# Information Entropy of Biometric Data in a Recurrent Neural Network with Low Connectivity

## TL;DR

This paper studies how a sparsely connected neural network stores and processes biometric data like retinal maps and fingerprints using information entropy.

## Contribution

The study introduces a novel analysis of information entropy in low-connectivity recurrent neural networks for biometric pattern retrieval.

## Key findings

- Low connectivity and synaptic noise significantly affect information retention in the network.
- Theoretical predictions align well with simulation results for pattern retrieval performance.
- Real biometric data retrieval validates the network's applicability to structured patterns.

## Abstract

In this paper, we explore the storage capacity and maximal information content of a random recurrent neural network characterized by a very low connectivity. A specific set of patterns is embedded into the network according to the Hebb prescription, a fundamental principle in neural learning. We thoroughly examine how various properties of the network, such as its connectivity and the level of synaptic noise, influence its performance and information retention capabilities, which is evaluated through an entropy measure. Our theoretical analyses are complemented by extensive simulations, and the results are validated through comparisons with the retrieval of real biometric patterns, including retinal vessel maps and fingerprints. This comprehensive approach provides deeper insights into the functionality and limitations of finite-connectivity neural networks and their applicability to the retrieval of complex, structured patterns.