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Predicting the Future with Multi-scale Successor Representations

View ORCID ProfileIda Momennejad, View ORCID ProfileMarc W. Howard
doi: https://doi.org/10.1101/449470
Ida Momennejad
1Columbia University
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Marc W. Howard
2Boston University
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Abstract

The successor representation (SR) is a candidate principle for generalization in reinforcement learning, computational accounts of memory, and the structure of neural representations in the hippocampus. Given a sequence of states, the SR learns a predictive representation for every given state that encodes how often, on average, each upcoming state is expected to be visited, even if it is multiple steps ahead. A discount or scale parameter determines how many steps into the future SR’s generalizations reach, enabling rapid value computation, subgoal discovery, and flexible decision-making in large trees. However, SR with a single scale could discard information for predicting both the sequential order of and the distance between states, which are common problems in navigation for animals and artificial agents. Here we propose a solution: an ensemble of SRs with multiple scales. We show that the derivative of multi-scale SR can reconstruct both the sequence of expected future states and estimate distance to goal. This derivative can be computed linearly: we show that a multi-scale SR ensemble is the Laplace transform of future states, and the inverse of this Laplace transform is a biologically plausible linear estimation of the derivative. Multi-scale SR and its derivative could lead to a common principle for how the medial temporal lobe supports both map-based and vector-based navigation.

Footnotes

  • ida.m{at}columbia.edu, marc777{at}bu.edu

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-ND 4.0 International license.
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Posted October 22, 2018.
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Predicting the Future with Multi-scale Successor Representations
Ida Momennejad, Marc W. Howard
bioRxiv 449470; doi: https://doi.org/10.1101/449470
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Predicting the Future with Multi-scale Successor Representations
Ida Momennejad, Marc W. Howard
bioRxiv 449470; doi: https://doi.org/10.1101/449470

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