On the space of coefficients of a Feed Forward Neural Network

Dinesh Valluri; Rory Campbell

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arXiv · 2109.03362

On the space of coefficients of a Feed Forward Neural Network

Dinesh Valluri·Rory Campbell

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Abstract

We define and establish the conditions for `equivalent neural networks' - neural networks with different weights, biases, and threshold functions that result in the same associated function. We prove that given a neural network $\mathcal{N}$ with piece-wise linear activation, the space of coefficients describing all equivalent neural networks is given by a semialgebraic set. This result is obtained by studying different representations of a given piece-wise linear function using the Tarski-Seidenberg theorem.

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Dinesh Valluri, Rory Campbell. 2021-09-07. On the space of coefficients of a Feed Forward Neural Network. https://arxiv.org/abs/2109.03362

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