The Convallis Rule for Unsupervised Learning in Cortical Networks

The phenomenology and cellular mechanisms of cortical synaptic plasticity are becoming known in increasing detail, but the computational principles by which cortical plasticity enables the development of sensory representations are unclear. Here we describe a framework for cortical synaptic plasticity termed the “Convallis rule”, mathematically derived from a principle of unsupervised learning via constrained optimization. Implementation of the rule caused a recurrent cortex-like network of simulated spiking neurons to develop rate representations of real-world speech stimuli, enabling classification by a downstream linear decoder. Applied to spike patterns used in in vitro plasticity experiments, the rule reproduced multiple results including and beyond STDP. However STDP alone produced poorer learning performance. The mathematical form of the rule is consistent with a dual coincidence detector mechanism that has been suggested by experiments in several synaptic classes of juvenile neocortex. Based on this confluence of normative, phenomenological, and mechanistic evidence, we suggest that the rule may approximate a fundamental computational principle of the neocortex.Author Summary: The circuits of the sensory cortex are able to extract useful information from sensory inputs because of their exquisitely organized synaptic connections. These connections are wired largely through experience-dependent synaptic plasticity. Although many details of both the phenomena and cellular mechanisms of cortical synaptic plasticity are now known, an understanding of the computational principles by which synaptic plasticity wires cortical networks lags far behind this experimental data. In this study, we provide a theoretical framework for cortical plasticity termed the “Convallis rule”. The computational power of this rule is demonstrated by its ability to cause simulated cortical networks to learn representations of real-world speech data. Application of the rule to paradigms used to probe synaptic plasticity in vitro reproduced a large number of experimental findings, and the mathematical form of the rule is consistent with a dual coincidence detector mechanism that has been suggested experimentally in juvenile neocortex. Based on this confluence of normative, phenomenological, and mechanistic evidence, we suggest that the rule may approximate a fundamental computational principle of the neocortex.