Integrating Temporal Information to Spatial Information in a Neural Circuit
This work addresses a fundamental computational task in brain-inspired neural networks, but it is incremental as it builds on existing models with specific theoretical improvements.
The paper tackles the problem of translating temporal information into spatial information in spiking neural networks by defining and solving two coding problems (FCSC and TSC) with networks using O(log T) neurons and terminating in time 1, while proving a lower bound of T neurons for time 0 solutions.
In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times; such spiking neural networks are inspired by networks of neurons and synapses that occur in brains. We consider the problem of translating temporal information into spatial information in such networks, an important task that is carried out by actual brains. Specifically, we define two problems: "First Consecutive Spikes Counting (FCSC)" and "Total Spikes Counting (TSC)", which model spike and rate coding aspects of translating temporal information into spatial information respectively. Assuming an upper bound of $T$ on the length of the temporal input signal, we design two networks that solve these two problems, each using $O(\log T)$ neurons and terminating in time $1$. We also prove that there is no network with less than $T$ neurons that solves either question in time $0$.