[Paper Review] Finding Continuity and Discontinuity in Fish Schools via Integrated Information Theory

Takayuki Niizato, Kotaro Sakamoto+4 more|arXiv (Cornell University)|Dec 3, 2018

Complex Network Analysis Techniques4 citations

TL;DR

This study applies Integrated Information Theory (IIT 3.0) via PyPhi to analyze collective behavior in real fish schools (Plecoglossus altivelis), revealing that group size induces discontinuous transitions in system-level integration. It finds that leadership emerges only at four or more fish, a shift undetected by mutual information or Boids models, demonstrating Φ as a sensitive measure of intrinsic causal structure in small-scale collective systems.

ABSTRACT

Collective behaviour is known to be the result of diverse dynamics and is sometimes likened to a living system. Although many studies have revealed the dynamics of various collective behaviours, their main focus was on the information process inside the collective, not on the whole system itself. For example, the qualitative difference between two elements and three elements as a system has rarely been investigated. Tononi et al. have proposed Integrated Information Theory (IIT) to measure the degree of consciousness $Φ$. IIT postulates that the amount of information loss caused by certain partitions is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here we applied IIT (in particular, IIT 3.0 using PyPhi) to analyse real fish schools ({\it Plecoglossus altivelis}). Our hypothesis in this study is a very simple one: a living system evolves to raise its $Φ$ value. If we accept this hypothesis, IIT reveals the existence of continuous and discontinuous properties as group size varies. For example, leadership in the fish school emerged for a school size of four or above; but not below three. Furthermore, this transition was not observed by measuring mutual information or in a simple Boids model. This result suggests that integrated information $Φ$ can reveal some inherent properties which cannot be observed using other measures. We also discuss how the fish recognition of the figure-ground relation, that is, what determines the relevant ON and OFF states, may reveal various optimal paths for obtaining the functional evolution of collective behaviour.

Motivation & Objective

• To investigate whether integrated information Φ can detect qualitative changes in collective behavior as group size increases.
• To test the hypothesis that living systems evolve to maximize Φ, implying a link between functional integration and consciousness-like properties.
• To identify system-level transitions (continuity vs. discontinuity) in fish schools that are invisible to traditional measures like mutual information.
• To explore how figure-ground perception (ON/OFF states) may guide optimal evolutionary paths in collective behavior.
• To demonstrate that IIT provides a causal structure analysis beyond pairwise correlations or information transfer metrics.

Proposed method

• Applied IIT 3.0 using the PyPhi library to compute integrated information Φ for real-time trajectories of Plecoglossus altivelis schools.
• Calculated cause and effect repertoires for all possible mechanisms (subsets of individuals) within each group size, using conditional probability distributions over past and future states.
• Defined φ as the minimum of cause and effect irreducibility, with the minimum-information partition (MIP) used to quantify irreducibility of each mechanism.
• Computed system-level Φ as the divergence between the full cause-effect structure (CES) and the CES of the system under the MIP, using Earth Mover’s Distance (EMD) in concept space.
• Evaluated transitions in Φ across group sizes from 2 to 8 fish, comparing results to mutual information and a Boids model.
• Used a 'cut one' approximation to reduce computational cost, evaluating only 2N bipartitions per system.

Experimental results

Research questions

• RQ1 Does integrated information Φ detect discontinuous transitions in collective behavior that are missed by standard information-theoretic measures?
• RQ2 At what group size does leadership emerge in fish schools, and is this transition reflected in Φ?
• RQ3 How does Φ compare to mutual information and Boids model dynamics in capturing emergent group properties?
• RQ4 Can the figure-ground perception of individuals (ON/OFF states) be linked to the optimization of functional integration in collective systems?
• RQ5 Is there a causal structure in fish schools that reflects intrinsic, irreducible integration, as quantified by Φ?

Key findings

• Leadership emerged in fish schools only at group sizes of four or more, a discontinuous transition not observed in smaller groups.
• This transition was not detectable using mutual information or in a standard Boids model, indicating Φ captures unique system-level properties.
• Φ values increased with group size, showing a non-monotonic pattern with a sharp rise at N=4, suggesting a qualitative shift in integration.
• The MIP analysis revealed that the system's causal structure became irreducible at N≥4, indicating a true emergence of integrated information.
• Figure-ground recognition (ON/OFF states) may guide the evolution of optimal collective paths by shaping the causal architecture of the system.
• IIT 3.0 via PyPhi successfully identified intrinsic causal constraints in real animal groups, demonstrating its utility beyond neuroscience applications.