Causal Spike Timing Dependent Plasticity Prevents Assembly Fusion in Recurrent Networks

The organization of neurons into functionally related assemblies is a fundamental feature of cortical networks, yet our understanding of how these assemblies maintain distinct identities while sharing members remains limited. Here we analyze how spike-timing-dependent plasticity (STDP) shapes the formation and stability of overlapping neuronal assemblies in recurrently coupled networks of spiking neuron models. Using numerical simulations and an associated mean-field theory, we demonstrate that the temporal structure of the STDP rule, specifically its degree of causality, critically determines whether assemblies that share neurons maintain segregation or merge together after training is completed. We find that causal STDP rules, where potentiation/depression occurs strictly when presynaptic spikes precede/proceed postsynaptic spikes, allow assemblies to remain distinct even with substantial overlap in membership. This stability arises because causal STDP effectively cancels the symmetric correlations introduced by common inputs from shared neurons. In contrast, acausal STDP rules lead to assembly fusion when overlap exceeds a critical threshold, due to unchecked growth of common input correlations. Our results provide theoretical insight into how spike-timing-dependent learning rules can support distributed representation where individual neurons participate in multiple assemblies while maintaining functional specificity.