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Logarithmic distributions prove that intrinsic learning is Hebbian.

Gabriele Scheler1

  • 1Carl Correns Foundation for Mathematical Biology, Mountain View, CA, 94040, USA.

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Summary

Brain neurons consistently exhibit lognormal distributions for spike rates, synaptic weights, and intrinsic excitability (gain). This universal property, observed across diverse brain areas, is maintained by Hebbian learning rules.

Keywords:
Hebbian learningintrinsic excitabilitylognormal distributions.neural circuitsneural codingneural networksrate codingspike frequencysynaptic weights

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Systems Neuroscience

Background:

  • Neuronal properties like spike rates, synaptic weights, and intrinsic excitability (gain) exhibit significant variability across different brain regions.
  • Understanding the statistical distributions of these properties is crucial for comprehending neural computation and network function.
  • Previous research has suggested various distributions, but a unifying principle across diverse neuronal populations and brain areas has been elusive.

Purpose of the Study:

  • To investigate the statistical distributions of neuronal spike rates, synaptic weights, and intrinsic excitability across a wide range of brain areas.
  • To determine if these distributions exhibit consistent patterns, such as heavy tails or lognormal characteristics, irrespective of brain area, connectivity, neurotransmitter, or activation level.
  • To develop and test a computational model of adaptive learning rules that can generate and maintain the observed lognormal distributions.

Main Methods:

  • Analysis of experimental data on spike rates, synaptic weights, and intrinsic excitability from multiple brain regions (auditory cortex, visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei).
  • Statistical analysis to identify and characterize the distributions of these neuronal properties, focusing on heavy-tailed and lognormal patterns.
  • Development of a generic neural network model incorporating adaptive learning rules to simulate the emergence and maintenance of lognormal distributions.

Main Results:

  • Consistent heavy-tailed, specifically lognormal, distributions were found for neuronal spike rates, synaptic weights, and intrinsic excitability across all examined brain areas.
  • This lognormal distribution pattern remained consistent regardless of factors like connectivity type (recurrent vs. feed-forward), neurotransmitter (GABA vs. glutamate), or neuronal activation level.
  • The computational model demonstrated that strong Hebbian learning applied to both synaptic weights and intrinsic gains is necessary to produce and sustain these experimentally observed lognormal distributions.

Conclusions:

  • Lognormal distributions represent a fundamental, general functional property of neuronal rates, weights, and gains across diverse brain systems.
  • Hebbian learning is essential not only for synaptic plasticity but also for regulating intrinsic neuronal excitability, providing a unified mechanism for maintaining these distributions.
  • This finding resolves a long-standing question regarding the plasticity mechanisms governing intrinsic excitability in neural networks.