Free probability and random matrices
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Operator-algebraic and combinatorial tools for the spectral behavior of large random matrices.
Members (6)
- themeSelf-attention spectra
Spectral and signal-propagation analysis of transformer self-attention layers; Gaussian-equivalence and deviation from Marchenko-Pastur.
Featured: Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
- conceptRandom matrix spectra
Asymptotic eigenvalue distributions of structured random matrices.
- conceptFree group representation
Approximate representations generated by random orthogonal matrices.
- conceptAsymptotic freeness
When independent random matrices become free in the large-dimensional limit, justifying free-probability propagation through DNN layers.
Featured: Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron : The Haar Orthogonal Case
- themeQuantum probability and easy quantum groups
Boolean / free / classical independence and the easy-quantum-group symmetry underlying de Finetti-type theorems.
Featured: De Finetti theorem for a Boolean anaolgue of easy quantum groups
- themeRandom matrix parameter estimation
Recovering random-matrix model parameters from spectral statistics — identifiability, Cauchy-noise losses, and free deterministic equivalents.
Featured: Cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents
Findings — subtree (6)
Papers (6)
- Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
- Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron : The Haar Orthogonal Case
- Cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents
- Free deterministic equivalent Z-scores of compound Wishart models: A goodness of fit test of 2DARMA models
- Identifiability of parametric random matrix models
- De Finetti theorem for a Boolean anaolgue of easy quantum groups
Notes — subtree (7)
- 自由対話 Free Talking
線型独立性を自由性と読み替えるところから、加群・モノイド・群・自由代数まで。行列とユークリッド空間の具体例だけで橋渡しする話。
- AISTATS2026に論文が2本採択されました
- Random Matrices, Free Probability, and Deep Neural Networks
- IMI: ランダム行列と深層神経回路
- Asymptotic Freeness of MLP and Related Topics
- Asymptotic Freeness of Jacobians of MLP
- 深層学習の数理にて：自由確率論とランダムDNN, AISTATS2021採択論文解説
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