用拓扑方法设计卷积核，提升语音识别性能
Topological Deep Learning for Speech Data
- 基于拓扑分析设计感知拓扑的卷积核
- 在低噪声环境下音素识别准确率显著提升
- 适合对模型可解释性与跨域泛化有要求的研究者
拓扑数据分析（TDA）为深度学习提供了新颖的数学工具。受Carlsson等人启发，本研究设计了拓扑感知的卷积核，显著提升了语音识别网络性能。理论上，通过研究矩阵空间上的正交群作用，建立了纤维丛分解，从而提出新的滤波器生成方法。实际上，所提出的正交特征（OF）层在音素识别任务中表现优异，尤其在低噪声条件下，并展现出良好的跨域适应能力。该工作揭示了TDA在神经网络优化中的潜力，为数学与深度学习的交叉研究开辟了新路径。
原文摘要 · Abstract (English)
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.
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