Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
University of California（加利福尼亚大学）；Northeastern University（东北大学）；Khoury College of Computer Science（Khoury计算机学院）；Computer Science and Engineering（计算机科学与工程学院）
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into convolutional neural networks. Specifically, we employ a variety of methods each tailored to enforce a different symmetry. Our models are both theoretically and experimentally robust to distributional shift by symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh Bénard convection and real-world ocean currents and temperatures. Compared with image or text applications, our work is a significant step towards applying equivariant neural networks to high-dimensional systems with complex dynamics. We open-source our simulation, data, and code at \url{https://github.com/Rose-STL-Lab/Equivariant-Net}.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Michigan State University（密歇根州立大学）；Zhejiang University（浙江大学）
In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction function by a simple linear regression. We show that under appropriate assumptions about the integral operator, this approach is able to achieve an improved regression error bound better than existing bounds of supervised learning. We also verify the effectiveness of the proposed algorithm by an empirical study.
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Keio University（庆应义塾大学）；The University of Tokyo（东京大学）
Numerous invariant (or equivariant) neural networks have succeeded in handling invariant data such as point clouds and graphs. However, a generalization theory for the neural networks has not been well developed, because several essential factors for the theory, such as network size and margin distribution, are not deeply connected to the invariance and equivariance. In this study, we develop a novel generalization error bound for invariant and equivariant deep neural networks. To describe the effect of invariance and equivariance on generalization, we develop a notion of a \textit{quotient fe…
This paper presents a RKHS, in general, of vector-valued functions intended to be used as hypothesis space for multi-task classification. It extends similar hypothesis spaces that have previously considered in the literature. Assuming this space, an improved Empirical Rademacher Complexity-based generalization bound is derived. The analysis is itself extended to an MKL setting. The connection between the proposed hypothesis space and a Group-Lasso type regularizer is discussed. Finally, experimental results, with some SVM-based Multi-Task Learning problems, underline the quality of the derived…
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；The University of Tokyo（东京大学）；University of Tokyo（东京大学）
Recent studies have demonstrated that noise in stochastic gradient descent (SGD) is closely related to generalization: A larger SGD noise, if not too large, results in better generalization. Since the covariance of the SGD noise is proportional to $η^2/B$, where $η$ is the learning rate and $B$ is the minibatch size of SGD, the SGD noise has so far been controlled by changing $η$ and/or $B$. However, too large $η$ results in instability in the training dynamics and a small $B$ prevents scalable parallel computation. It is thus desirable to develop a method of controlling the SGD noise without …
Golisano College of Computing and Information Sciences（戈利萨诺计算与信息科学学院）；Rochester Institute of Technology（罗切斯特理工学院）
Deep learning models have shown state-of-the-art performance in many inverse reconstruction problems. However, it is not well understood what properties of the latent representation may improve the generalization ability of the network. Furthermore, limited models have been presented for inverse reconstructions over time sequences. In this paper, we study the generalization ability of a sequence encoder decoder model for solving inverse reconstructions on time sequences. Our central hypothesis is that the generalization ability of the network can be improved by 1) constrained stochasticity and…
We consider a model of robust learning in an adversarial environment. The learner gets uncorrupted training data with access to possible corruptions that may be affected by the adversary during testing. The learner's goal is to build a robust classifier, which will be tested on future adversarial examples. The adversary is limited to $k$ possible corruptions for each input. We model the learner-adversary interaction as a zero-sum game. This model is closely related to the adversarial examples model of Schmidt et al. (2018); Madry et al. (2017). Our main results consist of generalization bounds…
The randomized-feature approach has been successfully employed in large-scale kernel approximation and supervised learning. The distribution from which the random features are drawn impacts the number of features required to efficiently perform a learning task. Recently, it has been shown that employing data-dependent randomization improves the performance in terms of the required number of random features. In this paper, we are concerned with the randomized-feature approach in supervised learning for good generalizability. We propose the Energy-based Exploration of Random Features (EERF) algo…
Anticorrelated Noise Injection for Improved Generalization
ETH Zurich（苏黎世联邦理工学院）；INRIA（法国国家信息与自动化研究所）；Ecole Normale Supérieure（巴黎高等师范学院）；PSL Research University（巴黎文理研究大学）；University of Oslo（奥斯陆大学）；University of Basel（巴塞尔大学）
