Active Inference — The Learn Arc, Part 43: Session §8.4 — Continuous play

Series: The Learn Arc — 50 posts through the Active Inference workbench.
Previous: Part 42 — Session §8.3: Action on sensors

Hero line. Session 8.4 is the sandbox. Continuous-time agent running Eq 4.19, live sliders on every precision and every derivative order, a world you can perturb at will. The session where intuition finally outruns equations.

Why a play session

Chapter 8 taught three heavy concepts in a row: generalized coordinates, the quadratic F, and action via sensory gradient descent. Each is cleaner in isolation than in combination. Session 8.4 is the antidote — a free-form workbench where you break one knob at a time and watch the whole agent react.

Five beats

1. Every precision is a slider. Sensory, dynamical, state, action, per-order. Push one up and the agent trusts that channel more. Push one to zero and that channel effectively disappears from the gradient.

2. Order truncation is a dial. Start at order 2 (position + velocity). Bump to 4 (add acceleration + jerk). Watch the tracker handle more violent trajectories — until the precision matrix stops being well-conditioned.

3. World dynamics are swappable. Linear drift, harmonic oscillator, double pendulum, noisy random walk. The agent does not know which world it is in; it infers. Mismatched dynamics produce visible, systematic prediction error.

4. Perturbation buttons. One-shot impulse on the world. Slow drift on the sensors. Step change on the preference vector C. Each perturbation isolates exactly one term in Eq 4.19. Good for building a "which knob does what" map.

5. The belief is visible everywhere. Position, velocity, acceleration traces overlaid on the true trajectory. Error bars drawn from the posterior precision. If the belief diverges, you can see exactly when and where.

Why it matters

Most Active Inference papers give you equations and a single canned demo. The framework has too many interacting parts for that to build real intuition. Session 8.4 flips the ratio — one equation, a hundred experiments. By the end of the session most people can predict what a precision change will do before they make it. That is when the math stops being abstract.

Quiz

• What happens to the belief if you drop sensory precision to zero while keeping dynamical precision high?
• Why does increasing the order of generalized coordinates eventually destabilize the tracker?
• Which slider isolates reflex-like behavior from goal-directed behavior?

Run it yourself

mix phx.server
# open http://localhost:4000/learn/session/8/s4_continuous_play

Cookbook recipe: continuous/sandbox — the full playground. Linked labs: free-energy-forge (build your own F terms) and laplace-tower (visualize the generalized-coord tower). Spend twenty minutes moving sliders before you read Chapter 9.

Next

Part 44: Session §9.1 — Fit to data. Chapter 9 opens. We stop asking how an agent acts and start asking how we fit an Active Inference model to real behavior: parameter inference, likelihood on trajectories, and what it takes to call your model "the one that explains the data."

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