On the space of coefficients of a Feed Forward Neural Network

• URL: http://arxiv.org/abs/2109.03362v1
• Date: Tue, 7 Sep 2021 22:47:50 GMT
• Title: On the space of coefficients of a Feed Forward Neural Network
• Authors: Dinesh Valluri and Rory Campbell
• Abstract summary: We prove that given a neural network $mathcalN$ 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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