| Abstract: |
| A theory in neuroscience proposes that groups of co-active neurons form a basis for neural processing. Following other researchers' work on threshold-linear networks, which are firing rate models where the activation function is a rectifier, we model the collection of all possible ensembles of neurons (i.e., the collection of permitted sets) as a collection of binary strings that indicate which neurons are considered responsive. Unlike the threshold-linear regime, however, we allow the activation function to be piecewise differentiable. We construct the collection of permitted sets by imposing a threshold on the responsiveness of the neuron to input at the steady state. Furthermore, when the synaptic weight matrix is almost rank one, we prove that the collection of permitted sets is a convex code. If time permits, we will present how our framework might be applicable other neuronal network models. |
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