Self-Supervised Lie Algebra Representation Learning via Optimal Canonical Metric.

Area of Science:

• Computer Science
• Machine Learning
• Computer Vision

Background:

• Learning discriminative representations with limited training samples is a key challenge in visual categorization.
• Prior work suggests self-supervised learning improves performance, but canonical metrics in Lie groups are theoretically flawed for this task.

Purpose of the Study:

• To propose a theoretically sound optimization measurement for representation learning on Lie groups.
• To introduce a novel self-supervised Lie algebra network (SLA-Net) for improved visual categorization with limited data.

Main Methods:

• Proving that canonical metrics on Lie algebra are valid optimization measurements.
• Developing the self-supervised Lie algebra network (SLA-Net) framework.
• Minimizing canonical metric distance in a vector space to avoid complex manifold calculations.
• Simultaneously optimizing parameters for self-supervised learning and supervised classification.

Main Results:

• Demonstrated the theoretical correctness of using canonical metrics on Lie algebra.
• SLA-Net effectively learns representations for visual categorization with limited samples.
• Achieved improved generalization capabilities through joint optimization.

Conclusions:

• The proposed SLA-Net framework offers a theoretically valid and effective approach for representation learning in low-data regimes.
• SLA-Net outperforms existing methods on eight public datasets for visual categorization.
• This work advances self-supervised learning techniques for challenging computer vision tasks.