神经网络是如何学会群乘法的 ：一篇论文里的傅里叶、不可约表示与深度的代数学
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TL;DR - An exposition of a 2026 arXiv paper showing how neural networks learn sequential finite-group multiplication through irreducible-representation channels. It provides a mathematical account of learning order and why depth can replace exponentially growing width.
- Group Fourier analysis predicts that representation channels are learned sequentially, favoring strong, low-dimensional components.
- A shallow polynomial MLP requires width exponential in sequence length due to the Waring rank of multiplicative interactions.
- RNNs and logarithmic-depth MLPs exploit associativity to reuse binary composition modules at width independent of sequence length.
- Hidden representations become block-diagonal by irreducible representation, separating algebraic channels across layers.
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神经网络是如何学会群乘法的 ：一篇论文里的傅里叶、不可约表示与深度的代数学
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Semantic Scholar citations 4 · Semantic Scholar influential citations 0
TL;DR - An exposition of a 2026 arXiv paper showing how neural networks learn sequential finite-group multiplication through irreducible-representation channels. It provides a mathematical account of learning order and why depth can replace exponentially growing width.
- Group Fourier analysis predicts that representation channels are learned sequentially, favoring strong, low-dimensional components.
- A shallow polynomial MLP requires width exponential in sequence length due to the Waring rank of multiplicative interactions.
- RNNs and logarithmic-depth MLPs exploit associativity to reuse binary composition modules at width independent of sequence length.
- Hidden representations become block-diagonal by irreducible representation, separating algebraic channels across layers.