A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel
A persistent empirical observation is that trained neural networks outperform their neural tangent kernel (NTK) limit on tasks with compositional structure, yet a quantitative account of $\textbf{when}$ and $\textbf{by how much}$ has been lacking. Working on the unit circle, we give such an account through a dichotomy between two complexity measures of the target: its $\textbf{Fourier complexity}$, which controls NTK kernel regression, and its $\textbf{architectural complexity}$, which controls learning over depth-$L$, width-$w$ ReLU networks with the variation norm of the weights bounded by $
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- PossiblePossibly related (embedding) · 46%Principled approaches for extending neural architectures to function spaces for operator learning →
- LinkedLinked via arxiv author · 85%Arkaprabha Ganguli →
“A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel”
- LinkedLinked via arxiv author · 85%Emil Constantinescu →
“A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel”
- FuzzySimilar title/name (fuzzy) · 59%aymericdamien/TopDeepLearning →
“Fuzzy title match (0.73): “A Function-Space Dichotomy for Compositional Learning: Expon” ≈ “aymericdamien/TopDeepLearning””
- FuzzySimilar title/name (fuzzy) · 59%microsoft/semantic-kernel →
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