← LearnWorkbench ▸·Path:

ACTIVE INFERENCE ATLAS

A standalone educational sim game for the continuous-time predictive-coding and active-inference material in your pages: Laplace approximation, generalized coordinates, hierarchical message passing, cortical microcircuits, policy inference, action, and a simplified neuromodulator/precision lab. It is faithful at the level of the equations’ roles and message flow, while using compact linear teaching-world maps so the math stays visible and editable.
Standalone HTML
Hierarchy Forge
Cortical Circuit Lab
Policy & Basal Ganglia Lab
Neuromodulator Bench
Guided Lessons

Scenario Bay

Load a teaching world, then rewire it. Presets span simple predictive coding, layered cortex, and active policy selection.

Global Controls

Gradient descent

lr μ
lr u
lr π

Sensory stream

base
gain
Πy / ζ

Hierarchy Builder

Add/remove levels and generalized orders, then edit each level’s precision and linear generative maps.

Session Log

Total F
0.000
target pending
Fy
0.000
sensory
Fx
0.000
dynamics
Fv
0.000
hierarchy
Best π
0.000
—
Action u
0.000
y = base + gain·u
GoalTour active inference end-to-end: predictive coding, cortical mapping, policy selection, and neuromodulator precision.
WatchTotal F at the top — the tab canvases are four views of the same state.
First moveIn Hierarchy Forge, click Belief step. Then try the neuromodulator bench.

Machine Status

Total F
0.000
Sensory
0.000
½ Πy εy²
Dynamics
0.000
Σ ½ Πx||εx||²
Hierarchy
0.000
Σ ½ Πv||εv||²
Policy
0.000
E.G. + ambiguity
Action u
0.000
y = base + gain·u

Hierarchy Forge

Cortical Circuit Lab

PopulationTeaching role here
SP (superficial pyramidal)Carries ascending prediction errors.
DP (deep pyramidal)Sends descending predictions and participates in policy/action related outputs in this teaching view.
SS (spiny stellate)Receives input and local sensory drive.
II (inhibitory interneurons)Implements gain control / shaping of local message passing.

Policy & Basal Ganglia Lab

Policies

Posterior over policies is computed as softmax(-G - F_policy_bias), with dopamine-like γ sharpening or flattening the softmax.

Neuromodulator Bench

ModulatorMapped teaching roleSlider effect here
AcetylcholineLikelihood precision ζChanges Πy
NoradrenalineTransition precision ωChanges Πx
DopaminePolicy precision γSharpens policy posterior
SerotoninPreference / interoceptive likelihood χChanges preference strength in G

Guided Lessons

Lesson 1 — Laplace approximation

Around the posterior mode μ, the log density is approximated by a quadratic. A quadratic log density means a Gaussian local approximation. In the sim, this shows up as free energy being a sum of precision-weighted squared prediction errors.

Lesson 2 — Generalized coordinates

D shifts generalized coordinates upward: Dμ[k] = μ[k+1]. Free-energy minima should satisfy “the motion of the mode is the mode of the motion.”

Lesson 3 — Predictive coding hierarchy

Lower levels send errors upward. Higher levels send predictions downward. In the sim, εx links orders within a level, while εv links levels together.

Lesson 4 — Action

Action only changes sensory data directly. That is why the action gradient uses the lowest-level sensory error channel.

Lesson 5 — Policies

A policy posterior can be written as softmax(-G - F). Here G collects preference mismatch and ambiguity cost; dopamine-like precision γ controls sharpness.

Lesson 6 — Neuromodulators

The sim uses a simplified mapping: acetylcholine ↔ likelihood precision, noradrenaline ↔ transition precision, dopamine ↔ policy precision, serotonin ↔ preferences/interoception.

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.