SGD on neural network weights induces a BBP phase transition that detaches signal eigenvalues from the random bulk, yielding an analytically solvable phase diagram for trainability in a linear teacher-student model.
[19]Valigi P., Baron J.W., Neri I., Biroli G.andCam- marota C.,J
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Unsupervised Hebbian networks show a sharp spectral transition in the interaction matrix that marks the onset of generalization when dataset quality allows separation of informative and noisy eigenvalue bulks.
For quadratic Euclidean random matrices, the average largest eigenvalue is explicitly determined by low-order moments of the point distribution, while the top eigenvector components concentrate on a hypersurface controlled by the same parameters.
For a rank-one spiked Wigner model with random per-entry noise variances, exact cavity equations give the outlier eigenvector distribution and a possibly non-monotonic BBP transition line.
citing papers explorer
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Spectral phase transitions and trainability in neural network learning dynamics
SGD on neural network weights induces a BBP phase transition that detaches signal eigenvalues from the random bulk, yielding an analytically solvable phase diagram for trainability in a linear teacher-student model.
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Spectral criteria for generalization in unsupervised Hebbian nets
Unsupervised Hebbian networks show a sharp spectral transition in the interaction matrix that marks the onset of generalization when dataset quality allows separation of informative and noisy eigenvalue bulks.
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Largest eigenvalue and top eigenvector statistics of large Euclidean random matrices
For quadratic Euclidean random matrices, the average largest eigenvalue is explicitly determined by low-order moments of the point distribution, while the top eigenvector components concentrate on a hypersurface controlled by the same parameters.
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BBP transition and the leading eigenvector of the spiked Wigner model with inhomogeneous noise
For a rank-one spiked Wigner model with random per-entry noise variances, exact cavity equations give the outlier eigenvector distribution and a possibly non-monotonic BBP transition line.