Langer, van Oostrum, and Ay Link Free Energy Minimization to Integrated Information
Do the two most mathematically developed theories of consciousness point in the same direction, or two different ones? Carlotta Langer, Jesse van Oostrum, and Nihat Ay give the question an empirical answer instead of a philosophical one. Their paper, “Integrated Information in the Active Inference Framework” (arXiv:2608.14165, posted 14 August 2026), trains simulated agents using Karl Friston’s active inference framework, then measures how much information those agents’ internal states integrate using tools from Giulio Tononi’s Integrated Information Theory. The result is a correlation, not a proof of identity. Agents that get better at minimizing free energy also tend to integrate more information internally, and the relationship strengthens as the agent’s internal model grows larger.
Two Theories That Usually Do Not Talk to Each Other
Active inference and Integrated Information Theory ask about different things by design. Active inference describes an agent’s relationship to its environment. A generative model predicts sensory observations, perception updates that model to match what actually arrives, and action changes the world so incoming observations match the model’s predictions. The single quantity that ties all of this together is variational free energy, an upper bound on the surprise of the agent’s observations, and the whole framework is a claim about what any self-organizing system must do to keep existing.
IIT looks somewhere else entirely. It ignores the agent’s relationship to its environment and asks only about the causal structure inside the system, whether the “brain” or “controller” contains parts that cannot be reduced to functioning independently. The theory’s central quantity, phi, measures how much a system’s parts are connected to each other in a way that no decomposition into independent pieces reproduces. An agent could in principle have a very good relationship with its environment and a very low phi, or the reverse, and the two theories offer no formal reason either result should be surprising.
It has been suggested before, notably by Friston himself with Wanja Wiese and Allan Hobson in a 2020 Entropy paper, that minimizing free energy might tend to produce higher integrated information as a side effect. Langer, van Oostrum, and Ay’s contribution is to actually run the experiment rather than argue from first principles for the connection.
How the Experiment Is Built
The agents in the study navigate a small racetrack environment using two wheels that can spin fast or slow, with two binary sensors detecting nearby walls. Each agent’s internal generative model, the state variable it uses to track and predict its environment, was split into two, three, or four separate internal nodes, so the researchers could ask whether the size of the internal model changes the relationship between free energy and integration. Agents were trained with the standard active inference learning rules, a Dirichlet-prior Bayesian update over the model’s parameters, for fifty thousand steps, with measurements taken every thousand.
Four different quantities were compared against the resulting free energy. The first, denoted Phi_T, is the measure Langer and Ay introduced in their own 2020 paper, built from a sum of conditional mutual information terms and cheap enough to compute at the scale this experiment needed. The second and third are the phi calculations from IIT 3.0 and IIT 4.0 themselves, far more expensive and correspondingly limited to the smaller agents in the study. The fourth is multiinformation, a general information-theoretic measure of total correlation among a system’s parts that is not specific to any consciousness theory.
What the Correlations Show, and What They Do Not
The clearest result concerns Phi_T and multiinformation. At the largest internal model size tested, four binary nodes, both measures were strongly negatively correlated with free energy using the Spearman correlation, meaning agents with lower free energy tended to have higher integrated information, and that relationship got stronger as the internal model grew from two nodes to four. IIT 3.0’s phi showed a similar trend, weaker overall. IIT 4.0’s phi and its related system-level quantity showed only a weak relationship to the agent’s underlying prediction error, correlations the paper reports as lying roughly between 0 and negative 0.3.
A second finding complicates any simple headline. Being good at minimizing free energy did not reliably make an agent good at the actual task of avoiding walls. The correlation between an agent’s success rate and its free energy was close to zero across all three model sizes, and a small number of agents achieved very low free energy while almost never avoiding a wall. The authors are explicit about the implication in their discussion: there is a relationship between minimizing free energy and integrating information, but not necessarily a relationship between the free energy an agent achieves and the amount of consciousness IIT would assign it, since IIT’s phi values in this experiment tracked something closer to internal structure than to competent behavior.
Where This Sits Among Other Attempts at the Same Bridge
This is not the only recent attempt to connect these two frameworks mathematically. Kearney’s 2026 maximum-caliber analysis derives a different kind of bridge, treating both phi and free energy as projections of the same non-equilibrium statistical mechanics rather than testing the connection empirically on trained agents. The two papers complement each other. Kearney’s argument is that the connection must hold as a matter of physics; Langer, van Oostrum, and Ay show what the connection actually looks like when specific simulated agents are trained and measured, including the parts of the picture, like the weak IIT 4.0 correlations and the null result on task success, that a purely physical argument would not predict.
A more skeptical companion to both is the 2026 adversarial review by Andrew Corcoran and colleagues, which Langer, van Oostrum, and Ay cite directly, examining where IIT and predictive processing frameworks make genuinely diverging predictions rather than assuming compatibility. Read together with this paper, the honest picture is a partial, size-dependent correlation between two specific mathematical quantities in a specific class of small simulated agents, not a demonstration that the theories collapse into one another. IIT’s own recent methodological work, including the Tononi lab’s QStr technique for recovering intrinsic causal structure from extrinsic probes, continues to treat phi as measuring something IIT alone defines, a stance this correlation does not disturb.
Comparison to The Consciousness AI
This project’s architecture is not itself formulated as an active inference agent with an explicit variational free energy term, so no version of this correlation has been tested against it, and none is claimed here. What the paper offers the project is a conceptual caution rather than a tool. If a system’s generative model integrates information as a side effect of getting better at prediction, then any future active-inference-style component the project might build would need its own integrated information check rather than an assumption that good prediction implies rich internal structure. The paper’s own null result on task success versus free energy is the sharper warning: a system minimizing the right mathematical quantity is not automatically a system doing anything a consciousness researcher would call functioning well.
What This Changes and What It Leaves Open
The correlation Langer, van Oostrum, and Ay report is real, size-dependent, and stronger for the cheaper integrated information measure than for IIT’s own official calculations, which is itself informative about which parts of IIT the correlation actually touches. It does not establish that active inference and Integrated Information Theory are describing the same phenomenon, and the paper’s own discussion is careful not to claim that. What it establishes is a testable empirical link between two theories that are usually compared only in prose, and a method, small simulated agents with a controllable internal model size, that other groups can extend to check whether the relationship holds at larger scales or under different task structures. The broader measurement context for the theories on both sides of this bridge is tracked in AI Consciousness in 2026, the state of the field.
Source: Carlotta Langer, Jesse van Oostrum, and Nihat Ay, “Integrated Information in the Active Inference Framework,” arXiv:2608.14165 [cs.IT], posted 14 August 2026. https://arxiv.org/abs/2608.14165, DOI 10.48550/arXiv.2608.14165.
Researchers covered here
- Carlotta LangerMax Planck Institute of Molecular Cell Biology and Genetics, Dresden; Center for Systems Biology DresdenMeasures of integrated information for embodied and active inference agents
- Jesse van OostrumHamburg University of TechnologyMathematical formalization of active inference in discrete time
- Nihat AyHamburg University of Technology; external professor, Santa Fe Institute; honorary professor, Leipzig UniversityInformation geometry and information-theoretic measures of complexity and causal integration
- Karl FristonUniversity College London. Chief Scientist, VERSES AIThe free energy principle and active inference