Population codes enable learning from few examples by shaping inductive bias

  1. Blake Bordelon
  2. Cengiz Pehlevan  Is a corresponding author
  1. Harvard University, United States

Abstract

Learning from a limited number of experiences requires suitable inductive biases. To identify how inductive biases are implemented in and shaped by neural codes, we analyze sample-efficient learning of arbitrary stimulus-response maps from arbitrary neural codes with biologically-plausible readouts. We develop an analytical theory that predicts the generalization error of the readout as a function of the number of observed examples. Our theory illustrates in a mathematically precise way how the structure of population codes shapes inductive bias, and how a match between the code and the task is crucial for sample-efficient learning. It elucidates a bias to explain observed data with simple stimulus-response maps. Using recordings from the mouse primary visual cortex, we demonstrate the existence of an efficiency bias towards low frequency orientation discrimination tasks for grating stimuli and low spatial frequency reconstruction tasks for natural images. We reproduce the discrimination bias in a simple model of primary visual cortex, and further show how invariances in the code to certain stimulus variations alter learning performance. We extend our methods to time-dependent neural codes and predict the sample efficiency of readouts from recurrent networks. We observe that many different codes can support the same inductive bias. By analyzing recordings from the mouse primary visual cortex, we demonstrate that biological codes have lower total activity than other codes with identical bias. Finally, we discuss implications of our theory in the context of recent developments in neuroscience and artificial intelligence. Overall, our study provides a concrete method for elucidating inductive biases of the brain and promotes sample-efficient learning as a general normative coding principle.

Data availability

Mouse V1 neuron responses to orientation gratings and preprocessing code were obtained from a publicly available dataset: https://github.com/MouseLand/stringer-et-al-2019, [8, 9].Responses to ImageNet images and preprocessing code were obtained from another publicly available dataset, https://github.com/MouseLand/stringer-pachitariu-et-al-2018b [10, 11].The code generated by the authors for this paper is also available https://github.com/Pehlevan-Group/sample_efficient_pop_codes

The following previously published data sets were used

Article and author information

Author details

  1. Blake Bordelon

    John A Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, United States
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-0455-9445
  2. Cengiz Pehlevan

    John A Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, United States
    For correspondence
    cpehlevan@seas.harvard.edu
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-9767-6063

Funding

National Science Foundation (DMS-2134157)

  • Blake Bordelon
  • Cengiz Pehlevan

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Copyright

© 2022, Bordelon & Pehlevan

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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  1. Blake Bordelon
  2. Cengiz Pehlevan
(2022)
Population codes enable learning from few examples by shaping inductive bias
eLife 11:e78606.
https://doi.org/10.7554/eLife.78606

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https://doi.org/10.7554/eLife.78606

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