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Networks based on coordinated spike coding can encode information with high efficiency in the spike trains of individual neurons. These networks exhibit single-neuron variability and tuning curves as typically observed in cortex, but paradoxically coincide with a precise, non-redundant spike-based population code. However, it has remained unclear whether the specific synaptic connectivities required in these networks can be learnt with local learning rules. Here, we show how to learn the required architecture. Use coding efficiency as an objective, we derive spike-timing-dependent learning rules for a recurrent neural network, and we provide exact solutions for the networks' convergence to an optimal state. As a result, we deduce an entire network from its input distribution and a firing cost. After learning, basic biophysical quantities such as voltages, firing thresholds, excitation, inhibition, or spikes acquire precise functional interpretations. Author summary: Spiking neural networks can encode information with high efficiency in the spike trains of individual neurons if the synaptic weights between neurons are set to specific, optimal values. In this regime, the networks exhibit irregular spike trains, high trial-to-trial variability, and stimulus tuning as typically observed in cortex. The strong variability on the level of single neurons paradoxically coincides with a precise, non-redundant spike-based population code. However, it has remained unclear whether the specific synaptic connectivities required in these spiking networks can be learnt with local learning rules. In this study, we show how the required architecture can be learnt. We derive local and biophysically plausible learning rules for a recurrent neural networks from first principles. We show both mathematically and using numerical simulations that these learning rules drive the networks into the optimal state, and we show that the optimal state is governed by the statistics of the input signals. After learning, the voltages of individual neurons can be interpreted as measuring the instantaneous error of the code, given by the error between the desired output signal and the actual output signal. [ABSTRACT FROM AUTHOR]

All of our perceptual experiences arise from the activity of neural populations. Here we study the formation of such percepts under the assumption that they emerge from a linear readout, i.e., a weighted sum of the neurons’ firing rates. We show that this assumption constrains the trial-to-trial covariance structure of neural activities and animal behavior. The predicted covariance structure depends on the readout parameters, and in particular on the temporal integration window w and typical number of neurons K used in the formation of the percept. Using these predictions, we show how to infer the readout parameters from joint measurements of a subject’s behavior and neural activities. We consider three such scenarios: (1) recordings from the complete neural population, (2) recordings of neuronal sub-ensembles whose size exceeds K, and (3) recordings of neuronal sub-ensembles that are smaller than K. Using theoretical arguments and artificially generated data, we show that the first two scenarios allow us to recover the typical spatial and temporal scales of the readout. In the third scenario, we show that the readout parameters can only be recovered by making additional assumptions about the structure of the full population activity. Our work provides the first thorough interpretation of (feed-forward) percept formation from a population of sensory neurons. We discuss applications to experimental recordings in classic sensory decision-making tasks, which will hopefully provide new insights into the nature of perceptual integration. [ABSTRACT FROM AUTHOR]

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated. [ABSTRACT FROM AUTHOR]