BBP transitions become discontinuous when eigenvalue density vanishes faster than linearly at the edge, producing a jump in eigenvector overlap and an extended pre-critical regime with informative eigenvectors in deformed Gaussian and reweighted Wishart ensembles.
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cond-mat.dis-nn 2years
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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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Discontinuous BBP transitions
BBP transitions become discontinuous when eigenvalue density vanishes faster than linearly at the edge, producing a jump in eigenvector overlap and an extended pre-critical regime with informative eigenvectors in deformed Gaussian and reweighted Wishart ensembles.
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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.