相关论文: Generalization Bounds for Equivariant Networks on …

While standard statistical inference techniques and machine learning generalization bounds assume that tests are run on data selected independently of the hypotheses, practical data analysis and machine learning are usually iterative and…

Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate \emph{scaled} ResNet in the limit of infinitely deep and wide…

We derive a tight generalization bound for quantum machine learning that is applicable to a wide range of supervised tasks, data, and models. Our bound is both efficiently computable and free of big-O notation. Furthermore, we point out…

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…

Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high average accuracy is accompanied by low accuracy in a minority group. Despite algorithmic efforts to improve the minority group accuracy,…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

In this work, we explore the trade-offs of explicit structural priors, particularly group equivariance. We address this through theoretical analysis and a comprehensive empirical study. To enable controlled and fair comparisons, we…

We consider information-theoretic bounds on expected generalization error for statistical learning problems in a networked setting. In this setting, there are $K$ nodes, each with its own independent dataset, and the models from each node…

We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for…

Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has…

Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…

Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…

Practitioners in diverse fields such as healthcare, economics and education are eager to apply machine learning to improve decision making. The cost and impracticality of performing experiments and a recent monumental increase in electronic…

Model-based neural networks provide unparalleled performance for various tasks, such as sparse coding and compressed sensing problems. Due to the strong connection with the sensing model, these networks are interpretable and inherit prior…

Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is…

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire…