Cooperative coding of continuous variables in networks with sparsity constraint
A hallmark of biological and artificial neural networks is that neurons tile the range of continuous sensory inputs and intrinsic variables with overlapping responses. It is characteristic for the underlying recurrent connectivity in the cortex that neurons with similar tuning predominantly excite each other. The reason for such an architecture is not clear. Using an analytically tractable model, we show that it can naturally arise from a cooperative coding scheme. In this scheme neurons with similar responses specifically support each other by sharing their computations to obtain the desired population code. This sharing allows each neuron to effectively respond to a broad variety of inputs, while only receiving few feedforward and recurrent connections. Few strong, specific recurrent connections then replace many feedforward and less specific recurrent connections, such that the resulting connectivity optimizes the number of required synapses. This suggests that the number of required synapses may be a crucial constraining factor in biological neural networks. Synaptic savings increase with the dimensionality of the encoded variables. We find a trade-off between saving synapses and response speed. The response speed improves by orders of magnitude when utilizing the window of opportunity between excitatory and delayed inhibitory currents that arises if, as found in experiments, spike frequency adaptation is present or strong recurrent excitation is balanced by strong, shortly-lagged inhibition. Author summaryNeurons represent continuous sensory or intrinsic variables in their joint activity, with rather broad and overlapping individual response profiles. In particular there are often many neurons with highly similar tuning. In the cortex, these neurons predominantly excite each other. We provide a new explanation for this type of recurrent excitation, showing that it can arise in a novel cooperative coding scheme that minimizes the number of required synapses. This suggests the number of required synapses as a crucial constraining factor in biological neural networks. In our cooperative coding scheme, neurons use few strong and specific excitatory connections to share their computations with those neurons that also need it. This way, neurons can generate a large part of their response by leveraging inputs from neurons with similar responses. This allows to replace many feedforward and less specific recurrent connections by few specific recurrent connections. We find a trade-off between saving synapses and response speed. Theoretical estimates and numerical simulations show that specific features of biological single neurons and neural networks can drastically increase the response speed, improving the trade-off.