# Integrating Temporal Information to Spatial Information in a Neural Circuit

## TL;DR

This paper designs efficient neural networks inspired by brain activity that convert temporal spike patterns into spatial information, solving key problems with minimal neurons and proving lower bounds on network size.

## Contribution

It introduces two neural network models for translating temporal to spatial information, achieving optimal size and speed, inspired by biological neural circuits.

## Key findings

- Networks solve FCSC and TSC problems with O(log T) neurons in time 1.
- Proves no smaller network can solve these problems in time 0.
- Establishes lower bounds on network size for these tasks.

## Abstract

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 $0$.