Information Field Theory for Collective Behavior

Understanding the emergence of distributed intelligence in animal societies
by using real sensory data, deep learning, and information field theory

Max Planck Institute of Animal Behavior

Department for the Ecology of Animal Societies

Communication and Collective Movement (CoCoMo) Group

The Fundamental Challenge

How do complex patterns arise from simple components?

Lagrangian

Tracks individuals (particles)

No statistical mechanics

Eulerian

Treats group as fluid

Loses individual resolution

The Paradigm Shift

"Treating animal groups not just as moving particles, but as active matter governed by internal state configurations."

The Physics Analogy:

Quantum Physics: Bound electrons are described by quantum numbers, not just coordinates.
This Proposal: Identify "Behavioral State Configurations" that encode future actions.

[cite: 12, 13, 62, 63]

The Foundation: MeerKAT Dataset

graph LR A(Audio) -->|High Res| D{Fusion} B(GPS) -->|Position| D C(Accelerometer) -->|Movement| D D --> E[Animal2Vec Encoder] E --> F[Behavioral Neural Network]

Subject: Free-ranging Meerkats (Suricata suricatta)
Volume: ~10,000 hours of synchronized multi-modal data
Goal: Decode the "Internal Architecture" of social groups

[cite: 16, 93, 94, 97]

Phase 1: The Behavioral NN

Moving from Ethograms ("Sleeping") to Discrete Embeddings.

        # CONCEPTUAL PSEUDO-CODE

        class BehavioralNN(Model):

          def forward(self, audio, gps, acc):

            embedding = Animal2Vec(audio, gps, acc)

            # Quantize to discrete states (akin to quantum states)

            states = DiVeQ_Quantization(embedding)

            return states

Using GPT-style Next-Token Prediction to learn temporal causality.

[cite: 96, 100, 101, 103]

Phase 2: Information Field Theory

Modeling the "Social Hamiltonian" $\hat{H}$

\[ \partial_{t}|\Phi\rangle = \hat{W}|\Phi\rangle \]

Where $|\Phi(t)\rangle$ is the probability vector of the entire society in configuration space.

We solve for the propagator $\hat{U}(t) = \exp(\hat{W}t)$ to find conditional probabilities of state transitions.

[cite: 113, 114, 115, 122]

Detecting Critical States

Using Entropies as Order Parameters

Shannon Entropy

Signals maximal spatial delocalization (Chaos vs Order).

Von Neumann Entropy

Tracks information decay from the initial state.

"Is the group adapting to a critical state to enable rapid switching between individual and collective action?"

[cite: 27, 123, 124, 189]

Phase 3: From Theory to Reality

graph TD A[Phase 1 & 2 Models] --> B[Agentic World Model] B --> C[Simulate Scenarios] C --> D{Hypothesis Testing} D --> E[Field Playback Experiments] E -->|Validation| A

Closing the loop: Testing "Black Box" predictions with real audio playback in the Kalahari.

[cite: 208, 209, 216, 219]

Impact & Conclusion

New Lens: Quantifying "Collective Will" in a mathematical vector space[cite: 17].
Innovation: Bridging Deep Learning (GNNs) with Statistical Physics (Hamiltonians)[cite: 66].
Transferability: A framework for understanding emergent dynamics in animals and humans[cite: 221].