Understanding the training dynamics of CoLaNET by its simplified model

Training complex, biologically plausible Spiking Neural Networks (SNNs) with local learning rules is a significant challenge for theoretical analysis. Here we address this problem by developing a comprehensive analytical theory for the learning dynamics of CoLaNET, a recently proposed columnar SNN. In particular, we consider a simplified model that captures the core algorithmic logic of CoLaNET’s training process. We derive closed-form expressions that accurately predict the number of emergent microcolumns, the complete temporal evolution of synaptic weights, and the model’s learning curve. Our theoretical predictions show excellent quantitative agreement with numerical simulations of the simplified model and successfully capture the qualitative behavior of the full spiking CoLaNET. Furthermore, our analysis reveals that the spike-based, asynchronous competition in the full model delays neuronal specialization and slows down the training process relative to its simplified counterpart. This work provides a scalable theoretical foundation for understanding and configuring biologically inspired SNNs and highlights a key difference introduced by spike-based dynamics.