| 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 neural networks 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 active. Unlike the threshold-linear regime, however, we allow the activation function to be differentiable with finitely many discontinuities. 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 spiking network simulations in order to conjecture how our results might be applicable to more realistic neural networks. |
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