论文检索

Deep Learning · Graph Neural Networks

Dominik Fuchsgruber, Tom Wollschläger, Bertrand Charpentier, Antonio Oroz, Stephan Günnemann

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: **(1)** We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. **(2)** We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. **(3)** Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.

Applications

Xiao Luo, Yiyang Gu, Huiyu Jiang, Hang Zhou, Jinsheng Huang, Wei Ju, Zhiping Xiao, Ming Zhang, Yizhou Sun

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Prototypical Graph ODE (PGODE) to address the problem. The core of PGODE is to incorporate prototype decomposition from contextual knowledge into a continuous graph ODE framework. Specifically, PGODE employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of PGODE compared to various baselines.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Jongha (Jon) Ryu, Xiangxiang Xu, Hasan Sabri Melihcan Erol, Yuheng Bu, Lizhong Zheng, Gregory Wornell

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific simulation problems. For high-dimensional eigenvalue problems, training neural networks to parameterize the eigenfunctions is considered as a promising alternative to the classical numerical linear algebra techniques. This paper proposes a new optimization framework based on the low-rank approximation characterization of a truncated singular value decomposition, accompanied by new techniques called *nesting* for learning the top-$L$ singular values and singular functions in the correct order. The proposed method promotes the desired orthogonality in the learned functions implicitly and efficiently via an unconstrained optimization formulation, which is easy to solve with off-the-shelf gradient-based optimization algorithms. We demonstrate the effectiveness of the proposed optimization framework for use cases in computational physics and machine learning.

Probabilistic Methods · Variational Inference

Brooks(Ruijia) Niu, Dongxia Wu, Kai Kim, Yian Ma, Duncan Watson-Parris, Rose Yu

Multi-fidelity surrogate modeling aims to learn an accurate surrogate at the highest fidelity level by combining data from multiple sources. Traditional methods relying on Gaussian processes can hardly scale to high-dimensional data. Deep learning approaches utilize neural network based encoders and decoders to improve scalability. These approaches share encoded representations across fidelities without including corresponding decoder parameters. This hinders inference performance, especially in out-of-distribution scenarios when the highest fidelity data has limited domain coverage. To address these limitations, we propose Multi-fidelity Residual Neural Processes (MFRNP), a novel multi-fidelity surrogate modeling framework. MFRNP explicitly models the residual between the aggregated output from lower fidelities and ground truth at the highest fidelity. The aggregation introduces decoders into the information sharing step and optimizes lower fidelity decoders to accurately capture both in-fidelity and cross-fidelity information. We show that MFRNP significantly outperforms state-of-the-art in learning partial differential equations and a real-world climate modeling task. Our code is published at: https://github.com/Rose-STL-Lab/MFRNP

Optimization · Sampling and Optimization

Qiang Fu, Ashia Wilson

We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.

Applications · Physics

Hong Chul Nam, Julius Berner, Anima Anandkumar

We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient solution of high-dimensional Poisson equations. Leveraging stochastic representations and Walk-on-Spheres methods, we develop novel losses for neural networks based on the recursive solution of Poisson equations on spheres inside the domain. The resulting method is highly parallelizable and does not require spatial gradients for the loss. We provide a comprehensive comparison against competing methods based on PINNs, the Deep Ritz method, and (backward) stochastic differential equations. In several challenging, high-dimensional numerical examples, we demonstrate the superiority of NWoS in accuracy, speed, and computational costs. Compared to commonly used PINNs, our approach can reduce memory usage and errors by orders of magnitude. Furthermore, we apply NWoS to problems in PDE-constrained optimization and molecular dynamics to show its efficiency in practical applications.

Deep Learning · Everything Else

Kai Liu, Ruohui Wang, Jianfei Gao, Kai Chen

Over the past few years, as large language models have ushered in an era of intelligence emergence, there has been an intensified focus on scaling networks. Although Neural Architecture Search (NAS) methods have been proposed to automate this process, they suffer from low search efficiency. This study introduces Differentiable Model Scaling (DMS), increasing the efficiency for searching optimal width and depth in networks. DMS can model both width and depth in a direct and fully differentiable way, making it easy to optimize. We have evaluated our DMS across diverse tasks, ranging from vision tasks to NLP tasks and various network architectures, including CNNs and Transformers. Results consistently indicate that our DMS can find improved structures and outperforms state-of-the-art NAS methods. Specifically, for image classification on ImageNet, our DMS improves the top-1 accuracy of EfficientNet-B0 and Deit-Tiny by 1.4% and 0.6%, respectively, and outperforms the state-of-the-art zero-shot NAS method, ZiCo, by 1.3% while requiring only 0.4 GPU days for searching. For object detection on COCO, DMS improves the mAP of Yolo-v8-n by 2.0%. For language modeling, our pruned Llama-7B outperforms the prior method with lower perplexity and higher zero-shot classification accuracy. Our code is available at https://github.com/LKJacky/Differentiable-Model-Scaling.

