World
A realistic ReplicaCAD apartment is rendered in Habitat-Sim. The agent receives egocentric observations and travels between collision-free inspection viewpoints on the navigation mesh.
Embodied AI · Active inference · World models
Find the mug.
An embodied agent searches a realistic home by maintaining beliefs about where a mug is likely to be, choosing informative places to inspect, and revising its plan when the evidence contradicts its expectations.
4
semantic hypotheses
32 s
continuous embodied search
Explicit
belief and policy readout
The demonstration
Belief-guided search in a realistic 3D home
The agent begins with a semantic prior, searches the most useful locations, treats absence as evidence, and moves continuously through the apartment until the cup is found.
The scientific idea
A world model that can expose its reasoning
The central object is not a fixed action policy. It is a structured belief about hidden states of the world, together with a model of what each possible action is expected to reveal.
Belief
The hidden state is the mug location. The agent maintains a categorical posterior over four semantic sites and updates it whenever a location is inspected.
Action
Each candidate inspection is scored by travel distance, current probability of success and expected information gain. The lowest-scoring policy is selected.
1
Start with a semantic prior
→
Mugs are usually more likely in kitchens and dining areas.
2
Evaluate search policies
→
Which inspection is useful, informative and reachable?
3
Act and observe
→
The agent moves to a viewpoint and gathers visual evidence.
4
Revise and replan
Negative evidence changes the posterior and the next action.
Accessible maths
The complete demo in three ideas
The implementation uses deliberately transparent equations. Each term has a visible role in the behaviour shown in the video.
Update beliefs with evidence
\[
q_{t+1}(L_j)
=
\frac{p(o_{t+1}\mid L_j)\,q_t(L_j)}
{\sum_k p(o_{t+1}\mid L_k)\,q_t(L_k)}
\]
\(L_j\) is a possible mug location. When an inspected site is empty, its likelihood is reduced to 0.05 while the alternatives retain likelihood 1. The probability mass therefore moves elsewhere rather than simply disappearing.
Value information
\[
\mathrm{IG}_i
=
H[q_t(L)]
-
\mathbb{E}_{o\mid \pi_i}
\left[H\!\left(q_{t+1}(L\mid o,\pi_i)\right)\right]
\]
Entropy \(H[q]=-\sum_j q(L_j)\log q(L_j)\) measures uncertainty. An inspection is informative when it is expected to make the posterior sharper, whether the mug is found or ruled out.
Select the next inspection
\[
G_i
=
0.20\,d_i
-
3.00\,q_t(L_i)
-
1.50\,\mathrm{IG}_i
\]
\(d_i\) is the navigation distance to inspection site \(i\). The second term favours locations where the mug is currently likely. The third favours actions that reduce uncertainty. Lower \(G_i\) is preferred.
In plain language:
go somewhere plausible and informative, while accounting for the effort needed
to get there.
How this relates to expected free energy
In the broader active inference formulation, policies are evaluated using expected free energy:
\[
G(\pi)
\approx
\underbrace{\mathbb{E}[-\log p(o\mid C)]}_{\text{goal alignment}}
+
\underbrace{\mathbb{E}[H(p(o\mid s))]}_{\text{ambiguity}}
-
\underbrace{I(s;o\mid\pi)}_{\text{information gain}}
\]
The house-search demo uses a compact, interpretable approximation at the semantic planning level. This keeps every component visible in the readout rather than hiding the decision inside a learned policy network.
Why it matters
Negative evidence becomes part of intelligent behaviour
Many systems can act when the target is visible. A more demanding problem is deciding what to look for, where to look next, and how to recover when the first explanation is wrong.
Beliefs, uncertainty and candidate actions remain visible throughout.
The policy changes online as evidence changes the posterior.
Knowledge about rooms, objects and likely locations guides efficient search.
Actions take time and must respect spatial constraints in a physical scene.
Current scope
A controlled proof of concept, with a clear route forward
This demonstration is designed to make the inference loop legible. It does not claim general household autonomy.
Hand-specified semantic prior
The initial probabilities encode ordinary knowledge about where mugs tend to be found.
Idealised visual detection
A semantic simulator channel confirms whether the cup is visible from the chosen viewpoint.
Hierarchical control
Active inference selects semantic destinations while Habitat handles local navigation.
Learned vision and uncertain detection
Replace the idealised detector with a vision model that returns graded, fallible evidence.
Unseen homes and richer hypotheses
Test transfer across layouts, object categories and learned semantic relationships.
Manipulation and lower-level inference
Extend the hierarchy from search decisions to grasping, locomotion and continuous control.
Read the paper
Active Inference World Models: From Embodied Control to General-Purpose Adaptive Intelligence
The preprint develops the wider argument for world models grounded in active inference, linking embodied control, semantic priors, adaptive decision-making and general-purpose intelligence.
Shaw, A. D. & Berndt, L. C. S. (2026). Active Inference World Models: From Embodied Control to General-Purpose Adaptive Intelligence. Zenodo.