Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices

TL;DR

This paper explores Riemannian geometry for a class of low-parametric orthogonal matrices, deriving essential tools and proposing efficient algorithms. The approach enables smooth manifold structure and efficient computation. It has applications in deep learning architectures.

Why It Matters

The proposed method offers a balanced expressivity-efficiency trade-off, which is crucial for deep learning models. It can be used for parameter-efficient fine-tuning of large language models and other applications. This can lead to improved performance and reduced computational costs.

Key Findings

• Riemannian structure for low-parametric orthogonal matrices
• Efficient algorithms for implementation
• Applications in deep learning and language models