Xiaochuan Gong, Jie Hao, Mingrui Liu

This paper studies the problem of stochastic bilevel optimization where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level function is strongly convex. This problem is motivated by meta-learning applied to sequential data, such as text classification using recurrent neural networks, where the smoothness constant of the upper-level loss function scales linearly with the gradient norm and can be potentially unbounded. Existing algorithm crucially relies on the nested loop design, which requires significant tuning efforts and is not practical. In this paper, we address this issue by proposing a Single Loop bIlevel oPtimizer (SLIP). The proposed algorithm first updates the lower-level variable by a few steps of stochastic gradient descent, and then simultaneously updates the upper-level variable by normalized stochastic gradient descent with momentum and the lower-level variable by stochastic gradient descent. Under standard assumptions, we show that our algorithm finds an $\epsilon$-stationary point within $\widetilde{O}(1/\epsilon^4)$[Here $\widetilde{O}(\cdot)$ compresses logarithmic factors of $1/\epsilon$ and $1/\delta$, where $\delta\in(0,1)$ denotes the failure probability.] oracle calls of stochastic gradient or Hessian-vector product, both in expectation and with high probability. This complexity result is nearly optimal up to logarithmic factors without mean-square smoothness of the stochastic gradient oracle. Our proof relies on (i) a refined characterization and control of the lower-level variable and (ii) establishing a novel connection between bilevel optimization and stochastic optimization under distributional drift. Our experiments on various tasks show that our algorithm significantly outperforms strong baselines in bilevel optimization.

Yang Zhao, Hao Zhang, Xiuyuan Hu

Gradient regularization (GR), which aims to penalize the gradient norm atop the loss function, has shown promising results in training modern over-parameterized deep neural networks. However, can we trust this powerful technique? This paper reveals that GR can cause performance degeneration in adaptive optimization scenarios, particularly with learning rate warmup. Our empirical and theoretical analyses suggest this is due to GR inducing instability and divergence in gradient statistics of adaptive optimizers at the initial training stage. Inspired by the warmup heuristic, we propose three GR warmup strategies, each relaxing the regularization effect to a certain extent during the warmup course to ensure the accurate and stable accumulation of gradients. With experiments on Vision Transformer family, we confirm the three GR warmup strategies can effectively circumvent these issues, thereby largely improving the model performance. Meanwhile, we note that scalable models tend to rely more on the GR warmup, where the performance can be improved by up to 3% on Cifar10 compared to baseline GR. Code is available at https://github.com/zhaoyang-0204/gnp.

Deep Learning · Generative Models and Autoencoders

Bao Nguyen, Binh Nguyen, Trung Hieu Nguyen, Viet Anh Nguyen

Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal transport method designed to effectively learn generative models of conditional distributions, particularly in scenarios characterized by limited sample sizes. Our method relies on the minimax training of two neural networks: a generative network parametrizing the inverse cumulative distribution functions of the conditional distributions and another network parametrizing the conditional Kantorovich potential. To prevent overfitting, we regularize the objective function by penalizing the Lipschitz constant of the network output. Our experiments on real-world datasets show the effectiveness of our algorithm compared to state-of-the-art conditional distribution learning techniques. Our implementation can be found at https://github.com/nguyenngocbaocmt02/GENTLE.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Yi-Xuan Sun, Ya-Lin Zhang, BIN HAN, Longfei Li, JUN ZHOU

The strong performance of neural networks typically hinges on the availability of extensive labeled data, yet acquiring ground-truth labels is often challenging. Instead, noisy supervisions from multiple sources, e.g., by multiple well-designed rules, are more convenient to collect. In this paper, we focus on the realistic problem of learning from multiple noisy label sources, and argue that prior studies have overlooked the crucial *self-cognition* ability of neural networks, i.e., the inherent capability of autonomously distinguishing noise during training. We theoretically analyze this ability of neural networks when meeting multiple noisy label sources, which reveals that neural networks possess the capability to recognize both instance-wise noise within each single noisy label source and annotator-wise quality among multiple noisy label sources. Inspired by the theoretical analyses, we introduce an approach named Self-cognitive Denoising for Multiple noisy label sources (SDM), which exploits the self-cognition ability of neural networks to denoise during training. Furthermore, we build a selective distillation module following the theoretical insights to optimize computational efficiency. The experiments on various datasets demonstrate the superiority of our method.

