Models, networks and algorithmic complexity
This provides a theoretical framework linking neural networks to algorithmic complexity, primarily for cognitive neuroscience applications.
The paper demonstrates that models, classification functions, invariances, and datasets are algorithmically equivalent when properly defined, and shows that neural networks implement models with perturbations propagating strongly and a descriptive power hierarchy aligning with recursive function theory.
I aim to show that models, classification or generating functions, invariances and datasets are algorithmically equivalent concepts once properly defined, and provide some concrete examples of them. I then show that a) neural networks (NNs) of different kinds can be seen to implement models, b) that perturbations of inputs and nodes in NNs trained to optimally implement simple models propagate strongly, c) that there is a framework in which recurrent, deep and shallow networks can be seen to fall into a descriptive power hierarchy in agreement with notions from the theory of recursive functions. The motivation for these definitions and following analysis lies in the context of cognitive neuroscience, and in particular in Ruffini (2016), where the concept of model is used extensively, as is the concept of algorithmic complexity.