Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.
arXiv preprint arXiv:2512.03325 , year=
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A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
Linear associative memories store up to p_c log p_c / d^2 = 1/2 associations, with optimal weights pushing correct scores just above the extreme value of competing outputs.
This review synthesizes representative advances in high-dimensional statistics, highlights common themes and open problems, and points to key entry works.
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Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.
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Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
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Factual recall in linear associative memories: sharp asymptotics and mechanistic insights
Linear associative memories store up to p_c log p_c / d^2 = 1/2 associations, with optimal weights pushing correct scores just above the extreme value of competing outputs.
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High-Dimensional Statistics: Reflections on Progress and Open Problems
This review synthesizes representative advances in high-dimensional statistics, highlights common themes and open problems, and points to key entry works.
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