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.

Reviewing Editor

  1. Thomas Serre, Brown University, United States

Version history

  1. Preprint posted: March 31, 2021 (view preprint)
  2. Received: March 14, 2022
  3. Accepted: December 15, 2022
  4. Accepted Manuscript published: December 16, 2022 (version 1)
  5. Version of Record published: January 13, 2023 (version 2)

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.

Metrics

  • 1,660
    views
  • 302
    downloads
  • 3
    citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

  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

Share this article

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

Further reading

    1. Neuroscience
    Yu-Feng Xie, Jane Yang ... Steven A Prescott
    Research Article

    Nociceptive sensory neurons convey pain-related signals to the CNS using action potentials. Loss-of-function mutations in the voltage-gated sodium channel NaV1.7 cause insensitivity to pain (presumably by reducing nociceptor excitability) but clinical trials seeking to treat pain by inhibiting NaV1.7 pharmacologically have struggled. This may reflect the variable contribution of NaV1.7 to nociceptor excitability. Contrary to claims that NaV1.7 is necessary for nociceptors to initiate action potentials, we show that nociceptors can achieve similar excitability using different combinations of NaV1.3, NaV1.7, and NaV1.8. Selectively blocking one of those NaV subtypes reduces nociceptor excitability only if the other subtypes are weakly expressed. For example, excitability relies on NaV1.8 in acutely dissociated nociceptors but responsibility shifts to NaV1.7 and NaV1.3 by the fourth day in culture. A similar shift in NaV dependence occurs in vivo after inflammation, impacting ability of the NaV1.7-selective inhibitor PF-05089771 to reduce pain in behavioral tests. Flexible use of different NaV subtypes exemplifies degeneracy – achieving similar function using different components – and compromises reliable modulation of nociceptor excitability by subtype-selective inhibitors. Identifying the dominant NaV subtype to predict drug efficacy is not trivial. Degeneracy at the cellular level must be considered when choosing drug targets at the molecular level.

    1. Neuroscience
    Mischa Vance Bandet, Ian Robert Winship
    Research Article

    Despite substantial progress in mapping the trajectory of network plasticity resulting from focal ischemic stroke, the extent and nature of changes in neuronal excitability and activity within the peri-infarct cortex of mice remains poorly defined. Most of the available data have been acquired from anesthetized animals, acute tissue slices, or infer changes in excitability from immunoassays on extracted tissue, and thus may not reflect cortical activity dynamics in the intact cortex of an awake animal. Here, in vivo two-photon calcium imaging in awake, behaving mice was used to longitudinally track cortical activity, network functional connectivity, and neural assembly architecture for 2 months following photothrombotic stroke targeting the forelimb somatosensory cortex. Sensorimotor recovery was tracked over the weeks following stroke, allowing us to relate network changes to behavior. Our data revealed spatially restricted but long-lasting alterations in somatosensory neural network function and connectivity. Specifically, we demonstrate significant and long-lasting disruptions in neural assembly architecture concurrent with a deficit in functional connectivity between individual neurons. Reductions in neuronal spiking in peri-infarct cortex were transient but predictive of impairment in skilled locomotion measured in the tapered beam task. Notably, altered neural networks were highly localized, with assembly architecture and neural connectivity relatively unaltered a short distance from the peri-infarct cortex, even in regions within ‘remapped’ forelimb functional representations identified using mesoscale imaging with anaesthetized preparations 8 weeks after stroke. Thus, using longitudinal two-photon microscopy in awake animals, these data show a complex spatiotemporal relationship between peri-infarct neuronal network function and behavioral recovery. Moreover, the data highlight an apparent disconnect between dramatic functional remapping identified using strong sensory stimulation in anaesthetized mice compared to more subtle and spatially restricted changes in individual neuron and local network function in awake mice during stroke recovery.