相关论文: Statistical Learning Guarantees for Group-Invarian…

We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…

The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element…

Symmetries are known to improve the empirical performance of machine learning models, yet theoretical guarantees explaining these gains remain limited. Prior work has focused mainly on compact group symmetries and often assumes that the…

Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are…

By inferring latent groups in the training data, recent works introduce invariant learning to the case where environment annotations are unavailable. Typically, learning group invariance under a majority/minority split is empirically shown…

Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…

In this study, we introduce a method for learning group (known or unknown) equivariant functions by learning the associated quadratic form $x^T A x$ corresponding to the group from the data. Certain groups, known as orthogonal groups,…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

Equivariant neural networks play a pivotal role in analyzing datasets with symmetry properties, particularly in complex data structures. However, integrating equivariance with Markov properties presents notable challenges due to the…

In this article we study the structure of $\Gamma$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

Equivariant networks capture the inductive bias about the symmetry of the learning task by building those symmetries into the model. In this paper, we study how equivariance relates to generalization error utilizing PAC Bayesian analysis…

Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…

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,…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not suffer from noise, but a challenge is the amount of data…

Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…