Non-Vacuous Generalisation Bounds for Shallow Neural Networks

• URL: http://arxiv.org/abs/2202.01627v2
• Date: Fri, 4 Feb 2022 15:41:51 GMT
• Title: Non-Vacuous Generalisation Bounds for Shallow Neural Networks
• Authors: Felix Biggs, Benjamin Guedj
• Abstract summary: We focus on a specific class of shallow neural networks with a single hidden layer. We derive new generalisation bounds through the PAC-Bayesian theory. Our bounds are empirically non-vacuous when the network is trained with vanilla gradient descent on MNIST and Fashion-MNIST.
• Score: 5.799808780731661
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We focus on a specific class of shallow neural networks with a single hidden layer, namely those with $L_2$-normalised data and either a sigmoid-shaped Gaussian error function ("erf") activation or a Gaussian Error Linear Unit (GELU) activation. For these networks, we derive new generalisation bounds through the PAC-Bayesian theory; unlike most existing such bounds they apply to neural networks with deterministic rather than randomised parameters. Our bounds are empirically non-vacuous when the network is trained with vanilla stochastic gradient descent on MNIST and Fashion-MNIST.

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