What Type of Inference is Active Inference?

arXiv:2606.04935 · cs.AI · Submitted 2026-06-03 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: We're looking at the paper: "What Type of Inference is Active Inference?".

Jane: Here's the gist of the paper. The gist The VFE of an augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent and yielding a full variational characterization of EFE-based planning How it works 1.

Tom: The paper reformulates Active Inference by showing that the VFE of an augmented model can be written as the VFE of the predictive model plus explicit entropy-correction terms, which makes the EFE contribution transparent This decomposition is achieved by combining two entropy corrections: a planning correction and epistemic corrections 2.

Jane: Proper EFE-based planning requires combining two entropy corrections: the planning correction of Lázaro-Gredilla et al.

2024: , which turns the expected-utility variational objective into policy optimization, and the epistemic corrections of Nuijten et al.

Title and authors: Tom: We’re now looking at the beginning of "What Type of Inference is Active Inference?" and the authors are Wouter W. L. Nuijten, Mykola Lukashchuk, and Thijs van de Laar with Bert de Vries as supervisor.

Jane: So, what's the big takeaway from just looking at those names and that title? What’s the actual core idea they are pushing?

Lu: The title suggests they are investigating the fundamental nature of active inference itself, asking what kind of inference we are really performing when we use expected free energy.

Tom: They immediately point out that recent work showed EFE minimization can be written as Variational Free Energy minimization on a generative model augmented with epistemic priors.

Jane: That sounds like they are trying to bridge the gap between the theoretical goal of active inference and the practical implementation using generative models and uncertainty about the model itself.

Meng: If you’re thinking about running this on production systems, I need to know if this framework is still tractable when we add all these explicit entropy correction terms.

Lalam: The paper establishes that the VFE of an augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent.

Tom: That transparency is key because it lets you isolate exactly what part of the planning process is handling uncertainty versus just pure prediction.

Jane: So, they are essentially showing that we can separate how much of our objective is about predicting the next step versus how much is about reducing our ignorance about the model parameters.

Lu: They then prove that proper EFE-based planning requires combining these epistemic corrections with a planning correction that turns marginal inference into policy optimization, yielding a full variational characterization of EFE-based planning.

Tom: That's the core finding: you need both the entropy corrections and the specific planning correction to get proper EFE-based planning.

Jane: It clarifies exactly which corrections are needed for cross-entropy planning versus full expected free energy based planning.

The paper's summary: Tom: Now let's look at the actual summary of "What Type of Inference is Active Inference?" and what it summarizes about the process.

Jane: They summarize that this work shows how to write the VFE as a predictive model's VFE plus those entropy correction terms we just talked about.

Lu: Specifically, they show that proper EFE-based planning requires combining those epistemic corrections with a planning correction that turns marginal inference into policy optimization.

Meng: So, the summary boils down to this: to do EFE-based planning right, you have to combine two specific types of corrections into your objective function.

Lalam: They give us the full EFE-based planning objective expression, which is given by min q Fpˆq + X T t=one 2H

q(ytxt, θ): − H

q(xtxt−one ut): − H

q(ytxt): <ref:2606.04935#pg1>.

Tom: That formula is the meat of it. It’s a combination of the planning correction and the EFE correction derived from Theorem one <ref:2606.04935#pg1>.

Jane: It looks like they’ve put everything into one equation that defines the objective for what they call EFE-based planning.

Lu: They derive this objective by adding the planning correction of Lázaro-Gredilla et al. two thousand twenty-four to the marginal-EFE corrections from Theorem one <ref:2606.04935#pg2>.

Tom: So, it’s not just a theoretical idea; they actually derived this combined objective by combining known components into a new structure.

Jane: It’s about showing that this structure is what properly captures the goal-directed and information-seeking behaviors of active inference together.

The paper's improvements: Tom: Let’s talk about the specific improvements they suggest, which are really focused on how to make this work better than just using marginal VFE minimization.

Jane: They show how epistemic priors identify the corrections that transform marginal VFE minimization into EFE minimization through three different lemmas.

Lu: Lemma four shows that the state epistemic prior contributes minus H

q(xtxt−one ut): to the objective function.

Meng: That means they are explicitly saying that uncertainty about the current state transition is a cost we need to account for in our objective.

Lalam: And Lemma five shows that the action epistemic prior contributes plus H

q(ytxt, θ): minus H

q(ytxt): to the objective.

Tom: So, they are using these specific entropy corrections to produce EFE minimization inside a marginal variational objective.

Jane: They also have Lemma six showing that the observation epistemic prior contributes plus H

q(ytxt, θ): minus H

q(ytxt): to the objective as well.

Lu: These three lemmas collectively produce EFE minimization inside a marginal variational objective, which is a significant step because it shows how to move from simple marginal VFE minimization toward true EFE minimization.

Meng: If we can achieve this, it means we are using uncertainty about what the environment will do and what the observations will tell us in a way that actually drives goal-directed behavior.

