# Mixing Complexity and its Applications to Neural Networks

## TL;DR

This paper introduces mixing complexity as a new framework to analyze neural networks under space constraints, revealing limitations and capabilities of bounded-memory learning algorithms.

## Contribution

It applies mixing complexity to neural networks, providing novel insights into what can be learned with bounded-memory algorithms.

## Key findings

- Mixing complexity measures neural network learnability under memory constraints.
- Bounded-memory algorithms have fundamental limitations in learning certain functions.
- The framework offers new theoretical tools for analyzing neural network training.

## Abstract

We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time tradeoffs that we call mixing complexity. This notion was devised in order to measure the (in)ability to learn using a bounded-memory algorithm. In this paper we describe how we use mixing complexity to obtain new results on what can and cannot be learned using neural networks.