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.

Appendix 1

1.1 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

1.2 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