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A Neuronal Least-Action Principle for Real-Time Learning in Cortical Circuits

View ORCID ProfileWalter Senn, Dominik Dold, Akos F. Kungl, Benjamin Ellenberger, Jakob Jordan, Yoshua Bengio, João Sacramento, Mihai A. Petrovici
doi: https://doi.org/10.1101/2023.03.25.534198
Walter Senn
aDepartment of Physiology, University of Bern
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  • For correspondence: senn@pyl.unibe.ch
Dominik Dold
aDepartment of Physiology, University of Bern
bKirchhoff-Institute for Physics, Heidelberg University
cEuropean Space Research and Technology Centre, European Space Agency
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Akos F. Kungl
aDepartment of Physiology, University of Bern
bKirchhoff-Institute for Physics, Heidelberg University
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Benjamin Ellenberger
aDepartment of Physiology, University of Bern
fInsel Data Science Center, University Hospital Bern
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Jakob Jordan
aDepartment of Physiology, University of Bern
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Yoshua Bengio
dMILA, University of Montreal
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João Sacramento
eDepartment of Computer Science, ETH Zurich
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Mihai A. Petrovici
aDepartment of Physiology, University of Bern
bKirchhoff-Institute for Physics, Heidelberg University
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Abstract

One of the most fundamental laws of physics is the principle of least action. Motivated by its predictive power, we introduce a neural least-action principle that we apply to motor control. The central notion is the somato-dendritic mismatch error within individual neurons. The principle postulates that the somato-dendritic mismatch errors across all neurons in a cortical network are minimized by the voltage dynamics. Ongoing synaptic plasticity reduces the somato-dendritic mismatch error within each neuron and performs gradient descent on the output cost in real time. The neuronal activity is prospective, ensuring that dendritic errors deep in the network are prospectively corrected to eventually reduce motor errors. The neuron-specific errors are represented in the apical dendrites of pyramidal neurons, and are extracted by a cortical microcircuit that ‘explains away’ the feedback from the periphery. The principle offers a general theoretical framework to functionally describe real-time neuronal and synaptic processing.

Competing Interest Statement

The authors have declared no competing interest.

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-NC-ND 4.0 International license.
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Posted March 25, 2023.
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A Neuronal Least-Action Principle for Real-Time Learning in Cortical Circuits
Walter Senn, Dominik Dold, Akos F. Kungl, Benjamin Ellenberger, Jakob Jordan, Yoshua Bengio, João Sacramento, Mihai A. Petrovici
bioRxiv 2023.03.25.534198; doi: https://doi.org/10.1101/2023.03.25.534198
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A Neuronal Least-Action Principle for Real-Time Learning in Cortical Circuits
Walter Senn, Dominik Dold, Akos F. Kungl, Benjamin Ellenberger, Jakob Jordan, Yoshua Bengio, João Sacramento, Mihai A. Petrovici
bioRxiv 2023.03.25.534198; doi: https://doi.org/10.1101/2023.03.25.534198

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