Source
Smith, Schwartenbeck, Parr and Friston (2020), LIT-615 (Frontiers in Computational Neuroscience), read in full in NOTE-485. The supplementary script was not run.
What was actually shown
Setting. A partially observed MDP with one hidden-state factor of up to eight animals (four birds, four fish), three binary features and a report factor. Dirichlet learning on the likelihood A and, for reduction, on the prior over states D. Learning is unsupervised: reporting is disabled, so there is no feedback. Gaussian noise of variance 0.001 breaks symmetry in flat columns.
Expansion (Figs. 4–5).
- One new concept from a flat column: reporting reached 100% after about 50 exposures to all eight animals, over eight runs.
- Two new concepts: mean accuracy 98.75% (SD 2%) after 2,000 trials.
- Four new birds: six of eight runs reached 92.50–98.8%; two stalled at 72.50% by overgeneralising.
- With seven concepts known and one spare, 80 trials of known animals left the spare unused, and 20 trials of a new one filled it.
Reduction (Table 1, 100 runs each). The winning reduced model kept the true number of concepts in 56 runs of 100 with seven presented, 69 with six, 80 with five and 45 with four. With three presented, a two-concept model won in 89 runs and the true model was second-best in 55; with two presented, five-concept and four-concept models won (57 and 43). As NOTE-485 transcribes the table, the true count never won for two or three (its summary, which said “rarely”, is corrected in its version 2). Wrong winners usually learned a coarser concept, with a small evidence gap. With the likelihood given and only D learned, the correct model won in every run.
What could have come out otherwise. The spare slot could have absorbed known animals, duplicating states. It did not. Reduction could have recovered the true count reliably. It did not when the likelihood was learned.
What this does not say
- That expansion is model comparison. New slots are engaged by state inference and are not scored by evidence. Only removal uses reduction (NOTE-485, Limitations).
- That the structure is learned from scratch. The number of slots and the features are supplied by the modeller; that is the open question the authors name.
- That reduction failures come from likelihood learning. That is inferred from the given-likelihood control, not isolated (C4, weak).
- That it scales. Eight concepts, six binary features, two time points. Other initialisations of the noise changed Table 1’s pattern.
- That the brain has reserve columns or prunes in sleep. Both are predictions with no direct evidence (C6, C7).
Connections
- It applies the reduction identity of THEORY-081, that a model differing only in its prior has its evidence from the full posterior, in its Dirichlet form, to a parent model that was itself learned. THEORY-079 shows where reduction can mislead in singular models under the Laplace approximation; the Dirichlet form here is not that case, but the imperfect recovery is a reminder that the identity is exact only for the posterior it is given.
- The Raja et al. critique (LIT-598) bears on it: what the agent “learns” is bounded by slots and features the modeller supplied.
Note of 2026-10-29: what holds it back
Kept Proposed by the sixteenth status review. NOTE-485 read the paper in full, but the first clause, that a bounded generative model can learn its own structure with no further machinery, generalises past one toy domain of eight concepts and six binary features under one symmetry-breaking initialisation. No larger runs compared with a non-parametric learner are in the record. Narrowing it to the toy runs would make it promotable on one study, but would free nothing while CLAIM-337’s other grounds, THEORY-662 and THEORY-577, are Proposed.