# Capacity of a spiking network with preserved weight distribution: a game-theory-inspired study

**Authors:** Maayan Levy & Tim P. Vogels

**Presentation type:** Short talk at SNUFA 2023 online workshop (7-8 Nov 2023)

## Abstract

How changes in synaptic connections lead to learning and memory is a central question in Neuroscience. Previous modeling efforts have focused on biologically realistic learning rules and dynamics, but no known model has been shown to perform successful learning while preserving a realistic distribution of synaptic weights (lognormal), as found experimentally. It thus remains unknown how constraining the initial and final distribution of synaptic weights impacts the operational principles of the learning rule as well as the capacity of the network. Here we set up a spiking neural network with a “trading floor” of synaptic weights, where weights can be swapped between excitatory synapses according to a functional or structural plasticity rule. Swapping allows for retention of the distribution while remaining agnostic to the implementation of the learning rule. We then test the network for pattern completion of corrupted visual inputs as a measure of memory. We find that while both functional and structural rules lead to pattern completion, the minimum synaptic change necessary to store a pattern and the resulting dynamics differ. We find that functional plasticity requires broad reconfiguration of weights, but is self-stabilizing and does not lead to runaway excitation. In contrast, structural plasticity of a small number of connections is sufficient for learning, yet results in aberrant network behavior. To explore the pattern capacity of the network, we swap synapses in response to multiple stimuli and pattern sizes. We conceptualize the patterns as players in a game, with utility function designed to optimize storage while preserving existing resources, i.e. the weights. Leveraging this paradigm, we demonstrate the impact of distribution parameters on pattern capacity. Our work thus ties together network topology, capacity and the nature of plasticity rules and pioneers the use of game-theory in the study of learning and memory.