Predictive power of a Bayesian effective action for fully-connected one hidden layer neural networks in the proportional limit
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910304243286016 |
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| author | Baglioni, P. Pacelli, R. Aiudi, R. Di Renzo, F. Vezzani, A. Burioni, R. Rotondo, P. |
| author_facet | Baglioni, P. Pacelli, R. Aiudi, R. Di Renzo, F. Vezzani, A. Burioni, R. Rotondo, P. |
| contents | We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of validity of a recently-derived Bayesian effective action for shallow architectures in the proportional limit. We explore the predictive power of the theory as a function of the parameters (the temperature $T$, the magnitude of the Gaussian priors $λ_1$, $λ_0$, the size of the hidden layer $N_1$ and the size of the training set $P$) by comparing the experimental and predicted generalization error. The very good agreement between the effective theory and the experiments represents an indication that global rescaling of the infinite-width kernel is a main physical mechanism for kernel renormalization in FC Bayesian standard-scaled shallow networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_11004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Predictive power of a Bayesian effective action for fully-connected one hidden layer neural networks in the proportional limit Baglioni, P. Pacelli, R. Aiudi, R. Di Renzo, F. Vezzani, A. Burioni, R. Rotondo, P. Disordered Systems and Neural Networks Statistical Mechanics We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of validity of a recently-derived Bayesian effective action for shallow architectures in the proportional limit. We explore the predictive power of the theory as a function of the parameters (the temperature $T$, the magnitude of the Gaussian priors $λ_1$, $λ_0$, the size of the hidden layer $N_1$ and the size of the training set $P$) by comparing the experimental and predicted generalization error. The very good agreement between the effective theory and the experiments represents an indication that global rescaling of the infinite-width kernel is a main physical mechanism for kernel renormalization in FC Bayesian standard-scaled shallow networks. |
| title | Predictive power of a Bayesian effective action for fully-connected one hidden layer neural networks in the proportional limit |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2401.11004 |