Can LLM agents refine cognitive models to recover human algorithms?

Refinement, not generation from scratch

The paper treats cognitive algorithm discovery as a program refinement problem rather than a blank-slate generation task. Researchers first write a cognitive model as a probabilistic program: code that specifies how a person's actions depend on the task state, plus latent parameters that must be inferred. That program is handed to a system of LLM agents whose job is bounded. They compare model predictions with observed behavior, propose code-level edits inside constraints the researchers specify, and check that the revised program still preserves the intended structure.

This division of labor is the paper's central design choice. Human expertise supplies the hypothesis and the interpretability of the base model; the LLM agents supply flexible, targeted variation that a researcher might not have anticipated. Revisions then flow into a probabilistic inference module that handles latent-variable inference and data likelihood computation, so every candidate revision is scored by the same statistical standard as the original model. The comparison is therefore between programs judged on fit, not between programs judged on how plausible their code looks.

A puzzle task with several competing strategies

The evaluation uses a problem-solving paradigm designed to expose a variety of cognitive algorithms, with three base strategy families: Color Blocking, Spatial, and Two-Phase Filling. Each family is a different hypothesis about how participants organize the same task. Color Blocking, for instance, predicts that a person completes one color at a time; Two-Phase Filling predicts that a person first infers a valid ordering of colors and then commits to one ordering to finish the board.

The base models were fit to the final correctly completed trial for each participant. Participants who never completed a trial correctly were excluded, leaving 49 trials in the small-complex condition, 51 in small-simple, and 41 in large-simple. Baseline fits were numerically stable, with finite-fit coverage of 95–100% across conditions, but fit varied meaningfully between participants: some were well explained by a base strategy and others were not. That leftover variation is the room the refinement pipeline is meant to exploit.

Most proposed revisions survived an executability audit

The pipeline was run twice for each participant and each of the three base strategy models, producing 846 candidate revised programs. An audit module validated 733 of them (86.6%); the remaining programs were excluded because they stayed non-executable after the allowed repair attempts. This is a concrete measure of how often the agent system produced code that could actually be run and scored, not a measure of whether the revisions were psychologically meaningful.

Audited revisions were then clustered by the semantic similarity of their natural-language revision proposals, and three representative programs closest to each cluster centroid were selected. That yielded 24 prototypical revised models used in the later analyses. The clustering step matters for interpretation: the paper's claims about recurring innovations rest on these clusters, and the cluster descriptions themselves are LLM-generated for interpretation only and were not used in modeling or analysis.

Fit improved for just over half of participants

The headline improvement is computed as a difference in per-step log marginal likelihood: the score of the best-fitting strategy selected over both base and revised programs, minus the score of the best-fitting base strategy alone. For 53.2% (74/139) of participants, adding revised strategies produced a meaningful improvement, meaning the best-explaining model was not in the original base set but in the revised space.

A second, different comparison appears alongside it and should not be conflated with the first. When improvements are evaluated within each strategy family separately, gains appear across all three: 54% for Color Blocking, 76.9% for Spatial, and 80.4% for Two-Phase. These within-family rates include cases where a revised variant improves a base model that was not the participant's overall winner, so they answer a different question than the 53.2% overall figure. The paper's representative case illustrates the qualitative kind of change involved: a participant reasonably fit by base Color Blocking was better fit by a variant that repairs colors damaged by an earlier turn-off event, a behavior the base algorithm does not encode.

Gains persist on held-out data, recovery is partial

To test whether the improvements generalize beyond the data used to build the revisions, the 24 prototypical revised programs were evaluated on a held-out dataset. There, 52.6% (72/137) of trials showed improved fit under a revised program. Because this evaluation uses data not involved in generating or selecting revisions, it addresses the concern that the gains were fitted to the refinement trajectories.

A separate synthetic recovery test probes a harder question: can the pipeline recover a known strategy? Trajectories were generated from the CB damaged 2 strategy and the pipeline was applied to individual trajectories. Of 215 valid revised programs, 111 (51.6%) achieved a higher mean held-out log likelihood across 40 held-out trials than the base Color Blocking program, while 18 (8.4%) recovered at least 75% of the predictive gap between the two models; 104 (48.4%) did not improve on the base model at all. The authors suggest the variability may partly reflect overfitting to idiosyncratic features of the single trajectory used to generate each revision. These are different success criteria — beating the base model versus closing most of the gap — and the paper reports both.

Revisions concentrate on local repair and tie-breaking

Across 462 total revision proposals, the revisions clustered tightly in semantic space: 6 clusters for Color Blocking, 3 for Spatial, and 6 for Two-Phase, with a small subset of clusters accounting for most revisions in each family. The dominant themes were locally grounded behavioral adjustments — damage repair, local corrective actions, and deterministic tie-breaking — and these appeared as the largest cluster or clusters in all three families. They account for roughly 73% of Color Blocking revisions (161/222), 67% of Spatial revisions (8/12), and 79% of Two-Phase revisions (180/228).

The authors describe this concentration as an unanticipated feature of the results. It is worth separating what was measured from what it means: the clustering and the percentages are empirical, while the reading that these innovations capture meaningful behavioral variability in this task is the authors' interpretation. The paper's own limitations section goes further, noting that improved data likelihood alone is an insufficient indicator of meaningful innovation, which here was assessed only heuristically.

One paradigm, one iteration, one LLM

The scope conditions are narrow and stated plainly. The analysis covers a single problem-solving paradigm, uses just one iteration of the propose-revise loop, and relies on a single underlying LLM. The authors frame this as a deliberate narrow-and-deep choice and say it is important to test whether other algorithmically structured settings reveal further insight. The synthetic recovery result also shows that trajectory-level refinement can overfit a single participant's or trial's idiosyncrasies rather than recovering the underlying strategy.

The limitation the authors call perhaps most important is overfitting to individual participants, trials, or tasks, with effective partial pooling and program compression across contexts named as a clear priority for future work. A second open issue is that no current approach, including this one, systematically relates discovered programs to broader theoretical frameworks beyond lower-level procedural constraints. Both limits qualify how far the fit improvements should be read as evidence about human cognition rather than about model flexibility.

The useful signal is the recurring revision, not the raw gain

The most decision-relevant result here is not that fit improved for a majority of participants; it is that the improvements concentrated into a small set of recurring, interpretable modifications, dominated by damage repair and local corrective behavior, and that these recurred across all three strategy families. That pattern is what distinguishes this pipeline from unconstrained model generation: the revisions stayed executable, stayed within researcher-specified structure, and still landed on a compact set of behavioral innovations rather than scattering across arbitrary code changes.

The practical threshold the paper supports is therefore a split. When a revised program beats the base model and belongs to a dominant, recurring cluster, it is a candidate substantive hypothesis about how participants deviate from the idealized algorithm. When a revision wins only on the refinement data, or appears as a one-off in the synthetic recovery test where only 8.4% of programs closed at least 75% of the predictive gap, the gain is better read as flexibility than as recovered cognition. The paper's own priority for future work — pooling and compression across participants and contexts — follows directly from that distinction.

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