论文检索

General Machine Learning · Transfer, Multitask and Meta-learning

Ming Zhang, Qixin Zhang, Xiao Luo, Junyu Luo, Wei Ju, Zhiping Xiao, Ming Zhang

Test-time adaptation aims to adapt a well-trained model using test data only, without accessing training data. It is a crucial topic in machine learning, enabling a wide range of applications in the real world, especially when it comes to data privacy. While existing works on test-time adaptation primarily focus on Euclidean data, research on non-Euclidean graph data remains scarce. Prevalent graph neural network methods could encounter serious performance degradation in the face of test-time domain shifts. In this work, we propose a novel method named Adaptive Subgraph-based Selection and Regularized Prototype Supervision (ASSESS) for reliable test-time adaptation on graphs. Specifically, to achieve flexible selection of reliable test graphs, ASSESS adopts an adaptive selection strategy based on fine-grained individual-level subgraph mutual information. Moreover, to utilize the information from both training and test graphs, ASSESS constructs semantic prototypes from the well-trained model as prior knowledge from the unknown training graphs and optimizes the posterior given the unlabeled test graphs. We also provide a theoretical analysis of the proposed algorithm. Extensive experiments verify the effectiveness of ASSESS against various baselines.

Deep Learning · Graph Neural Networks

Shuo Wang, Shunyang Huang, Jinghui Yuan, Zhixiang Shen, zhao kang

Fusing heterogeneous information remains a persistent challenge in modern data analysis. While significant progress has been made, existing approaches often fail to account for the inherent heterogeneity of object patterns across different semantic spaces. To address this limitation, we propose the **Cooperation of Experts (CoE)** framework, which encodes multi-typed information into unified heterogeneous multiplex networks. By transcending modality and connection differences, CoE provides a powerful and flexible model for capturing the intricate structures of real-world complex data. In our framework, dedicated encoders act as domain-specific experts, each specializing in learning distinct relational patterns in specific semantic spaces. To enhance robustness and extract complementary knowledge, these experts collaborate through a novel **large margin** mechanism supported by a tailored optimization strategy. Rigorous theoretical analyses guarantee the framework’s feasibility and stability, while extensive experiments across diverse benchmarks demonstrate its superior performance and broad applicability.

Deep Learning · Graph Neural Networks

Michael Sun, Orion Foo, Gang Liu, Wojciech Matusik, Jie Chen

Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains challenging to decode them in a principled manner, because the nodes of a DAG can have many different topological orders. In this work, we propose a grammar-based approach to constructing a principled, compact and equivalent sequential representation of a DAG. Specifically, we view a graph as derivations over an unambiguous grammar, where the DAG corresponds to a unique sequence of production rules. Equivalently, the procedure to construct such a description can be viewed as a lossless compression of the data. Such a representation has many uses, including building a generative model for graph generation, learning a latent space for property prediction, and leveraging the sequence representational continuity for Bayesian Optimization over structured data.

Deep Learning · Graph Neural Networks

Masahiro Negishi, Thomas Gärtner, Pascal Welke

We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the _functional_ distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to _structural_ distances on graphs that ignore task-specific information. To address this gap, we distill the distance between MPNN embeddings into an interpretable graph distance. Our method uses optimal transport on the Weisfeiler Leman Labeling Tree (WILT), where the edge weights reveal subgraphs that strongly influence the distance between embeddings. This approach generalizes two well-known graph kernels and can be computed in linear time. Through extensive experiments, we demonstrate that MPNNs define the relative position of embeddings by focusing on a small set of subgraphs that are known to be functionally important in the domain.

Deep Learning · Graph Neural Networks

Zhaoxuan Kan, Husheng Han, shangyi shi, Tenghui Hua, Hang Lu, Xiaowei Li, Jianan Mu, Xing Hu

Graph Convolutional Neural Networks (GCNs) have gained widespread popularity in various fields like personal healthcare and financial systems, due to their remarkable performance. Despite the growing demand for cloud-based GCN services, privacy concerns over sensitive graph data remain significant. Homomorphic Encryption (HE) facilitates Privacy-Preserving Machine Learning (PPML) by allowing computations to be performed on encrypted data. However, HE introduces substantial computational overhead, particularly for GCN operations that require rotations and multiplications in matrix products. The sparsity of GCNs offers significant performance potential, but their irregularity introduces additional operations that reduce practical gains. In this paper, we propose FicGCN, a HE-based framework specifically designed to harness the sparse characteristics of GCNs and strike a globally optimal balance between aggregation and combination operations. FicGCN employs a latency-aware packing scheme, a Sparse Intra-Ciphertext Aggregation (SpIntra-CA) method to minimize rotation overhead, and a region-based data reordering driven by local adjacency structure. We evaluated FicGCN on several popular datasets, and the results show that FicGCN achieved the best performance across all tested datasets, with up to a $4.10\times$ improvement over the latest design.

