Equivalence of Personalized PageRank and Successor Representations

TL;DR

This paper shows that personalized PageRank and successor representations, two algorithms used to model hippocampal functions like memory retrieval and navigation, are mathematically equivalent and rely on the same underlying graph-based representation.

Contribution

It demonstrates the isomorphism between personalized PageRank and successor representations, suggesting a unified computational role for the hippocampus in processing graph-based information.

Findings

Personalized PageRank and successor representations are mathematically isomorphic.

Both algorithms rely on the stationary distribution of a random walk on a graph.

The hippocampus may compute this shared representation for various functions.

Abstract

The hippocampus appears to implement two core but highly distinct functions in the brain: long term memory retrieval and planning and spatial navigation. Naively, these functions appear very different algorithmically. In this short note, we demonstrate that two powerful algorithms that have each independently been proposed to underlie the hippocampal operation for each function -- personalized page-rank for memory retrieval, and successor representations for planning and navigation, are in fact isomorphic and utilize the same underlying representation -- the stationary distribution of a random walk on a graph. We hypothesize that the core computational function of the hippocampus is to compute this representation on arbitrary input graphs.