# The integrated information Φ of an integrate and fire network

## TL;DR

This study applies Integrated Information Theory to a simulated neuron network, finding that it can integrate information but is sensitive to noise.

## Contribution

The study provides empirical findings on how integrate-and-fire networks behave under Integrated Information Theory.

## Key findings

- The network can have non-zero Φ values under certain conditions.
- Network complexity does not correlate with Φ value.
- Integrated information increases with the neurons' time constant.

## Abstract

Integrated Information Theory is a theoretical framework proposing that consciousness is a fundamental property of systems capable of integrating information. To bridge the gap between the theoretical concept and the practical use in actual neurobiological systems, we have applied the Integrated Information Theory approach to a simulated network of integrate and fire neurons (IAF). The primary contribution of this study is several empirical findings. Our analysis shows that such a network can possess a non-zero Φ value under certain conditions and parameter settings. Additionally, our research indicates that the complexity of the network’s dynamics doesn’t necessarily correlate with its Φ value. On the other hand, the quantity of integrated information within the network appears to grow with the IAF neurons’ time constant, which reflects their integrative capacity. Furthermore, our examination of the integrate and fire network with internal random fluctuations demonstrates that the integrated information measure, as defined in IIT version 3.0, is not resilient to noise.

In this study, we explored how Integrated Information Theory (IIT), one of the leading theories of consciousness, can be applied to a small network of simulated neurons. Specifically, we used a network of artificial integrate-and-fire neurons that mimic some properties of real ones to test how much information such a network can integrate, which IIT quantifies using a value called Φ. Our findings indicate that under certain conditions, these networks can indeed integrate information and produce non-zero Φ values. However, we also discovered that the network’s complexity doesn’t necessarily correlate with the amount of information it integrates. Instead, the ability of neurons to retain information over time (their time constant) appears to have a more significant impact. Importantly, we also found that the integrated information measure is sensitive to noise—random fluctuations that are always present in real brains. This suggests that the version of IIT used in our study is responsive to the noisy nature of biological systems. Overall, our study presents several empirical findings on testing the IIT framework in a simple neural system and underscores the key limitations of applying this theory to realistic neuronal models.