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The Gradient Clusteron: A model neuron that learns via dendritic nonlinearities, structural plasticity, and gradient descent

View ORCID ProfileToviah Moldwin, Menachem Kalmenson, View ORCID ProfileIdan Segev
doi: https://doi.org/10.1101/2020.12.15.417790
Toviah Moldwin
2Edmond and Lily Safra Center for Brain Sciences, the Hebrew University of Jerusalem, Jerusalem, Israel
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  • For correspondence: Toviah.moldwin@mail.huji.ac.il
Menachem Kalmenson
1Department of Neurobiology, the Hebrew University of Jerusalem, Jerusalem, Israel
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Idan Segev
1Department of Neurobiology, the Hebrew University of Jerusalem, Jerusalem, Israel
2Edmond and Lily Safra Center for Brain Sciences, the Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract

Synaptic clustering on neuronal dendrites has been hypothesized to play an important role in implementing pattern recognition. Neighboring synapses on a dendritic branch can interact in a synergistic, cooperative manner via the nonlinear voltage-dependence of NMDA receptors. Inspired by the NMDA receptor, the single-branch clusteron learning algorithm (Mel 1991) takes advantage of location-dependent multiplicative nonlinearities to solve classification tasks by randomly shuffling the locations of “under-performing” synapses on a model dendrite during learning (“structural plasticity”), eventually resulting in synapses with correlated activity being placed next to each other on the dendrite. We propose an alternative model, the gradient clusteron, or G-clusteron, which uses an analytically-derived gradient descent rule where synapses are “attracted to” or “repelled from” each other in an input- and location-dependent manner. We demonstrate the classification ability of this algorithm by testing it on the MNIST handwritten digit dataset and show that, when using a softmax activation function, the accuracy of the G-clusteron on the All-vs-All MNIST task (85.9%) approaches that of logistic regression (92.6%). In addition to the synaptic location update plasticity rule, we also derive a learning rule for the synaptic weights of the G-clusteron (“functional plasticity”) and show that the G-clusteron with both plasticity rules can achieve 89.5% accuracy on the MNIST task and can learn to solve the XOR problem from arbitrary initial conditions.

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 4.0 International license.
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Posted December 16, 2020.
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The Gradient Clusteron: A model neuron that learns via dendritic nonlinearities, structural plasticity, and gradient descent
Toviah Moldwin, Menachem Kalmenson, Idan Segev
bioRxiv 2020.12.15.417790; doi: https://doi.org/10.1101/2020.12.15.417790
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The Gradient Clusteron: A model neuron that learns via dendritic nonlinearities, structural plasticity, and gradient descent
Toviah Moldwin, Menachem Kalmenson, Idan Segev
bioRxiv 2020.12.15.417790; doi: https://doi.org/10.1101/2020.12.15.417790

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