A rat faces a T-shaped maze. At the junction, it must choose: go left or go right? One side has cheese 🧀, the other an electric shock ⚡.
But first it can visit a cue location that reveals which side is safe. This simple setup reveals the Coherence-Rupture-Regeneration dynamics of decision-making.
The rat accumulates coherence (builds certainty through observation), experiences rupture (the decision moment), and regenerates (selects action based on memory-weighted integration).
CRR treats each decision as a scale-invariant process: the agent metabolizes its accumulated past into future action at the rupture point δ(now).
The cue location is where coherence accumulates. Before visiting, the rat has low coherence about context — uncertainty about which side is safe.
After visiting the cue, coherence is high: the rat now has integrated, consistent knowledge about its environment.
L represents the local coherence field — how consistent the agent's state is with its environment at each moment.
CRR uses a generative process with explicit temporal dynamics:
How certain the agent is about context. Observation builds coherence; uncertainty depletes it.
Controls how memory is accessed. Low Ω = only recent high-coherence moments. High Ω = broad historical access.
Weights past states by coherence. High coherence moments dominate regeneration when Ω is small.
Past experiences of reward/punishment, weighted by coherence at time of experience.
At each rupture point δ(now), the rat evaluates possible actions via Regeneration Potential (R):
This decomposes into two natural components:
How much visiting a location will increase coherence. The cue has high coherence-building value when uncertainty is high.
Expected outcome weighted by exp(C/Ω). Higher coherence about reward location → stronger pull toward that action.
CRR naturally balances "information seeking" and "reward seeking" through the exp(C/Ω) weighting — both serve coherent regeneration.
Ω (omega) controls boundary flexibility — how the agent accesses its memory during regeneration:
Low Ω: Only highest-coherence memories accessible. Peaked, decisive action selection. The agent acts on its most certain knowledge.
High Ω: Broad memory access. More exploratory, considers diverse possibilities. The agent remains open to alternatives.
Watch the rat's behaviour emerge from CRR dynamics. With low initial coherence, the cue has high coherence-building value → the rat visits it first.
After building coherence at the cue, the memory-weighted preference for the correct side dominates → the rat goes to the cheese.
"Exploration vs exploitation" dissolves in CRR: both are aspects of coherent regeneration. Information-seeking builds coherence; reward-seeking realizes it.
Adjust the sliders to see how coherence weight, preference weight, and Ω affect the rat's choices.
Low coherence → agent seeks information first (coherence attractor dominates).
"At rupture, the agent metabolizes accumulated coherence into future action. The exp(C/Ω) weighting ensures that high-coherence moments dominate regeneration — we act from what we know most clearly."