For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship is less clear: existing analyses of the output margin give complicated bounds which sometimes depend exponentially on depth. In this work, we propose to instead analyze a new notion of margin, which we call the "all-layer margin." Our analysis reveals that the all-layer margin has a clear and direct relationship with generalization for deep models. This enabl…
Learning sketching matrices for fast and accurate low-rank approximation (LRA) has gained increasing attention. Recently, Bartlett, Indyk, and Wagner (COLT 2022) presented a generalization bound for the learning-based LRA. Specifically, for rank-$k$ approximation using an $m \times n$ learned sketching matrix with $s$ non-zeros in each column, they proved an $\tilde{\mathrm{O}}(nsm)$ bound on the \emph{fat shattering dimension} ($\tilde{\mathrm{O}}$ hides logarithmic factors). We build on their work and make two contributions. 1. We present a better $\tilde{\mathrm{O}}(nsk)$ bound ($k \le m$).…
Duke University（杜克大学）；The Ohio State University（俄亥俄州立大学）；Microsoft Research, Asia（微软研究院亚洲研究院（微软亚洲研究院））
The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in expectation. In this paper, we establish various generalization error bounds with probabilistic guarantee for the SGD. Specifically, for both general nonconvex loss functions and gradient dominant loss functions, we characterize the on-average stability of the iterates generated…
Rutgers University（罗格斯大学）；Queens College of CUNY（纽约市立大学皇后学院）；Indian Institute of Science（印度科学学院）；Stony Brook University（石溪大学）
Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a prominent one being algorithmic stability [18]. However, there are no known examples of smooth loss functions for which the analysis can be shown to be tight. Furthermore, apart from the properties of the loss function, data distribution has also been shown to be an important factor in generalization performance. This raises the question: is the stability analys…
MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics（南京航空航天大学计算机科学与技术学院）；MIIT Key Laboratory of Pattern Analysis and Machine Intelligence（信息科技部模式分析与机器智能重点实验室）；College of Design and Engineering, National University of Singapore（新加坡国立大学设计与工程学院）
Recent results suggest that reinitializing a subset of the parameters of a neural network during training can improve generalization, particularly for small training sets. We study the impact of different reinitialization methods in several convolutional architectures across 12 benchmark image classification datasets, analyzing their potential gains and highlighting limitations. We also introduce a new layerwise reinitialization algorithm that outperforms previous methods and suggest explanations of the observed improved generalization. First, we show that layerwise reinitialization increases …
Centre for Frontier AI Research (CFAR), A*STAR（新加坡科技研究局前沿人工智能研究中心）；National University of Singapore（新加坡国立大学）；Institute of High Performance Computing (IHPC), A*STAR（新加坡科技研究局高性能计算研究所）
Overparametrized Deep Neural Networks (DNNs) often achieve astounding performances, but may potentially result in severe generalization error. Recently, the relation between the sharpness of the loss landscape and the generalization error has been established by Foret et al. (2020), in which the Sharpness Aware Minimizer (SAM) was proposed to mitigate the degradation of the generalization. Unfortunately, SAM s computational cost is roughly double that of base optimizers, such as Stochastic Gradient Descent (SGD). This paper thus proposes Efficient Sharpness Aware Minimizer (ESAM), which boosts…
Machine learning models can be improved by adapting them to respect existing background knowledge. In this paper we consider multitask Gaussian processes, with background knowledge in the form of constraints that require a specific sum of the outputs to be constant. This is achieved by conditioning the prior distribution on the constraint fulfillment. The approach allows for both linear and nonlinear constraints. We demonstrate that the constraints are fulfilled with high precision and that the construction can improve the overall prediction accuracy as compared to the standard Gaussian proces…
Recently, Sharpness-Aware Minimization (SAM) algorithm has shown state-of-the-art generalization abilities in vision tasks. It demonstrates that flat minima tend to imply better generalization abilities. However, it has some difficulty implying SAM to some natural language tasks, especially to models with drastic gradient changes, such as RNNs. In this work, we analyze the relation between the flatness of the local minimum and its generalization ability from a novel and straightforward theoretical perspective. We propose that the shift of the training and test distributions can be equivalently…
University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）
Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer version of the rank operator). This leads to an interesting question of whether controlling these quantities might improve the generalization behaviour of NNs. To this end, we propose stable rank normalization (SRN), a novel, optimal, and computationally efficient weight-normalization scheme which minimizes the stable rank of a linear operator. Surprisingly we f…
Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first applying a graph convolution. To understand the merits of this approach, we study the classification of a mixture of Gaussians, where the data corresponds to the node attributes of a stochastic block model. We show that graph convolution extends the regime in which the data is linearly separable by a factor of roughly $1/\sqrt{D}$, where $D$ is the expected degr…
