Towards Machine Theory of Mind with Large Language Model-Augmented Inverse Planning

Eric Xue; Rebekah A. Gelp\'i; William A. Cunningham

REVIEW 4 major objections 6 minor 2 cited by

Towards Machine Theory of Mind with Large Language Model-Augmented Inverse Planning

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read LAIP, a hybrid that feeds LLM-generated hypotheses and action likelihoods into a Bayesian inverse-planning loop, produces preference posteriors that closely match a Bayes-optimal model while no LLM-only baseline does.

desk verdict Worthwhile hybrid architecture with real cross-LLM evidence, but the 'optimal' gold standard is under-specified and one update equation is invalid; referee it, but expect revisions. read the letter →

arxiv 2507.03682 v1 pith:5T6H6E2J submitted 2025-07-04 cs.AI cs.LG

Rebekah A. Gelpí , Eric Xue , William A. Cunningham This is my paper

classification cs.AIcs.LG

keywords theoryofmindinverseplanninglargelanguagemodelsBayesianinferencepreferencegoalbelieftrackingsocialcognition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

LAIP is a hybrid for machine theory of mind — the ability to infer another agent's beliefs, desires, and intentions — in which a large language model generates candidate hypotheses about an agent's preferences, the actions the agent might take under each hypothesis, and the likelihood of each action, while Bayes' rule converts those ingredients into a posterior over the agent's mental states. On a restaurants task adapted from classic inverse-planning experiments, the paper shows that LAIP's posterior closely tracks a Bayes-optimal model across seven LLMs of very different sizes (all correlations $r \geq .546$, $p < .001$), while no zero-shot or chain-of-thought baseline produces a posterior significantly correlated with the optimal model, and the ReAct and Reflexion baselines fall far short on the same inference. The improvement is largest for small models such as LLaMA 3-8B and Gemma 2 that normally underperform on theory-of-mind tasks, because computing the posterior with exact arithmetic offloads the step where small models fail. LAIP also scores higher than prior LLM-based methods on the MMToM-QA goal-inference benchmark (67.5% versus 61.7% overall, and 80.4% versus 30.7% on goals that require tracking an updated belief) and recovers the true preferences in an open-ended scenario where the action space is unconstrained. The paper's point is that the LLM supplies the open-ended world knowledge that hand-built Bayesian models lack, while the Bayesian update supplies the normative structure that prompting alone does not.

What carries the argument

The engine is the LAIP loop of Algorithm 1, a per-timestep Bayesian update: the LLM proposes a prior over preference hypotheses, then for each hypothesis $H_i$ it generates a set of candidate actions and the likelihood $P(A_j | H_i)$; after the true action $O$ is observed, the posterior is recomputed as $P(H | O) \propto P(O | A) P(A | H) P(H)$, either by exact arithmetic or by an LLM call. In the open-ended version, $P(O | A)$ is replaced by a softmax of the cosine similarity between the observed action and each generated action, because the observed action need not be among the generated ones. The load-bearing division of labor is that the LLM acts as what the paper calls a theory-and-action sampler in an unbounded hypothesis space, which sidesteps the frame problem — the need to pre-specify every possible mental state by hand — while the explicit Bayesian inversion supplies the normative constraint that prevents the shallow, brittle reasoning of zero-shot prompting.

What would settle it

Re-run Study 2 with the LLM's likelihoods $P(A|H)$ replaced by random permutations of the same numbers — identical values shuffled across hypothesis–action pairs — while keeping hypotheses, priors, and the Bayesian update untouched; if the posterior still correlates with the optimal model, the agreement is carried by the hypothesis set and prior rather than by the likelihoods the LLM is meant to supply. A complementary check is to collect human posterior judgments on the same ten trajectories, since the paper's claim of human-like reasoning is currently inherited from the optimal model's past fit to human data.

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Extended reading notes

Core claim

Stated as the authors would put it to a fair reader: a Bayesian inverse planner does not need a hand-specified hypothesis space if an LLM can generate the hypotheses, imagine the actions an agent holding each hypothesis would take, and judge the likelihood of those actions — and the posterior that results is not merely plausible but nearly identical to what an optimal observer with full knowledge of the environment would infer. In Study 2, where the same ten trajectories and the same hypothesis set were used across every model, the full LAIP model's posterior correlated significantly with the Bayes-optimal model for all seven LLMs (Pearson $r$ from .546 to .960), and this held even for models such as LLaMA 3-8B and Mixtral that show no such alignment when asked directly. No zero-shot or chain-of-thought baseline produced a posterior significantly correlated with the optimal model, and in Study 1 the ReAct and Reflexion baselines assigned only 3.7% and 0.3% posterior mass to the hypothesis that LAIP identified at 48.4%. LAIP's belief updates also moved most sharply between timesteps 2 and 3, exactly where the agent's action is most diagnostic of its preferences. On the MMToM-QA benchmark the same architecture beat a fine-tuned inverse planner (BIP-ALM), and in an unconstrained scenario it correctly treated situationally forced choices as non-diagnostic, assigning 37.1% of its posterior to the two true preferences versus 4.7% for the zero-shot baseline. The claim, in one line, is that hybridizing LLM generation with Bayesian inversion inherits the strengths of each component and the weaknesses of neither.

