The free energy principle (FEP) has been presented as a unified brain theory, as a general principle for the self-organization of biological systems, and most recently as a principle for a theory of every thing. Additionally, active inference has been proposed as the process theory entailed by FEP that is able to model the full range of biological and cognitive events. In this

We define and establish the conditions for 'equivalent neural networks' -neural networks with different weights, biases, and threshold functions which result in the same associated function. We prove that, given a neural network N with piecewise 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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