Data-Efficient Learning via Minimizing Hyperspherical Energy

TL;DR

This paper introduces a novel hyperspherical energy minimization approach for data-efficient learning, leveraging topological insights and active learning to improve performance with limited data.

Contribution

It proposes the MHEAL algorithm based on hyperspherical energy minimization, with theoretical guarantees and broad empirical validation across multiple data-efficient learning tasks.

Findings

MHEAL outperforms existing methods in data-efficient learning tasks.

Theoretical analysis confirms convergence and generalization of MHEAL.

Empirical results demonstrate effectiveness in clustering, distribution matching, and active learning.

Abstract

Deep learning on large-scale data is dominant nowadays. The unprecedented scale of data has been arguably one of the most important driving forces for the success of deep learning. However, there still exist scenarios where collecting data or labels could be extremely expensive, e.g., medical imaging and robotics. To fill up this gap, this paper considers the problem of data-efficient learning from scratch using a small amount of representative data. First, we characterize this problem by active learning on homeomorphic tubes of spherical manifolds. This naturally generates feasible hypothesis class. With homologous topological properties, we identify an important connection -- finding tube manifolds is equivalent to minimizing hyperspherical energy (MHE) in physical geometry. Inspired by this connection, we propose a MHE-based active learning (MHEAL) algorithm, and provide comprehensive theoretical guarantees for MHEAL, covering convergence and generalization analysis. Finally, we demonstrate the empirical performance of MHEAL in a wide range of applications on data-efficient learning, including deep clustering, distribution matching, version space sampling and deep active learning.