Spike-timing-dependent plasticity for neurons with recurrent connections

Area of Science:

• Computational Neuroscience
• Neural Network Dynamics

Background:

• Understanding synaptic plasticity is crucial for modeling neural learning.
• Recurrent neural networks (RNNs) offer complex computational capabilities but their learning dynamics are challenging to analyze.
• The Poisson neuron model provides a tractable framework for studying spiking neuron networks.

Purpose of the Study:

• To derive and analyze the learning equation for recurrently connected neural networks.
• To investigate the self-consistent dynamics of spiking rates and cross-correlations in such networks.
• To explore the solutions of the learning equation, particularly in the absence of external input.

Main Methods:

• Derivation of the learning equation for synaptic weight evolution in RNNs.
• Application of the Poisson neuron model to analyze network activity.
• Self-consistent determination of neuron spiking rates and cross-correlations.
• Analysis of the learning equation's fixed-point structure.

Main Results:

• The learning equation for recurrent networks with Poisson neurons was successfully derived.
• Spiking rates and cross-correlations were determined self-consistently as a function of synaptic inputs.
• The behavior of the learning equation was illustrated through a case with no external synaptic input.
• The fixed-point structure of the learning equation's solutions was discussed.

Conclusions:

• The derived learning equation provides a framework for understanding synaptic plasticity in recurrent spiking neural networks.
• The self-consistent analysis reveals how network activity depends on external inputs.
• The study offers insights into the stability and behavior of learning in complex neural architectures.