Topics in matrix analysis
Introduction to the theory of neural computation
Introduction to the theory of neural computation
The NEURON simulation environment
Neural Computation
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Phenomenological models of synaptic plasticity based on spike timing
Biological Cybernetics - Special Issue: Object Localization
Simple model of spiking neurons
IEEE Transactions on Neural Networks
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It has been established that homeostatic synaptic scaling plasticity can maintain neural network activity in a stable regime. However, the underlying learning rule for this mechanism is still unclear. Whether it is dependent on the presynaptic site remains a topic of debate. Here we focus on two forms of learning rules: traditional synaptic scaling (SS) without presynaptic effect and presynaptic-dependent synaptic scaling (PSD). Analysis of the synaptic matrices reveals that transition matrices between consecutive synaptic matrices are distinct: they are diagonal and linear to neural activity under SS, but become nondiagonal and nonlinear under PSD. These differences produce different dynamics in recurrent neural networks. Numerical simulations show that network dynamics are stable under PSD but not SS, which suggests that PSD is a better form to describe homeostatic synaptic scaling plasticity. Matrix analysis used in the study may provide a novel way to examine the stability of learning dynamics.