Conclusion: Tom: So to wrap up, the conclusion summarizes how this entire framework works and what it implies for planning systems.

Jane: It clarifies that the full EFE-based planning objective is formulated as a standard Bethe free energy over the modified factor graph, solved using message passing with channel reparameterization.

Lu: This leads to a construction where the four normalized conditional distributions are introduced as channels: rux(u1xzero), rxxu(xone times zero u1), ryxθ(y1xone θ), and ryx(y1xt).

Meng: So the system is jointly optimized over beliefs and these channels, which is a very specific way of doing things.

Lalam: This approach allows the VBP scheme to generalize to arbitrary time horizons by introducing a time-local channel at each time step, avoiding the min-max structure found in AIF by having only a single channel that enters only the dynamics kernel.

Tom: And they note that this VBP scheme continuously interpolates between marginal inference, which is a uniform channel, and full cross-entropy planning, which is the converged channel.

Jane: This interpolation suggests a flexible system where it can switch between simple inference and more complex planning as needed depending on the task.

Lu: They also mention that the opposing signs of the entropy corrections induce a min-max structure in the joint optimization over beliefs and channels, which in practice requires damped channel updates for stable convergence.

Meng: I’m hearing that means we need to be careful with how we update those channels if we want this to actually run reliably without it oscillating wildly.

Lalam: That damping parameter lambda also currently requires manual per-environment adjustment, which is a limitation they admit and restrict their analysis to discrete state spaces where exact factor evaluations are available.

Tom: It’s important to remember that this work provides a principled message-passing formulation of EFE-based planning.

Jane: It gives us a concrete way to build these systems based on known mathematical structures, moving away from ad hoc methods toward something more principled.

Wouter W. L. Nuijten, Mykola Lukashchuk, Thijs van de Laar, Bert de Vries

Department of Electrical Engineering, Eindhoven University of Technology · Lazy Dynamics

cs.AI

Submitted: 2026-06-03

Updated: 2026-07-07

Journal ref: Proc. of the 42nd Conference on Uncertainty in Artificial Intelligence (UAI 2026), PMLR 337:5003-5039

Code: https://github.com/biaslab/U

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 75/100

The gist: The gist The VFE of an augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent and yielding a full

Key concepts

VFE Decomposition: The VFE of an augmented model is broken down into the VFE of the predictive model and explicit entropy-correction terms. This makes the contribution from Expected Free Energy (EFE) transparent, allowing for a complete variational description of EFE-based planning.
Planning Correction: This correction transforms the expected-utility variational objective into policy optimization. It is derived from Lázaro-Gredilla et al. [2024] and focuses on how control decisions should be made based on expected utility.
Epistemic Corrections: These corrections turn marginal VFE minimization into EFE minimization by incorporating epistemic priors. They are derived from Nuijten et al. [2026b] and involve specific terms that modify the objective to account for uncertainty about model parameters.

Terminology

Ablation — 2× in this paper · explained in 1 episode
Active Inference — 2× in this paper · explained in 1 episode
Expected Free Energy — 1× in this paper
Generative Model — 1× in this paper · explained in 2 episodes
Variational Free Energy — 1× in this paper

Summary

The gist The VFE of an augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent and yielding a full variational characterization of EFE-based planning

How it works

The paper reformulates Active Inference by showing that the VFE of an augmented model can be written as the VFE of the predictive model plus explicit entropy-correction terms, which makes the EFE contribution transparent This decomposition is achieved by combining two entropy corrections: a planning correction and epistemic corrections
Proper EFE-based planning requires combining two entropy corrections: the planning correction of Lázaro-Gredilla et al. [2024], which turns the expected-utility variational objective into policy optimization, and the epistemic corrections of Nuijten et al. [2026b], which turn marginal VFE minimization into EFE minimization Together they yield a full variational characterization of EFE-based planning
The full EFE-based planning objective is given by the combination of the planning correction and the EFE correction, which is expressed as min q Fpˆ[q] +X T t=1 2H [q(ytxt, θ)] − H [q(xtxt−1, ut)] − H [q(ytxt)] This objective is derived by adding the planning correction of Lázaro-Gredilla et al. [2024] to the marginal-EFE corrections from Theorem 1

Entropy Corrections for EFE-Based Planning

The paper details how epistemic priors identify the corrections that transform marginal VFE minimization into EFE minimization Specifically, Lemma 4 shows that the state epistemic prior contributes − H [q(xtxt−1, ut)] to the objective Lemma 5 shows that the action epistemic prior contributes + H [q(ytxt, θ)] - H [q(ytxt)] to the objective Lemma 6 shows that the observation epistemic prior contributes H [q(ytxt, θ)] − H [q(ytxt)] to the objective These corrections produce EFE minimization inside a marginal variational objective

Message Passing for EFE-Based Planning

The full EFE-based planning objective is formulated as a standard Bethe free energy over the modified factor graph, which is solved using message passing with channel reparameterization The four normalized conditional distributions are introduced as channels: rux(u1x0), rxxu(x1x0, u1), ryxθ(y1x1, θ), and ryx(y1xt) The resulting objective is a standard Bethe free energy over the modified factor graph, jointly optimized over beliefs and channels