Theory · Online Learning and Bandits

Junze Deng, Qinhang Wu, Peizhong Ju, Sen Lin, Yingbin LIANG, Ness Shroff

Rehearsal-based methods have shown superior performance in addressing catastrophic forgetting in continual learning (CL) by storing and training on a subset of past data alongside new data in current task. While such a concurrent rehearsal strategy is widely used, it remains unclear if this approach is always optimal. Inspired by human learning, where sequentially revisiting tasks helps mitigate forgetting, we explore whether sequential rehearsal can offer greater benefits for CL compared to standard concurrent rehearsal. To address this question, we conduct a theoretical analysis of rehearsal-based CL in overparameterized linear models, comparing two strategies: 1) Concurrent Rehearsal, where past and new data are trained together, and 2) Sequential Rehearsal, where new data is trained first, followed by revisiting past data sequentially. By explicitly characterizing forgetting and generalization error, we show that sequential rehearsal performs better when tasks are less similar. These insights further motivate a novel Hybrid Rehearsal method, which trains similar tasks concurrently and revisits dissimilar tasks sequentially. We characterize its forgetting and generalization performance, and our experiments with deep neural networks further confirm that the hybrid approach outperforms standard concurrent rehearsal. This work provides the first comprehensive theoretical analysis of rehearsal-based CL.

Applications · Neuroscience, Cognitive Science

Qi Xu, Junyang Zhu, Dongdong Zhou, Hao Chen, Yang Liu, Jiangrong Shen, Qiang Zhang

Deep neural networks (DNNs) excel in computer vision tasks, especially, few-shot learning (FSL), which is increasingly important for generalizing from limited examples. However, DNNs are computationally expensive with scalability issues in real world. Spiking Neural Networks (SNNs), with their event-driven nature and low energy consumption, are particularly efficient in processing sparse and dynamic data, though they still encounter difficulties in capturing complex spatiotemporal features and performing accurate cross-class comparisons. To further enhance the performance and efficiency of SNNs in few-shot learning, we propose a few-shot learning framework based on SNNs, which combines a self-feature extractor module and a cross-feature contrastive module to refine feature representation and reduce power consumption. We apply the combination of temporal efficient training loss and InfoNCE loss to optimize the temporal dynamics of spike trains and enhance the discriminative power. Experimental results show that the proposed FSL-SNN significantly improves the classification performance on the neuromorphic dataset N-Omniglot, and also achieves competitive performance to ANNs on static datasets such as CUB and miniImageNet with low power consumption.

Applications · Everything Else

Haohan Zou, Jie Feng, Hao Zhao, Yuanyuan Shi

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for *high-dimensional* and *non-polynomial* systems. Given the symbolic nature of the Lyapunov function candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature. Full implementation is available on [Github](https://github.com/JieFeng-cse/Analytical-Lyapunov-Function-Discovery).

Optimization

Michael Sander, Vincent Roulet, Tianlin Liu, Mathieu Blondel

Energy-based models (EBMs) offer a flexible framework for parameterizing probability distributions using neural networks.However, learning EBMs by exact maximum likelihood estimation (MLE) is generally intractable, due to the need to compute the partition function.In this paper, we propose a novel min-min formulation for approximately learning probabilistic EBMs in combinatorially-large discrete spaces, such as sets or permutations. Our key idea is to jointly learn both an energy model and its log-partition, parameterized as a neural network. Our approach not only provides a novel tractable objective criterion to learn EBMs by stochastic gradient descent (without relying on MCMC), but also a novel means to estimate the log-partition function on unseen data points.On the theoretical side, we show that our approach recovers the optimal MLE solution when optimizing in the space of continuous functions.Furthermore, we show that our approach naturally extends to the broader family of Fenchel-Young losses, allowing us to obtainthe first tractable method for optimizing the sparsemax loss in combinatorially-large spaces.We demonstrate our approach on multilabel classification and label ranking.

Deep Learning · Attention Mechanisms

Binchi Zhang, Zaiyi Zheng, Zhengzhang Chen, Jundong Li

Symmetry in the parameter space of deep neural networks (DNNs) has proven beneficial for various deep learning applications. A well-known example is the permutation symmetry in Multi-Layer Perceptrons (MLPs), where permuting the rows of weight matrices in one layer and applying the inverse permutation to adjacent layers yields a functionally equivalent model. While permutation symmetry fully characterizes the equivalence set for MLPs, its discrete nature limits its utility for transformers. In this paper, we introduce rotation symmetry, a novel form of parameter space symmetry for transformers that generalizes permutation symmetry by rotating parameter matrices in self-attention layers. Unlike permutation symmetry, rotation symmetry operates in a continuous domain, thereby significantly expanding the equivalence set for transformers. Based on this property, we propose a theoretically optimal parameter matching algorithm as a plug-and-play module to enhance model fusion. We evaluate our approach using pre-trained transformers across diverse natural language and vision tasks. Experimental results demonstrate that our rotation symmetry-based matching algorithm substantially improves model fusion, highlighting the potential of parameter space symmetry to facilitate model fusion. Our code is available on https://github.com/zhengzaiyi/RotationSymmetry