University of Chinese Academy of Sciences（中国科学院大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Recently, learning a model that generalizes well on out-of-distribution (OOD) data has attracted great attention in the machine learning community. In this paper, after defining OOD generalization via Wasserstein distance, we theoretically show that a model robust to input perturbation generalizes well on OOD data. Inspired by previous findings that adversarial training helps improve input-robustness, we theoretically show that adversarially trained models have converged excess risk on OOD data, and empirically verify it on both image classification and natural language understanding tasks. Be…
We introduce the notion of heterogeneous calibration that applies a post-hoc model-agnostic transformation to model outputs for improving AUC performance on binary classification tasks. We consider overconfident models, whose performance is significantly better on training vs test data and give intuition onto why they might under-utilize moderately effective simple patterns in the data. We refer to these simple patterns as heterogeneous partitions of the feature space and show theoretically that perfectly calibrating each partition separately optimizes AUC. This gives a general paradigm of het…
Notwithstanding recent advances, syntactic generalization remains a challenge for text decoders. While some studies showed gains from incorporating source-side symbolic syntactic and semantic structure into text generation Transformers, very little work addressed the decoding of such structure. We propose a general approach for tree decoding using a transition-based approach. Examining the challenging test case of incorporating Universal Dependencies syntax into machine translation, we present substantial improvements on test sets that focus on syntactic generalization, while presenting improv…
Methods for improving deep neural network training times and model generalizability consist of various data augmentation, regularization, and optimization approaches, which tend to be sensitive to hyperparameter settings and make reproducibility more challenging. This work jointly considers two recent training strategies that address model generalizability: sharpness-aware minimization, and self-distillation, and proposes the novel training strategy of Sharpness-Aware Distilled Teachers (SADT). The experimental section of this work shows that SADT consistently outperforms previously published …
Data augmentation is a widely adopted technique for avoiding overfitting when training deep neural networks. However, this approach requires domain-specific knowledge and is often limited to a fixed set of hard-coded transformations. Recently, several works proposed to use generative models for generating semantically meaningful perturbations to train a classifier. However, because accurate encoding and decoding are critical, these methods, which use architectures that approximate the latent-variable inference, remained limited to pilot studies on small datasets. Exploiting the exactly reversi…
University of Texas Southwestern Medical Center（德克萨斯大学西南医学中心）
Natural science datasets frequently violate assumptions of independence. Samples may be clustered (e.g. by study site, subject, or experimental batch), leading to spurious associations, poor model fitting, and confounded analyses. While largely unaddressed in deep learning, this problem has been handled in the statistics community through mixed effects models, which separate cluster-invariant fixed effects from cluster-specific random effects. We propose a general-purpose framework for Adversarially-Regularized Mixed Effects Deep learning (ARMED) models through non-intrusive additions to exist…
Currently nearing human-level performance, Visual Question Answering (VQA) is an emerging area in artificial intelligence. Established as a multi-disciplinary field in machine learning, both computer vision and natural language processing communities are working together to achieve state-of-the-art (SOTA) performance. However, there is a gap between the SOTA results and real world applications. This is due to the lack of model generalisation. The RAMEN model \cite{Shrestha2019} aimed to achieve domain generalization by obtaining the highest score across two main types of VQA datasets. This stu…
Text-based games (TBGs) have become a popular proving ground for the demonstration of learning-based agents that make decisions in quasi real-world settings. The crux of the problem for a reinforcement learning agent in such TBGs is identifying the objects in the world, and those objects' relations with that world. While the recent use of text-based resources for increasing an agent's knowledge and improving its generalization have shown promise, we posit in this paper that there is much yet to be learned from visual representations of these same worlds. Specifically, we propose to retrieve im…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
While directly fine-tuning (FT) large-scale, pretrained models on task-specific data is well-known to induce strong in-distribution task performance, recent works have demonstrated that different adaptation protocols, such as linear probing (LP) prior to FT, can improve out-of-distribution generalization. However, the design space of such adaptation protocols remains under-explored and the evaluation of such protocols has primarily focused on distribution shifts. Therefore, in this work, we evaluate common adaptation protocols across distributions shifts and machine learning safety metrics (e.…
