes latency. Packrat is built as an extension to TorchServe and supports online reconfigurations to avoid serving downtime. Averaged across a range of batch sizes, Packrat improves inference latency by 1.43× to 1.83× on a range of commonly used DNNs.

Deep Learning · Large Language Models

Alina Shutova, Vladimir Malinovskii, Vage Egiazarian, Denis Kuznedelev, Denis Mazur, Surkov Nikita, Ivan Ermakov, Dan Alistarh

Efficient real-world deployments of large language models (LLMs) rely on Key-Value (KV) caching for processing and generating long outputs, reducing the need for repetitive computation. For large contexts, Key-Value caches can take up tens of gigabytes of device memory, as they store vector representations for each token and layer. Recent work has shown that the cached vectors can be compressed through quantization, pruning or merging, but these techniques often compromise quality towards higher compression rates. In this work, we aim to improve Key \& Value compression by exploiting two observations: 1) the inherent dependencies between keys and values across different layers, and 2) the existence of high-compression methods for internal network states (e.g. attention Keys \& Values). We propose AQUA-KV, an adaptive quantization for Key-Value caches that relies on compact adapters to exploit existing dependencies between Keys and Values, and aims to "optimally" compress the information that cannot be predicted. AQUA-KV significantly improves compression rates, while maintaining high accuracy on state-of-the-art LLM families. On Llama 3.2 LLMs, we achieve near-lossless inference at 2-2.5 bits per value with under $1\%$ relative error in perplexity and LongBench scores. AQUA-KV is one-shot, simple, and efficient: it can be calibrated on a single GPU within 1-6 hours, even for 70B models.

Deep Learning · Algorithms

Dongyeop Lee, Kwanhee Lee, Jinseok Chung, Namhoon Lee

Sparsifying neural networks often suffers from seemingly inevitable performance degradation, and it remains challenging to restore the original performance despite much recent progress.Motivated by recent studies in robust optimization, we aim to tackle this problem by finding subnetworks that are both sparse and flat at the same time.Specifically, we formulate pruning as a sparsity-constrained optimization problem where flatness is encouraged as an objective.We solve it explicitly via an augmented Lagrange dual approach and extend it further by proposing a generalized projection operation, resulting in novel pruning methods called SAFE and its extension, SAFE$^+$.Extensive evaluations on standard image classification and language modeling tasks reveal that SAFE consistently yields sparse networks with improved generalization performance, which compares competitively to well-established baselines.In addition, SAFE demonstrates resilience to noisy data, making it well-suited for real-world conditions.

Deep Learning · Theory

Neil Mallinar, Daniel Beaglehole, Libin Zhu, Adityanarayanan Radhakrishnan, Parthe Pandit, Misha Belkin

Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example of "emergence", where model ability manifests sharply through a phase transition. In this work, we show that the phenomenon of grokking is not specific to neural networks nor to gradient descent-based optimization. Specifically, we show that this phenomenon occurs when learning modular arithmetic with Recursive Feature Machines (RFM), an iterative algorithm that uses the Average Gradient Outer Product (AGOP) to enable task-specific feature learning with general machine learning models. When used in conjunction with kernel machines, iterating RFM results in a fast transition from random, near zero, test accuracy to perfect test accuracy. This transition cannot be predicted from the training loss, which is identically zero, nor from the test loss, which remains constant in initial iterations. Instead, as we show, the transition is completely determined by feature learning: RFM gradually learns block-circulant features to solve modular arithmetic. Paralleling the results for RFM, we show that neural networks that solve modular arithmetic also learn block-circulant features. Furthermore, we present theoretical evidence that RFM uses such block-circulant features to implement the Fourier Multiplication Algorithm, which prior work posited as the generalizing solution neural networks learn on these tasks. Our results demonstrate that emergence can result purely from learning task-relevant features and is not specific to neural architectures nor gradient descent-based optimization methods. Furthermore, our work provides more evidence for AGOP as a key mechanism for feature learning in neural networks.

Konrad Mundinger, Max Zimmer, Aldo Kiem, Christoph Spiegel, Sebastian Pokutta

We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem at the intersection of discrete geometry and extremal combinatorics that is concerned with coloring the plane while avoiding monochromatic unit-distance pairs. Using neural networks as approximators, we reformulate this mixed discrete-continuous geometric coloring problem with hard constraints as an optimization task with a probabilistic, differentiable loss function. This enables gradient-based exploration of admissible configurations that most significantly led to the discovery of two novel six-colorings, providing the first improvement in thirty years to the off-diagonal variant of the original problem (Mundinger et al., 2024a). Here, we establish the underlying machine learning approach used to obtain these results and demonstrate its broader applicability through additional numerical insights.