Deep Learning · Graph Neural Networks

Tao Feng, Yexin Wu, Guanyu Lin, Jiaxuan You

World models (WMs) demonstrate strong capabilities in prediction, generation, and planning tasks.Existing WMs primarily focus on unstructured data while cannot leverage the ubiquitous structured data, often represented as graphs, in the digital world. While multiple graph foundation models have been proposed, they focus on graph learning tasks and cannot extend to diverse multi-modal data and interdisciplinary tasks. To address these challenges, we propose the Graph World Model (GWM), a world model that supports both unstructured and graph-structured states with multi-modal information and represents diverse tasks as actions. The core of a GWM is a generic message-passing algorithm to aggregate structured information, either over a unified multi-modal token space by converting multi-modal data into text (GWM-T) or a unified multi-modal embedding space by modality-specific encoders (GWM-E). Notably, GWM introduces action nodes to support diverse tasks, where action nodes are linked to other nodes via direct reference or similarity computation. Extensive experiments on 6 tasks from diverse domains, including multi-modal generation and matching, recommendation, graph prediction, multi-agent, retrieval-augmented generation, and planning and optimization, show that the same GWM outperforms or matches domain-specific baselines' performance, benefits from multi-hop structures, and demonstrate strong zero-shot/few-shot capabilities on unseen new tasks. Our codes for GWM is released at https://github.com/ulab-uiuc/GWM.

Deep Learning · Theory

Javan Tahir, Surya Ganguli, Grant Rotskoff

With the emergence of large-scale pre-trained neural networks, methods to adapt such "foundation" models to data-limited downstream tasks have become a necessity.Fine-tuning, preference optimization, and transfer learning have all been successfully employed for these purposes when the target task closely resembles the source task, but a precise theoretical understanding of ``task similarity'' is still lacking. We adopt a \emph{feature-centric} viewpoint on transfer learning and establish a number of theoretical results that demonstrate that when the target task is well represented by the feature space of the pre-trained model, transfer learning outperforms training from scratch.We study deep linear networks as a minimal model of transfer learning in which we can analytically characterize the transferability phase diagram as a function of the target dataset size and the feature space overlap.For this model, we establish rigorously that when the feature space overlap between the source and target tasks is sufficiently strong, both linear transfer and fine-tuning improve performance, especially in the low data limit. These results build on an emerging understanding of feature learning dynamics in deep linear networks, and we demonstrate numerically that the rigorous results we derive for the linear case also apply to nonlinear networks.

Theory · Learning Theory

Liam Hodgkinson, Zhichao Wang, Michael Mahoney

Recent theoretical and empirical successes in deep learning, including the celebrated neural scaling laws, are punctuated by the observation that many objects of interest tend to exhibit some form of heavy-tailed or power law behavior. In particular, the prevalence of heavy-tailed spectral densities in Jacobians, Hessians, and weight matrices has led to the introduction of the concept of *heavy-tailed mechanistic universality* (HT-MU). Multiple lines of empirical evidence suggest a robust correlation between heavy-tailed metrics and model performance, indicating that HT-MU may be a fundamental aspect of deep learning efficacy. Here, we propose a general family of random matrix models---the *high-temperature Marchenko-Pastur (HTMP) ensemble*---to explore attributes that give rise to heavy-tailed behavior in trained neural networks. Under this model, spectral densities with power laws on (upper and lower) tails arise through a combination of three independent factors (complex correlation structures in the data; reduced temperatures during training; and reduced eigenvector entropy), appearing as an implicit bias in the model structure, and they can be controlled with an "eigenvalue repulsion'' parameter. Implications of our model on other appearances of heavy tails, including neural scaling laws, optimizer trajectories, and the five-plus-one phases of neural network training, are discussed.

Optimization · Convex

Erica Zhang, Fangzhao Zhang, Mert Pilanci

Active learning methods aim to improve sample complexity in machine learning. In this work, we investigate an active learning scheme via a novel gradient-free cutting-plane training method for ReLU networks of arbitrary depth and develop a convergence theory. We demonstrate, for the first time, that cutting-plane algorithms, traditionally used in linear models, can be extended to deep neural networks despite their nonconvexity and nonlinear decision boundaries. Moreover, this training method induces the first deep active learning scheme known to achieve convergence guarantees, revealing a geometric contraction rate of the feasible set. We exemplify the effectiveness of our proposed active learning method against popular deep active learning baselines via both synthetic data experiments and sentimental classification task on real datasets.

