Observation Noise and Initialization in Wide Neural Networks

• URL: http://arxiv.org/abs/2502.01556v1
• Date: Mon, 03 Feb 2025 17:39:45 GMT
• Title: Observation Noise and Initialization in Wide Neural Networks
• Authors: Sergio Calvo-Ordoñez, Jonathan Plenk, Richard Bergna, Alvaro Cartea, Jose Miguel Hernandez-Lobato, Konstantina Palla, Kamil Ciosek,
• Abstract summary: We introduce a textitshifted network that enables arbitrary prior mean functions. Our theoretical insights are validated empirically, with experiments exploring different values of observation noise and network architectures.
• Score: 9.163214210191814
• License:
• Abstract: Performing gradient descent in a wide neural network is equivalent to computing the posterior mean of a Gaussian Process with the Neural Tangent Kernel (NTK-GP), for a specific choice of prior mean and with zero observation noise. However, existing formulations of this result have two limitations: i) the resultant NTK-GP assumes no noise in the observed target variables, which can result in suboptimal predictions with noisy data; ii) it is unclear how to extend the equivalence to an arbitrary prior mean, a crucial aspect of formulating a well-specified model. To address the first limitation, we introduce a regularizer into the neural network's training objective, formally showing its correspondence to incorporating observation noise into the NTK-GP model. To address the second, we introduce a \textit{shifted network} that enables arbitrary prior mean functions. This approach allows us to perform gradient descent on a single neural network, without expensive ensembling or kernel matrix inversion. Our theoretical insights are validated empirically, with experiments exploring different values of observation noise and network architectures.

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