Optimizing Information-theoretical Generalization Bounds via Anisotropic
Noise in SGLD
- URL: http://arxiv.org/abs/2110.13750v1
- Date: Tue, 26 Oct 2021 15:02:27 GMT
- Title: Optimizing Information-theoretical Generalization Bounds via Anisotropic
Noise in SGLD
- Authors: Bohan Wang, Huishuai Zhang, Jieyu Zhang, Qi Meng, Wei Chen, Tie-Yan
Liu
- Abstract summary: We optimize the information-theoretical generalization bound by manipulating the noise structure in SGLD.
We prove that with constraint to guarantee low empirical risk, the optimal noise covariance is the square root of the expected gradient covariance.
- Score: 73.55632827932101
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Recently, the information-theoretical framework has been proven to be able to
obtain non-vacuous generalization bounds for large models trained by Stochastic
Gradient Langevin Dynamics (SGLD) with isotropic noise. In this paper, we
optimize the information-theoretical generalization bound by manipulating the
noise structure in SGLD. We prove that with constraint to guarantee low
empirical risk, the optimal noise covariance is the square root of the expected
gradient covariance if both the prior and the posterior are jointly optimized.
This validates that the optimal noise is quite close to the empirical gradient
covariance. Technically, we develop a new information-theoretical bound that
enables such an optimization analysis. We then apply matrix analysis to derive
the form of optimal noise covariance. Presented constraint and results are
validated by the empirical observations.
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