Deep Learning

Jacopo Graldi, Alessandro Breccia, Giulia Lanzillotta, Thomas Hofmann, Lorenzo Noci

Despite recent efforts, neural networks still struggle to learn in non-stationary environments, and our understanding of catastrophic forgetting (CF) is far from complete.In this work, we perform a systematic study on the impact of model scale and the degree of feature learning in continual learning. We reconcile existing contradictory observations on scale in the literature, by differentiating between *lazy* and *rich* training regimes through a variable parameterization of the architecture. We show that increasing model width is only beneficial when it reduces the amount of *feature learning*, yielding more laziness. Using the framework of dynamical mean field theory, we then study the infinite width dynamics of the model in the feature learning regime and characterize CF, extending prior theoretical results limited to the lazy regime. We study the intricate relationship between feature learning, task non-stationarity, and forgetting, finding that high feature learning is only beneficial with highly similar tasks. We identify a transition modulated by task similarity where the model exits an effectively lazy regime with low forgetting to enter a rich regime with significant forgetting. Finally, our findings reveal that neural networks achieve optimal performance at a critical level of feature learning, which depends on task non-stationarity and *transfers across model scales*. This work provides a unified perspective on the role of scale and feature learning in continual learning.

Optimization

Huizhuo Yuan, Yifeng Liu, Shuang Wu, zhou Xun, Quanquan Gu

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (**M**ake v**A**riance **R**eduction **S**hine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

Deep Learning · Theory

Mohammed Adnan, Rohan Jain, Ekansh Sharma, Rahul G. Krishnan, Yani Ioannou

The Lottery Ticket Hypothesis (LTH) suggests there exists a sparse LTH mask and weights thatachieve the same generalization performance as the dense model while using significantly fewer parameters. However, finding a LTH solution is computationally expensive, and a LTH sparsity mask does not generalize to other random weight initializations. Recent work has suggested that neural networks trained from random initialization find solutions within the same basin modulo permutation, and proposes a method to align trained models within the same loss basin. We hypothesize that misalignment of basins is the reason why LTH masks do not generalize to new random initializations and propose permuting the LTH mask to align with the new optimization basin when performing sparse training from a different random init. We empirically show a significant increase in generalization when sparse training from random initialization with the permuted mask as compared to using the non-permuted LTH mask, on multiple datasets (CIFAR-10/100 & ImageNet) and models (VGG11 & ResNet20/50).

Deep Learning · Graph Neural Networks

Ningyi Liao, Zihao Yu, Ruixiao Zeng, Siqiang Luo

Graph Neural Networks (GNNs) have shown promising performance, but at the cost of resource-intensive operations on graph-scale matrices. To reduce computational overhead, previous studies attempt to sparsify the graph or network parameters, but with limited flexibility and precision boundaries. In this work, we propose Unifews, a joint sparsification technique to unify graph and weight matrix operations and enhance GNN learning efficiency. The Unifews design enables adaptive compression across GNN layers with progressively increased sparsity, and is applicable to a variety of architectures with on-the-fly simplification. Theoretically, we establish a novel framework to characterize sparsified GNN learning in view of the graph optimization process, showing that Unifews effectively approximates the learning objective with bounded error and reduced computational overhead. Extensive experiments demonstrate that Unifews achieves efficiency improvements with comparable or better accuracy, including 10-20x matrix operation reduction and up to 100x acceleration on graphs up to billion-edge scale.

Theory · Optimization

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.

Probabilistic Methods · Bayesian Models and Methods

Alan Amin, Andres Potapczynski, Andrew Wilson

To understand how genetic variants in human genomes manifest in phenotypes - traits like height or diseases like asthma - geneticists have sequenced and measured hundreds of thousands of individuals. Geneticists use this data to build models that predict how a genetic variant impacts phenotype given genomic features of the variant, like DNA accessibility or the presence of nearby DNA-bound proteins. As more data and features become available, one might expect predictive models to improve. Unfortunately, training these models is bottlenecked by the need to solve expensive linear algebra problems because variants in the genome are correlated with nearby variants, requiring inversion of large matrices. Previous methods have therefore been restricted to fitting small models, and fitting simplified summary statistics, rather than the full likelihood of the statistical model. In this paper, we leverage modern fast linear algebra techniques to develop DeepWAS (Deep genome Wide Association Studies), a method to train large and flexible neural network predictive models to optimize likelihood. Surprisingly, we find that larger models only improve performance when using our full likelihood approach; when trained by fitting traditional summary statistics, larger models perform no better than small ones. We find larger models trained on more features make better predictions, potentially improving disease predictions and therapeutic target identification.