Shikai Qiu, Lechao Xiao, Andrew Wilson, Jeffrey Pennington, Atish Agarwala

Understanding neural network training dynamics at scale is an important open problem. Although realistic model architectures, optimizers, and data interact in complex ways that make predictive theory challenging, we show that compute-optimally trained models exhibit remarkably precise collective regularities. Specifically, loss curves from models of varying sizes collapse onto a single universal curve when training compute and loss are normalized to unity at the end of training. With learning rate decay, discrepancies between normalized curves fall below the noise floor of individual models' loss curves across random seeds, yielding an exceptionally tight collapse we term "supercollapse." We observe supercollapse across learning rate schedules, datasets, and architectures, including transformers trained on next-token prediction. This collapse breaks down when hyperparameters are scaled suboptimally, providing a practical indicator of proper scaling. We explain these phenomena by connecting collapse to the power-law structure in typical neural scaling laws, and analyzing a simple but effective model of SGD noise dynamics that accurately captures how learning rate schedules deform loss curves away from power laws while preserving universality, and why learning rate decay suppresses variance to enable supercollapse.

Kwangjun Ahn, Gagik Magakyan, Ashok Cutkosky

This work investigates the effectiveness of schedule-free methods, developed by A. Defazio et al. (NeurIPS 2024), in nonconvex optimization settings, inspired by their remarkable empirical success in training neural networks. Specifically, we show that schedule-free SGD achieves optimal iteration complexity for nonsmooth, non-convex optimization problems. Our proof begins with the development of a general framework for online-to-nonconvex conversion, which converts a given online learning algorithm into an optimization algorithm for nonconvex losses. Our general framework not only recovers existing conversions but also leads to two novel conversion schemes. Notably, one of these new conversions corresponds directly to schedule-free SGD, allowing us to establish its optimality. Additionally, our analysis provides valuable insights into the parameter choices for schedule-free SGD, addressing a theoretical gap that the convex theory cannot explain.

Haibo Chen, Xin Wang, Zeyang Zhang, Haoyang Li, Ling Feng, Wenwu Zhu

Graph foundation models (GFMs) aim to share graph knowledge across diverse domains and tasks to boost graph machine learning. However, existing GFMs rely on hand-designed and fixed graph neural network (GNN) architectures, failing to utilize optimal architectures *w.r.t.* specific domains and tasks, inevitably leading to suboptimal performance in diverse graph domains and tasks. In this paper, we explore graph neural architecture search (GNAS) for GFMs for the first time, which suffers from the problem of *architecture inconsistency*, i.e., the optimal architectures for different tasks and domains vary. We tackle this problem by discovering an invariant graph-architecture relationship across domains and tasks, which imposes three challenges: i) how to capture invariant and variant patterns; ii) how to customize architectures to adapt to diverse domains and tasks; iii) how to mitigate the data domination phenomenon during the architecture search process.To address these challenges, we propose **Auto**mated **G**raph **F**oundation **M**odel with Adaptive Architecture Customization (**AutoGFM**), providing a theoretical analysis to demonstrate the limitations of existing GNAS. Specifically, we first propose a disentangled contrastive graph encoder to learn invariant and variant patterns. Then, we design an invariant-guided architecture customization strategy to customize architectures for data from diverse domains and tasks. Finally, we propose a curriculum architecture customization mechanism to mitigate the phenomenon of particular data dominating the search process. Extensive experiments demonstrate that **AutoGFM** outperforms baselines, achieving state-of-the-art performance.

Deep Learning · Generative Models and Autoencoders

Jaemoo Choi, Jaewoong Choi, Dohyun Kwon

We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning OT Maps with neural networks, often generates spurious solutions that fail to transfer one distribution to another accurately. We identify a sufficient condition under which the max-min solution of Semi-dual Neural OT recovers the true OT Map. Moreover, to address cases when this sufficient condition is not satisfied, we propose a novel method, OTP, which learns both the OT Map and the Optimal Transport Plan, representing the optimal coupling between two distributions. Under sharp assumptions on the distributions, we prove that our model eliminates the spurious solution issue and correctly solves the OT problem. Our experiments show that the OTP model recovers the optimal transport map where existing methods fail and outperforms current OT-based models in image-to-image translation tasks. Notably, the OTP model can learn stochastic transport maps when deterministic OT Maps do not exist, such as one-to-many tasks like colorization.

Deep Learning · Large Language Models

Guan Zhong, Likang Wu, Hongke Zhao, Ming He, Jianping Fan

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. Through a series of experiments, we uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention (as in LLMs) nor fixed connectivity (as in GNNs) is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: \href{https://anonymous.4open.science/r/LLM_exploration-B21F}{anonymous.4open.science/LLM\_exploration-B21F}