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Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

2026-09-07 12:00 Science 🔥 40.2 heat score

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On September 7, 2026, arXiv cs.LG published the paper “Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning”. This study proposes to view deep learning as a neural low-degree filtering mechanism and constructs a spectral theory framework for hierarchical feature learning.

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A arXiv cs.LG en 2026-09-07 12:00

Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

arXiv:2605.13612v2 发布论文《Deep Learning as Neural Low-Degree Filtering》，提出 Neural LoFi 理论框架，将深度学习中层级特征学习定义为显式的迭代谱过程。该理论通过梯度训练极限使各层动力学解耦，预测表示逐层选择与标签最大低度相关方向，并解释概念涌现机制及深度如何通过低度组合性构建新特征。研究辅以全连接和卷积架构的机理实验，证明 Neural LoFi 优于懒随机特征基线，能恢复有意义的结构化滤波器，且其生成的表示与真实数据集上的早期梯度下降特征发现对齐。