Improved Scaling Laws via Weak-to-Strong Generalization in Random Feature Ridge Regression
Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）；Department of Applied and Computational Mathematics, Yale University（耶鲁大学应用与计算数学系）；Department of Statistics and Data Science, Yale University（耶鲁大学统计与数据科学系）
Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis -- even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly co…
Carnegie Mellon University（卡内基梅隆大学）；Yamaha Motor Co., Ltd.（雅马哈发动机有限公司）
In the task of Autonomous aerial filming of a moving actor (e.g. a person or a vehicle), it is crucial to have a good heading direction estimation for the actor from the visual input. However, the models obtained in other similar tasks, such as pedestrian collision risk analysis and human-robot interaction, are very difficult to generalize to the aerial filming task, because of the difference in data distributions. Towards improving generalization with less amount of labeled data, this paper presents a semi-supervised algorithm for heading direction estimation problem. We utilize temporal cont…
In order to promote the use of machine learning in 5G, the International Telecommunication Union (ITU) proposed in 2021 the second edition of the ITU AI/ML in 5G challenge, with over 1600 participants from 82 countries. This work details the second place solution overall, which is also the winning solution of the Graph Neural Networking Challenge 2021. We tackle the problem of generalization when applying a model to a 5G network that may have longer paths and larger link capacities than the ones observed in training. To achieve this, we propose to first extract robust features related to Queue…
LinkedIn Corporation（领英公司）；Massachusetts Institute of Technology（麻省理工学院）
Modern deep learning models are over-parameterized, where the optimization setup strongly affects the generalization performance. A key element of reliable optimization for these systems is the modification of the loss function. Sharpness-Aware Minimization (SAM) modifies the underlying loss function to guide descent methods towards flatter minima, which arguably have better generalization abilities. In this paper, we focus on a variant of SAM known as mSAM, which, during training, averages the updates generated by adversarial perturbations across several disjoint shards of a mini-batch. Recen…
Rutgers University（罗格斯大学）；Google Research（谷歌研究院）；University of Delaware（特拉华大学）
Adversarial data augmentation has shown promise for training robust deep neural networks against unforeseen data shifts or corruptions. However, it is difficult to define heuristics to generate effective fictitious target distributions containing "hard" adversarial perturbations that are largely different from the source distribution. In this paper, we propose a novel and effective regularization term for adversarial data augmentation. We theoretically derive it from the information bottleneck principle, which results in a maximum-entropy formulation. Intuitively, this regularization term enco…
Recent improvements in deep learning models and their practical applications have raised concerns about the robustness of these models against adversarial examples. Adversarial training (AT) has been shown effective to reach a robust model against the attack that is used during training. However, it usually fails against other attacks, i.e. the model overfits to the training attack scheme. In this paper, we propose a simple modification to the AT that mitigates the mentioned issue. More specifically, we minimize the perturbation $\ell_p$ norm while maximizing the classification loss in the Lag…
University of Minnesota Twin Cities（明尼苏达大学双城分校）；Microsoft Research（微软研究院）；Rothamsted Research（洛桑研究所）；University of Glasgow（格拉斯哥大学）
Measuring and monitoring soil organic carbon is critical for agricultural productivity and for addressing critical environmental problems. Soil organic carbon not only enriches nutrition in soil, but also has a gamut of co-benefits such as improving water storage and limiting physical erosion. Despite a litany of work in soil organic carbon estimation, current approaches do not generalize well across soil conditions and management practices. We empirically show that explicit modeling of cause-and-effect relationships among the soil processes improves the out-of-distribution generalizability of…
Learning Diverse Features in Vision Transformers for Improved Generalization
Idiap Research Institute（Idiap研究所）；Mila（米拉人工智能研究所）；University of Montreal（蒙特利尔大学）；University of Bucharest（布加勒斯特大学）；Gheorghe Mihoc - Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy（罗马尼亚科学院Gheorghe Mihoc-Caius Iacob数理统计与应用数学研究所）
Minibatching Offers Improved Generalization Performance for Second Order Optimizers
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Washington State University（华盛顿州立大学）；Rutgers, The State University of New Jersey（罗格斯新泽西州立大学）；University of Washington（华盛顿大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Despite the remarkable success achieved by graph convolutional networks for functional brain activity analysis, the heterogeneity of functional patterns and the scarcity of imaging data still pose challenges in many tasks. Transferring knowledge from a source domain with abundant training data to a target domain is effective for improving representation learning on scarce training data. However, traditional transfer learning methods often fail to generalize the pre-trained knowledge to the target task due to domain discrepancy. Self-supervised learning on graphs can increase the generalizabili…
