TY - JOUR
T1 - Reverse engineering neural networks to characterise their cost functions
JF - bioRxiv
DO - 10.1101/654467
SP - 654467
AU - Isomura, Takuya
AU - Friston, Karl
Y1 - 2019/01/01
UR - http://biorxiv.org/content/early/2019/05/31/654467.abstract
N2 - This work considers a class of biologically plausible cost functions for neural networks, where the same cost function is minimised by both neural activity and plasticity. In brief, we show that such cost functions can be cast as a variational bound on model evidence, or marginal likelihood, under an implicit generative model. Using generative models based on Markov decision processes (MDP), we show, analytically, that neural activity and plasticity perform Bayesian inference and learning, respectively, by maximising model evidence. Using mathematical and numerical analyses, we then confirm that biologically plausible cost functions—used in neural networks—correspond to variational free energy under some prior beliefs about the prevalence of latent states generating inputs. These prior beliefs are determined by particular constants (i.e., thresholds) that define the cost function. This means that the Bayes optimal encoding of latent or hidden states is achieved when, and only when, the network’s implicit priors match the process generating inputs. Our results suggest that when a neural network minimises its cost function, it is implicitly minimising variational free energy under optimal or sub-optimal prior beliefs. This insight is potentially important because it suggests that any free parameter of a neural network’s cost function can itself be optimised—by minimisation with respect to variational free energy.
ER -