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Mathematical formulations of Hebbian learning.

Wulfram Gerstner1, Werner M Kistler

  • 1Swiss Federal Institute of Technology Lausanne, Laboratory of Computational Neuroscience, EPFL-LCN, 1015 Lausanne EPFL, Switzerland. wulfram.gerstner@epfl.ch

Biological Cybernetics
|December 4, 2002
PubMed
Summary

This study reviews correlation-based Hebbian learning formulations. It demonstrates how different descriptions of neuronal activity and backpropagating action potentials (BPAPs) unify under an expansion framework, revealing intrinsic normalization properties.

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Synaptic Plasticity

Background:

  • Hebbian learning is a fundamental mechanism for synaptic plasticity.
  • Various formulations exist, differing in how neuronal activity is represented.
  • The role of backpropagating action potentials (BPAPs) in synaptic plasticity is actively researched.

Purpose of the Study:

  • To review and unify different correlation-based Hebbian learning formulations.
  • To explore the mathematical underpinnings of these formulations.
  • To investigate the emergence of spike-time-dependent plasticity and normalization.

Main Methods:

  • Review of existing mathematical models of Hebbian learning.
  • Derivation of different formulations from a unified expansion viewpoint.

Related Experiment Videos

  • Analysis of the conditions under which spike-time-dependent plasticity and normalization arise.

    • Main Results:

    • All reviewed formulations can be derived from a common expansion framework.
    • Correlation between presynaptic spikes and postsynaptic membrane potential is key without BPAPs.
    • Spike-time-dependent plasticity emerges with BPAPs, enabling temporal specificity.
    • Intrinsic normalization properties stabilize firing rates and lead to subtractive weight normalization.

    Conclusions:

    • A unified mathematical framework explains diverse Hebbian learning rules.
    • Backpropagating action potentials are crucial for spike-timing-dependent plasticity.
    • Hebbian learning possesses inherent normalization mechanisms crucial for stable neural networks.