Spatiotemporal Computations of an Excitable and Plastic Brain: Neuronal Plasticity Leads to Noise-Robust and Noise-Constructive Computations

It is a long-established fact that neuronal plasticity occupies the central role in generating neural function and computation. Nevertheless, no unifying account exists of how neurons in a recurrent cortical network learn to compute on temporally and spatially extended stimuli. However, these stimuli constitute the norm, rather than the exception, of the brain's input. Here, we introduce a geometric theory of learning spatiotemporal computations through neuronal plasticity. To that end, we rigorously formulate the problem of neural representations as a relation in space between stimulus-induced neural activity and the asymptotic dynamics of excitable cortical networks. Backed up by computer simulations and numerical analysis, we show that two canonical and widely spread forms of neuronal plasticity, that is, spike-timing-dependent synaptic plasticity and intrinsic plasticity, are both necessary for creating neural representations, such that these computations become realizable. Interestingly, the effects of these forms of plasticity on the emerging neural code relate to properties necessary for both combating and utilizing noise. The neural dynamics also exhibits features of the most likely stimulus in the network's spontaneous activity. These properties of the spatiotemporal neural code resulting from plasticity, having their grounding in nature, further consolidate the biological relevance of our findings.Author Summary: The world is not perceived as a chain of segmented sensory still lifes. Instead, it appears that the brain is capable of integrating the temporal dependencies of the incoming sensory stream with the spatial aspects of that input. It then transfers the resulting whole in a useful manner, in order to reach a coherent and causally sound image of our physical surroundings, and to act within it. These spatiotemporal computations are made possible through a cluster of local and coexisting adaptation mechanisms known collectively as neuronal plasticity. While this role is widely known and supported by experimental evidence, no unifying theory of how the brain, through the interaction of plasticity mechanisms, gets to represent spatiotemporal computations in its spatiotemporal activity. In this paper, we aim at such a theory. We develop a rigorous mathematical formalism of spatiotemporal representations within the input-driven dynamics of cortical networks. We demonstrate that the interaction of two of the most common plasticity mechanisms, intrinsic and synaptic plasticity, leads to representations that allow for spatiotemporal computations. We also show that these representations are structured to tolerate noise and to even benefit from it.