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LIT-615: An Active Inference Approach to Modeling Structure Learning: Concept Learning as an Example Case

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StatusActive — read in full 2026-10-03 (NOTE-485); worth reading as the record's worked example of structure learning in an active-inference agent: "model expansion" by spare hidden-state slots whose flat likelihoods win inference only for a truly novel stimulus, and "model reduction" by applying Bayesian model reduction to the agent's learned prior over states, so that unused slots are reset. It is a proof of concept with eight animals and six features. Reduction recovered the true number of concepts in 45–80% of 100 runs for 4–7 concepts, failed for 2–3, and succeeded every time only when the likelihood mapping was given rather than learned.
Tagsmodel-comparison, cognition, neuroscience, probabilistic-modeling
ExtendsLIT-614 — Bayesian model reduction
Cited as “paper” byNOTE-485 — An Active Inference Approach to Modeling Structure Learning: Concept Learning as an Example Case
Cited as “source” byTHEORY-564 — A bounded generative model can learn its own structure with no machinery beyond inference and learning: spare hidden-state slots with flat likelihoods get filled when an observation fits none of the learned causes, and Bayesian model reduction on the learned prior over states can return unneeded slots, though in a toy concept-learning task it recovers the true number of causes in only 45–80% of runs with four to seven causes, and never with two or three, unless the likelihood is given

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Ryan Smith, Philipp Schwartenbeck, Thomas Parr and Karl J. Friston (2020), Frontiers in Computational Neuroscience 14:41 — DOI-10.3389/fncom.2020.00041

Citation verified. The brief gave Smith, Schwartenbeck, Parr & Friston (2020) in Frontiers in Computational Neuroscience. That is correct in every particular, and it is open access.

Is this the paper the owner meant? The owner’s shorthand was “Smith, Friston et al.” on adding and removing latent factors by evidence. This is the paper with Smith first and Friston last that does both: latent states are added by engaging spare slots and removed by Bayesian model reduction. One qualification: what it adds and removes are levels of a single hidden-state factor (animal concepts), not whole factors, and expansion is done by inference into pre-allocated slots, not by comparing evidence. The nearest paper that grows and prunes structure by evidence more generally is Friston et al., Supervised structure learning (arXiv 2311.10300, 2023). Smith is not among its thirteen authors, so it does not fit “Smith, Friston et al.”. I filed this one and name the other only as a candidate, unread.

Key takeaways

  • Expansion as inference into spare capacity. Give the generative model more hidden-state levels than it needs, with near-flat likelihood columns. A novel feature pattern is better explained by a flat column than by any learned concept, so the agent infers the “empty” state and Dirichlet learning fills it in. Familiar animals never engage the spare slot: across 80 trials of known animals, then 20 of a new one, the slot stayed unused until the new animal appeared.
  • Reduction as Bayesian model reduction on D. After learning, the agent compares its posterior Dirichlet counts over initial states with reduced priors that drop subsets of concepts, using the Dirichlet BMR formula (Fig. 2), and resets the slots the winner drops.
  • It works when few concepts must go, and fails when many must. Over 100 runs per condition the true count won 56/100 for 7 animals, 69 for 6, 80 for 5 and 45 for 4. For 3 animals it won 0 (a 2-concept model won 89), and for 2 animals 0. With the true likelihood mapping given and only D learned, reduction was right in 100% of runs. The authors attribute the failures to imperfect likelihood learning.
  • Basic before subordinate. Starting from “bird vs fish”, the agent reached 93–98% accuracy on eight specific animals in seven of eight runs. Starting from nothing, it averaged 81.21% (SD 6.39). Learning the coarse categories first helped.

Standing in the record

Filed on 2026-10-03 at the owner’s request, in the model-comparison batch. No anthology topic holds it: it is a model of human concept learning and its neural basis, explicitly positioned against cognitive-science models (SUSTAIN, ART, ALCOVE, the rational model), and it carries no instruction for machine-learning practice.

It extends Bayesian model reduction (LIT-614). It cites that paper for post hoc model optimisation, and it applies the paper’s Dirichlet reduction to a new target, the agent’s prior over which hidden states exist, as the “reduction” half of a structure-learning scheme. Its description of BMR as “a generalization of … the use of the Savage Dickie ratio” is the same claim Friston & Penny (LIT-620) derive. Its citation for that, Cornish & Littenberg (2007), is a gravitational-wave data-analysis paper and an odd source for the point. The record’s statement of the ratio is Wagenmakers et al. (LIT-609).

Within the record’s free-energy holdings, it is the first that is about learning the structure of a generative model, not inferring states or planning in a fixed one. Sophisticated Inference (LIT-577) uses the same MDP formalism with given A, B, C and D matrices. The critique Raja et al. (LIT-598) make of such models, that perception and action are presupposed in the generative model handed to the agent, applies here too, in a specific form: the number of slots, the feature dimensions, and the two-time-point trial structure are all given. The paper says so itself (its open questions) and names learning them as future work. For cognition, it offers a formal model of category formation that a reader of that topic would expect to find, at proof-of-concept scale.

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