Topological Deep Learning for Speech Data

TL;DR

This paper introduces topology-aware convolutional kernels inspired by topological data analysis to enhance speech recognition networks, demonstrating improved performance and cross-domain adaptability through novel mathematical and practical approaches.

Contribution

It presents a new class of topology-aware kernels and a fiber-bundle decomposition method, advancing the integration of topological data analysis with deep learning for speech data.

Findings

Orthogonal Feature layer outperforms existing methods in phoneme recognition

Proposed kernels improve robustness in low-noise environments

Demonstrates cross-domain adaptability of the approach

Abstract

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically, by investigating orthogonal group actions on kernels, we establish a fiber-bundle decomposition of matrix spaces, enabling new filter generation methods. Practically, our proposed Orthogonal Feature (OF) layer achieves superior performance in phoneme recognition, particularly in low-noise scenarios, while demonstrating cross-domain adaptability. This work reveals TDA's potential in neural network optimization, opening new avenues for mathematics-deep learning interdisciplinary studies.