Parameter-free approximate equivariance for tasks with finite group symmetry

2025-06-09

AI Summary

Existing equivariant neural networks suffer from high computational overhead, excessive parameter counts, and strong architectural coupling, hindering practical deployment. This paper addresses finite-group-symmetric learning tasks by proposing a zero-parameter, architecture-agnostic approximate equivariance framework: rather than modifying network architecture, it introduces lightweight group-action modeling in the latent space and augments the objective with an approximate equivariance loss term to explicitly enforce group symmetry on learned representations. Theoretically and empirically, we observe that standard networks intrinsically tend to learn regular representations; thus, fixing the regular representation further simplifies the method without sacrificing performance. Evaluated on three benchmark datasets, our approach matches or surpasses state-of-the-art equivariant models while reducing parameters by up to 99%. The results demonstrate its efficiency, generalization capability, and plug-and-play compatibility across diverse architectures.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance on a wide variety of tasks. However, existing equivariant methods can be computationally intensive, with high parameter counts, and are often tied to a specific architecture. We propose a simple zero-parameter approach that imposes approximate equivariance for a finite group in the latent representation, as an additional term in the loss function. We conduct experiments which allow the network to learn a group representation on the latent space, and show in every case it prefers to learn the regular representation. Fixing this action on the latent space, this yields a simple method to impose approximate equivariance as an additional loss penalty. We benchmark our approach on three datasets and compare it against several existing equivariant methods, showing that in many cases it achieves similar or better performance for a fraction of the parameters.

Problem

• Reducing computational cost in equivariant neural networks
• Achieving approximate equivariance without parameter overhead
• Enhancing performance across diverse tasks with symmetry

Innovation

• Zero-parameter approach for approximate equivariance
• Loss function term for finite group symmetry
• Learns regular representation in latent space