Modeling Axonal Plasticity in Artificial Neural Networks

Abstract

Axonal growth and pruning are the brain’s primary method of controlling the structured sparsity of its neural circuits. Without long-distance axon branches connecting distal neurons, no direct communication is possible. Artificial neural networks have almost entirely ignored axonal growth and pruning, instead relying on implicit assumptions that prioritize dendritic/synaptic learning above all other concerns. This project proposes a new model called the axon game, which allows biologically-inspired axonal plasticity dynamics to be incorporated into most artificial neural network models in a computationally efficient manner. First, we demonstrate that the axon game replicates multiple previously defined pre-synaptic cortical maps. Second, we demonstrate that the axon game integrated with a synaptic learning model similar to the Laterally Interconnected Synergetically Self-Organizing Map (LISSOM), can simulate the interaction of axonal plasticity and synaptic plasticity within one model creating both pre-synaptic and post-synaptic cortical maps. Finally, it is shown that pre-synaptic and post-synaptic maps can be decoupled from one another. This decoupling depends on the relative sizes of dendritic and axonal arbors, and indicates a novel theoretical prediction about how axonal and synaptic dynamics interact.

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Appendix 1

Appendix 1

Simulation Settings for Sect. 6

This section contains the parameter settings for the axon game used in the section titled “Simulated Axonal Maps”. The version of the axon game implemented for this paper uses a simple auto-scale feature whereby some of the input parameters are adjusted to produce results that can be compared to a standard 100 × 100 scale simulation. The \({\alpha }_{APDV}\) is multiplied by a factor of the largest simulation dimension divided by 100 when an axis of the simulation is larger than 100. Additionally, the starting exuberance \(E{X}_{0}\) is also scaled by the same factor.

Symbol Value
Res 170 × 250
Co-Act Covariance
\(Seed\) True
\({\sigma }_{seed}\) 0
\({\sigma }_{y}^{diff}\) 10
\({\sigma }_{\eta }^{diff}\) 1
\({\alpha }_{N}\) 6
\({\alpha }_{S}^{0}\) 0.002
\({\alpha }_{S}^{1}\) 0.04
\({\alpha }_{R}\) 0.08
\({\alpha }_{C}\) 50
\({\alpha }_{global}\) 0.3
\({\alpha }_{local}\) 0.08
\({\beta }_{s}\) 0.1
\(B\) 8
\(k\) 200
\({t}_{end}\) 100
\(E{X}_{0}\) 1.5
\(E{X}_{k}\) 0.025
\({P}_{0}^{grow}\) 1
\({P}_{1}^{grow}\) 1

Simulation settings for Sect. 7

This section contains the simulation parameters used for the second set of demonstrations that combined the Axon game with H-LISSOM Tables 3 and 4

Table 3 Axon game
Table 4 H-LISSOM

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Ryland, J. Modeling Axonal Plasticity in Artificial Neural Networks. Neural Process Lett (2021). https://doi.org/10.1007/s11063-021-10433-w

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Keywords

  • Axon
  • Pruning
  • Sparsity
  • Neural network
  • Cortical maps