Comparison of Objectives

Table 1 summarizes the progression, showing that the planning correction changes how control is posed (cross-entropy planning), the EFE correction changes what objective is optimized (marginal EFE), and only their combination yields proper EFE-based planning The observation-side corrections separate along the ambiguity/novelty split, as only the joint channelized scheme captures novelty, which is necessary for success in environments like RockSample and Wumpus World

Experimental Validation

Experiments on three grid-world environments show that full EFE-based planning outperforms ablations that omit either the planning correction or the epistemic corrections In Frozen Lake, epistemic actions that change the observation model dominate performance, and in RockSample and Wumpus World, accounting for novelty becomes necessary for high retrieval rates The convergence behavior shows that VBP and AIF-MP converge reliably on Wumpus World at higher damping values

Conclusion

The paper clarifies the variational structure of active inference planning, showing that the combined objective leads directly to a message-passing construction via channel reparameterization The VBP scheme generalizes to arbitrary time horizons by introducing a time-local channel at each time step, and it avoids the min-max structure found in AIF by having a single channel that enters only the dynamics kernel This structure allows the VBP scheme to continuously interpolate between marginal inference (uniform channel) and full cross-entropy planning (converged channel) The paper concludes that the joint channelized scheme captures novelty, which is necessary for success when sensing actions affect only a single observation This work provides a principled message-passing formulation of EFE-based planning The paper also notes that the opposing signs of the entropy corrections induce a min-max structure in the joint optimization over beliefs and channels, which in practice requires damped channel updates for stable convergence This is an open problem in developing convergence theory for the channel-augmented scheme The paper also notes that the damping parameter λ also currently requires manual per-environment adjustment It restricts its analysis to discrete state spaces where exact factor evaluations are available This restriction is important for understanding how the channel reparameterization interacts with further factorization constraints on the variational posterior

Author Contributions

W.W.L. Nuijten and M. Lukashchuk contributed equally to this work, with W.W.L. Nuijten developing the entropy decomposition framework M Lukashchuk derived the message-passing scheme Both authors contributed to writing and experiments T. van de Laar contributed to the conceptualization of the method and supervision B de Vries has a supervisory and editorial role The paper is part of the project ROBUST: Trustworthy AI-based Systems for Sustainable Growth with project number KICH3.LTP.20.006, which is (partly) financed by the Dutch Research Council (NWO), GN Hearing, and the Dutch Ministry of Economic Affairs and Climate Policy (EZK) under the program LTP KIC 2020-2023 The references include work from Attias [Attias, 2003], Bertsekas [Bertsekas, 2012], Levine [Levine, 2018], Friston et al. [Friston et al., 2015], and Lázaro-Gredilla et al. [Lázaro-Gredilla et al., 2024] The paper also cites work from Blei et al. [Blei et al., 2017], Yedidia et al. [Yedidia et al., 2005], and Pearl [Pearl, 1982] The paper also cites work from Kappen et al. [Kappen et al., 2012] and Russell and Norvig [Russell and Norvig, 1995] The paper also cites work from Todorov [Todorov, 2008] and Millidge et al. [Millidge et al., 2021] The paper also cites work from Koudahl et al. [Koudahl et al., 2023] and van de Laar et al. [van de Laar et al., 2024] The paper also cites work from O’Donoghue et al. [O’Donoghue et al.

Improvements for AI systems

Variational Characterization of Expected Free Energy-based Planning: The system can perform full active inference planning by combining two entropy corrections: "the planning correction of Lázaro-Gredilla et al. [2024], which turns the expected-utility variational objective into policy optimization, and the epistemic corrections of Nuijten et al. [2026b], which turn marginal VFE minimization into EFE minimization."
Principled Message Passing Scheme: The system will utilize a principled message-passing family for these entropy-corrected objectives, which involves introducing auxiliary conditional distributions (channels) that resolve the circularity of posterior-dependent epistemic priors, allowing for both belief propagation and full active-inference planning within the same derivation.
Enhanced Exploration in Novelty Scenarios: When facing Novelty-driven sensing environments like RockSample or Wumpus World, the system can perform superior exploration by implementing full EFE-based planning which is shown to be the only method that captures novelty, the expected information gain about model parameters, outperforming methods that treat epistemic priors as literal priors.
Robustness Across Observation Model Changes: In environments like Frozen Lake where sensing actions change the observation model itself, the system can reliably adapt by using epistemic actions that change the observation model and achieving high success rates, such as ~96% success in those scenarios, because it accounts for ambiguity.
Convergence Stability via Channel Damping: The system will maintain stable convergence in complex stochastic environments like Frozen Lake or Wumpus World by applying geometric damping to channels, with the paper showing that VBP is stable at nearly all damping values (60–100%) and that the combination of planning and dynamics corrections yields a min-max structure that is managed by these updates.