On the space of coefficients of a Feed Forward Neural Network
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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 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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