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ANATOMY OF INFERENCE STUDIO

A detailed teaching sim for the anatomy-of-inference picture: habits, planning, goals, prediction, action, and the bridge from categorical policy messages to continuous predictive-coding control. It keeps the roles of the math faithful while using a compact editable teaching-world so every quantity stays visible. You can inspect policy posteriors, expected free energy, descending predictions, ascending prediction errors, hierarchical continuous-state updates, and action that only changes sensory input.
Standalone HTML
Inference Atlas
Policies, Habits, Goals
Continuous Control
Categorical to Continuous Bridge
Guided Lessons

Scenario Bay

Each scenario is a playable teaching-world. Start simple, then layer in habits, goal-sensitive policies, and the continuous action loop.

Global Controls

lr mu
lr u
lr pi
sensory Py
base y
act gain

Policy / Goal / Habit Lab

Edit policy proposals. Habits bias policy selection. Goals shape preference mismatch. Ambiguity adds an expected-information cost.
dopa gamma
goal chi

Continuous-State Builder

Each cortical region has a small generalized-coordinate predictive-coding stack. Higher regions send predictions downward; lower regions send errors upward.

Session Log

Total F
0.000
target pending
Expected G
0.000
policy avg
Best π
0.000
—
Action u
0.000
continuous output
Sensory ey
0.000
mismatch
Shape
2×2
regions × orders
GoalSee habits, goals, planning, prediction and action behave as one inferential system.
WatchTotal F falls with belief steps; best π shifts when you change habit/goal sliders.
First moveClick Belief step, then Policy step, then Action step. Or use Run full cycle.

Status Deck

Total F
0.000
Sensory
0.000
half Py ey squared
Dynamics
0.000
sum half Px ex squared
Hierarchy
0.000
sum half Pv ev squared
Expected G
0.000
policy average
Best pi
0.000
policy posterior
Action u
0.000
continuous output

Inference Atlas

Policies, Habits, Goals

Continuous Control

Categorical to Continuous Bridge

Message streamTeaching role here
HabitsPrior bias over policies.
GoalsPreference structure contributing to expected free energy.
PlanningPosterior over policies formed from softmax(-gamma G).
PredictionSelected categorical policy sends a descending continuous target.
ActionContinuous control reduces sensory prediction error.

Guided Lessons

1. Habits vs goal-sensitive control

Policy selection is influenced by both habit bias and expected free energy. A strong habit can dominate unless goal mismatch or ambiguity is costly enough.

2. Planning

Each policy proposes a control tendency and predicts a likely outcome. The posterior over policies weighs these proposals.

3. Prediction

The selected categorical outcome is translated into a continuous target or descending prediction for the lower predictive-coding machinery.

4. Action

Action does not directly change high-level beliefs. It changes sensory data, which then alters sensory prediction error.

5. Continuous predictive coding

Within a region, generalized orders are linked by D. Between regions, hidden causes connect the hierarchy.

6. Figure 5.5 theme

The point is not separate disconnected circuits. The point is a single inferential system spanning habits, policy inference, cortical predictions, and action.

Layered Equation Panel

Beat Script

Pick a learning path

You can switch any time from the top bar. The math on the canvas is identical across paths.