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Deep feedforward and recurrent rate-based neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation., Comment: Accepted in Neural Computation

Learning depends on changes in synaptic connections deep inside the brain. In multilayer networks, these changes are triggered by error signals fed back from the output, generally through a stepwise inversion of the feedforward processing steps. The gold standard for this process -- backpropagation -- works well in artificial neural networks, but is biologically implausible. Several recent proposals have emerged to address this problem, but many of these biologically-plausible schemes are based on learning an independent set of feedback connections. This complicates the assignment of errors to each synapse by making it dependent upon a second learning problem, and by fitting inversions rather than guaranteeing them. Here, we show that feedforward network transformations can be effectively inverted through dynamics. We derive this dynamic inversion from the perspective of feedback control, where the forward transformation is reused and dynamically interacts with fixed or random feedback to propagate error signals during the backward pass. Importantly, this scheme does not rely upon a second learning problem for feedback because accurate inversion is guaranteed through the network dynamics. We map these dynamics onto generic feedforward networks, and show that the resulting algorithm performs well on several supervised and unsupervised datasets. Finally, we discuss potential links between dynamic inversion and second-order optimization. Overall, our work introduces an alternative perspective on credit assignment in the brain, and proposes a special role for temporal dynamics and feedback control during learning., Comment: 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada

A key question in neuroscience is at which level functional meaning emerges from biophysical phenomena. In most vertebrate systems, precise functions are assigned at the level of neural populations, while single-neurons are deemed unreliable and redundant. Here we challenge this view and show that many single-neuron quantities, including voltages, firing thresholds, excitation, inhibition, and spikes, acquire precise functional meaning whenever a network learns to transmit information parsimoniously and precisely to the next layer. Based on the hypothesis that neural circuits generate precise population codes under severe constraints on metabolic costs, we derive synaptic plasticity rules that allow a network to represent its time-varying inputs with maximal accuracy. We provide exact solutions to the learnt optimal states, and we predict the properties of an entire network from its input distribution and the cost of activity. Single-neuron variability and tuning curves as typically observed in cortex emerge over the course of learning, but paradoxically coincide with a precise, non-redundant spike-based population code. Our work suggests that neural circuits operate far more accurately than previously thought, and that no spike is fired in vain.

Neurons in higher cortical areas, such as the prefrontal cortex, are known to be tuned to a variety of sensory and motor variables. The resulting diversity of neural tuning often obscures the represented information. Here we introduce a novel dimensionality reduction technique, demixed principal component analysis (dPCA), which automatically discovers and highlights the essential features in complex population activities. We reanalyze population data from the prefrontal areas of rats and monkeys performing a variety of working memory and decision-making tasks. In each case, dPCA summarizes the relevant features of the population response in a single figure. The population activity is decomposed into a few demixed components that capture most of the variance in the data and that highlight dynamic tuning of the population to various task parameters, such as stimuli, decisions, rewards, etc. Moreover, dPCA reveals strong, condition-independent components of the population activity that remain unnoticed with conventional approaches., Comment: 23 pages, 6 figures + supplementary information (21 pages, 15 figures)