What is the relation between Slow Feature Analysis and the Successor Representation?

TL;DR

This paper explores the mathematical and conceptual connections between Slow Feature Analysis and the Successor Representation, revealing their formal similarities and differences in representing states in Markov decision processes.

Contribution

It demonstrates a formal equivalence between SFA and SR in a one-hot encoded MDP and characterizes the nature of representations generated by SFA.

Findings

SFA and SR share mathematical properties and sensitivities.

A formal equivalence is shown in grid-like representations for one-hot MDPs.

SFA produces place-like representations distinct from traditional place-cell models.

Abstract

Slow feature analysis (SFA) is an unsupervised method for extracting representations from time series data. The successor representation (SR) is a method for representing states in a Markov decision process (MDP) based on transition statistics. While SFA and SR stem from distinct areas of machine learning, they share important properties, both in terms of their mathematics and the types of information they are sensitive to. This work studies their connection along these two axes. In particular, both SFA and SR are explored analytically, and in the setting of a one-hot encoded MDP, a formal equivalence is demonstrated in terms of the grid-like representations that occur as solutions/eigenvectors. Moreover, it is shown that the columns of the matrices involved in SFA contain place-like representations, which are formally distinct from place-cell models that have already been defined using SFA.