Deep Learning

Herilalaina Rakotoarison, Steven Adriaensen, Neeratyoy Mallik, Samir Garibov, Edward Bergman, Frank Hutter

With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.

Reinforcement Learning

Fares Fourati, Vaneet Aggarwal, Mohamed-Slim Alouini

In complex environments with large discrete action spaces, effective decision-making is critical in reinforcement learning (RL). Despite the widespread use of value-based RL approaches like Q-learning, they come with a computational burden, necessitating the maximization of a value function over all actions in each iteration. This burden becomes particularly challenging when addressing large-scale problems and using deep neural networks as function approximators. In this paper, we present stochastic value-based RL approaches which, in each iteration, as opposed to optimizing over the entire set of $n$ actions, only consider a variable stochastic set of a sublinear number of actions, possibly as small as $\mathcal{O}(\log(n))$. The presented stochastic value-based RL methods include, among others, Stochastic Q-learning, StochDQN, and StochDDQN, all of which integrate this stochastic approach for both value-function updates and action selection. The theoretical convergence of Stochastic Q-learning is established, while an analysis of stochastic maximization is provided. Moreover, through empirical validation, we illustrate that the various proposed approaches outperform the baseline methods across diverse environments, including different control problems, achieving near-optimal average returns in significantly reduced time.

Optimization · Zero-order and Black-box Optimization

Natalie Maus, Zhiyuan Jerry Lin, Maximilian Balandat, Eytan Bakshy

Bayesian Optimization (BO) is a technique for sample-efficient black-box optimization that employs probabilistic models to identify promising input for evaluation. When dealing with composite-structured functions, such as $f=g \circ h$, evaluating a specific location $x$ yields observations of both the final outcome $f(x) = g(h(x))$ as well as the intermediate output(s) $h(x)$. Previous research has shown that integrating information from these intermediate outputs can enhance BO performance substantially. However, existing methods struggle if the outputs $h(x)$ are high-dimensional. Many relevant problems fall into this setting, including in the context of generative AI, molecular design, or robotics. To effectively tackle these challenges, we introduce Joint Composite Latent Space Bayesian Optimization (JoCo), a novel framework that jointly trains neural network encoders and probabilistic models to adaptively compress high-dimensional input and output spaces into manageable latent representations. This enables effective BO on these compressed representations, allowing JoCo to outperform other state-of-the-art methods in high-dimensional BO on a wide variety of simulated and real-world problems.

Theory · Learning Theory

Chenghao Liu, Enming Liang, Minghua Chen

Since its debut in 2016, ResNet has become arguably the most favorable architecture in deep neural network (DNN) design. It effectively addresses the gradient vanishing/exploding issue in DNN training, allowing engineers to fully unleash DNN's potential in tackling challenging problems in various domains. Despite its practical success, an essential theoretical question remains largely open: how well/best can ResNet approximate functions? In this paper, we answer this question for several important function classes, including polynomials and smooth functions. In particular, we show that ResNet with constant width can approximate Lipschitz continuous function with a Lipschitz constant $\mu$ using $\mathcal{O}(c(d)(\varepsilon/\mu)^{-d/2})$ tunable weights, where $c(d)$ is a constant depending on the input dimension $d$ and $\epsilon>0$ is the target approximation error. Further, we extend such a result to Lebesgue-integrable functions with the upper bound characterized by the modulus of continuity. These results indicate a factor of $d$ reduction in the number of tunable weights compared with the classical results for ReLU networks. Our results are also order-optimal in $\varepsilon$, thus achieving optimal approximation rate, as they match a generalized lower bound derived in this paper. This work adds to the theoretical justifications for ResNet's stellar practical performance.

Theory · Learning Theory

Chenghao Liu, Minghua Chen

The prevalent employment of narrow neural networks, characterized by their minimal parameter count per layer, has led to a surge in research exploring their potential as universal function approximators. A notable result in this field states that networks with just a width of $d+1$ can approximate any continuous function for input dimension $d$ arbitrarily well. However, the optimal approximation rate for these narrowest networks, i.e., the optimal relation between the count of tunable parameters and the approximation error, remained unclear. In this paper, we address this gap by proving that ReLU networks with width $d+1$ can achieve the optimal approximation rate for continuous functions over the domain $[0,1]^d$ under $L^p$ norm for $p\in[1,\infty)$. We further show that for the uniform norm, a width of $d+11$ is sufficient. We also extend the results to narrow feed-forward networks with various activations, confirming their capability to approximate at the optimal rate. This work adds to the understanding of universal approximation of narrow networks.

