Data-Efficient Learning via Minimizing Hyperspherical Energy.

Area of Science:

• Machine Learning
• Computational Geometry
• Topology

Background:

• Deep learning thrives on large datasets, but data acquisition is costly in fields like medical imaging and robotics.
• Scenarios requiring learning from scratch with limited data are common and challenging.

Purpose of the Study:

• To develop a data-efficient learning approach for scenarios with limited representative data.
• To characterize data-efficient learning using active learning on spherical manifold tubes.

Main Methods:

• Characterized data-efficient learning via active learning on homeomorphic tubes of spherical manifolds.
• Established an equivalence between finding tube manifolds and minimizing hyperspherical energy (MHE).
• Proposed the MHE-based active learning (MHEAL) algorithm.

Main Results:

• Provided comprehensive theoretical guarantees for MHEAL, including convergence and generalization analysis.
• Demonstrated MHEAL's empirical effectiveness across various data-efficient learning applications.
• Showcased applications in deep clustering, distribution matching, version space sampling, and deep active learning.

Conclusions:

• MHEAL offers a robust solution for data-efficient learning from scratch.
• The connection between topological properties and hyperspherical energy minimization is key to the algorithm's success.
• The proposed method significantly advances learning capabilities in data-scarce domains.