Social Aspects · Accountability, Transparency and Interpretability

Yefan Zhou, Jianlong Chen, Qinxue Cao, Konstantin Schürholt, Yaoqing Yang

This paper considers ''model diagnosis'', which we formulate as a classification problem. Given a pre-trained neural network (NN), the goal is to predict the source of failure from a set of failure modes (such as a wrong hyperparameter, inadequate model size, and insufficient data) without knowing the training configuration of the pre-trained NN. The conventional diagnosis approach uses training and validation errors to determine whether the model is underfitting or overfitting. However, we show that rich information about NN performance is encoded in the optimization loss landscape, which provides more actionable insights than validation-based measurements. Therefore, we propose a diagnosis method called MD tree based on loss landscape metrics and experimentally demonstrate its advantage over classical validation-based approaches. We verify the effectiveness of MD tree in multiple practical scenarios: (1) use several models trained on one dataset to diagnose a model trained on another dataset, essentially a few-shot dataset transfer problem; (2) use small models (or models trained with small data) to diagnose big models (or models trained with big data), essentially a scale transfer problem. In a dataset transfer task, MD tree achieves an accuracy of 87.7%, outperforming validation-based approaches by 14.88%. Our code is available at [https://github.com/YefanZhou/ModelDiagnosis](https://github.com/YefanZhou/ModelDiagnosis).

Deep Learning · Attention Mechanisms

Junnan Liu, Qianren Mao, Weifeng Jiang, Jianxin Li

Knowledge graph reasoning plays a vital role in various applications and has garnered considerable attention. Recently, path-based methods have achieved impressive performance. However, they may face limitations stemming from constraints in message-passing neural networks, such as missing paths and information over-squashing. In this paper, we revisit the application of transformers for knowledge graph reasoning to address the constraints faced by path-based methods and propose a novel method KnowFormer. KnowFormer utilizes a transformer architecture to perform reasoning on knowledge graphs from the message-passing perspective, rather than reasoning by textual information like previous pretrained language model based methods. Specifically, we define the attention computation based on the query prototype of knowledge graph reasoning, facilitating convenient construction and efficient optimization. To incorporate structural information into the self-attention mechanism, we introduce structure-aware modules to calculate query, key, and value respectively. Additionally, we present an efficient attention computation method for better scalability. Experimental results demonstrate the superior performance of KnowFormer compared to prominent baseline methods on both transductive and inductive benchmarks.

Yulun Zhang, Kai Zhang, Luc Van Gool, Martin Danelljan, Fisher Yu

Lightweight image super-resolution (SR) methods have obtained promising results with moderate model complexity. These approaches primarily focus on a lightweight architecture design, but neglect to further reduce network redundancy. While some model compression techniques try to achieve more lightweight SR models with neural architecture search, knowledge distillation, or channel pruning, they typically require considerable extra computational resources or neglect to prune weights. To address these issues, we propose a flexible meta pruning (FMP) for lightweight image SR, where the network channels and weights are pruned simultaneously. Specifically, we control the network sparsity via channel vectors and weight indicators. We feed them into a hypernetwork, whose parameters act as meta-data for the parameters of the SR backbone. Consequently, for each network layer, we conduct structured pruning with channel vectors, which control the output and input channels. Besides, we conduct unstructured pruning with weight indicators to influence the sparsity of kernel weights, resulting in flexible pruning. During pruning, the sparsity of both channel vectors and weight indicators are regularized. We optimize the channel vectors and weight indicators with proximal gradient and SGD. We conduct extensive experiments to investigate critical factors in the flexible channel and weight pruning for image SR, demonstrating the superiority of our FMP when applied to baseline image SR architectures.

Deep Learning

Atli Kosson, Bettina Messmer, Martin Jaggi

This study investigates how weight decay affects the update behavior of individual neurons in deep neural networks through a combination of applied analysis and experimentation. Weight decay can cause the expected magnitude and angular updates of a neuron's weight vector to converge to a steady state we call rotational equilibrium. These states can be highly homogeneous, effectively balancing the average rotation---a proxy for the effective learning rate---across different layers and neurons. Our work analyzes these dynamics across optimizers like Adam, Lion, and SGD with momentum, offering a new simple perspective on training that elucidates the efficacy of widely used but poorly understood methods in deep learning. We demonstrate how balanced rotation plays a key role in the effectiveness of normalization like Weight Standardization, as well as that of AdamW over Adam with L2-regularization. Finally, we show that explicitly controlling the rotation provides the benefits of weight decay while substantially reducing the need for learning rate warmup.