Load-bearing premise

The whole result rests on one premise: the numbers a language model assigns to an agent's possible actions under each preference hypothesis, written $P(A|H)$, are honest estimates of how a rational agent holding that preference would actually behave; if they are biased or miscalibrated, Bayes' rule faithfully converts them into a distorted picture of the agent's mind, and the apparent agreement with the optimal model could be an artifact of shared assumptions rather than genuine inverse planning.

Editorial extensions

If this is right

Bayesian inverse planning can be exported to environments with too many hypotheses and actions to enumerate by hand: the LLM supplies the space and the arithmetic does the updating, so the model's reach is bounded by the LLM's world knowledge rather than by a researcher's hand-written state list.
Smaller LLMs become usable for social inference: with the posterior computed mathematically, LLaMA 3-8B, Gemma 2, and Mixtral all reach posteriors significantly correlated with the optimal model, a capability none of them shows when answering directly.
Tasks that require tracking what an agent knows are where the Bayesian scaffold matters most: LAIP's largest margin on MMToM-QA is on goal-given-updated-belief questions (80.4% versus 30.7% for the best prior text model), where an LLM must integrate belief changes that zero-shot systems ignore.
Open-ended social inference becomes tractable: the unconstrained-action study shows the model can condition on free-form action descriptions and avoid over-inferring preferences from choices that were forced by the situation.
The divergence analysis shows the model's belief dynamics are interpretable: the posterior shifts most (highest Hellinger distance and Jensen–Shannon divergence) between timesteps 2 and 3, exactly where a rational observer would gain the most information about the agent's preferences.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct human benchmark is the natural next test: the paper's bridge from LAIP to human reasoning runs through the optimal model's known fit to human data, so collecting human posterior judgments on the same ten trajectories would validate the likelihoods the LLM supplies rather than the optimal model's own assumptions.
Nothing in Algorithm 1 is food-specific, so the same loop should transfer to beliefs, intentions, and epistemic states; the large gain on MMToM-QA's belief-updated goals is an early sign of that generality.
A three-way ablation would locate the source of the gain: holding the hypothesis set fixed and swapping in the optimal model's analytic likelihoods, the LLM's likelihoods, and uniform likelihoods in turn would decompose how much of the correlation is carried by each ingredient — a decomposition the paper does not report.
A particle-filter variant is the cheap-compute version of the same promise: if hypotheses were proposed, weighted, and pruned on the fly rather than held at a fixed twenty, LAIP's cost would scale with the number of live hypotheses, directly addressing the computational burden the authors flag as a limitation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a worthwhile paper that deserves referee time, but the headlining claim ('closely matches optimal results') is only as strong as the arbitrarily parameterized optimal model, and one of the update equations is not a valid Bayesian update.

The core architecture is real. Using an LLM to generate both hypotheses and action likelihoods, then computing the posterior externally with Bayes' rule, is a clean extension of BIP-ALM and Zhi-Xuan et al. The cross-LLM results, particularly that smaller models improve more under LAIP-Full, are a useful empirical contribution. The Study 2 correlations are consistent across all 7 LLMs and no baseline matches them; that is genuine evidence the hybrid helps.

The soft spots are specific and fixable. First, the 'optimal model' fixes ε=0.01 and P(open)=0.95 with no sensitivity analysis. The stress-test concern lands: since the abstract's central claim is that LAIP closely matches optimal results, the paper needs to either justify those numbers or show the correlations hold across a range of plausible values. Second, the unconstrained study's update equation P(H|O)=softmax(S(O,A_i))P(A|H)P(H) is dimensionally inconsistent; the softmax of cosine similarities is not a likelihood for the observation. That section is a proof-of-concept, and the equation should be fixed or reframed. Third, the MMToM-QA section gives the reader too little: no prompt details, no run counts, no error bars, and the comparison to BIP-ALM is a single accuracy number per cell. The claimed advantage on goal-updated tasks is plausible but not yet demonstrated. The missing appendix references also suggest the manuscript is not fully assembled.

On the circularity worry: the hypothesis set is LLM-generated and the optimal model's 'correct' hypotheses come from that same set, so shared priors could inflate the correlations. I don't think this is fatal—the baselines receive the same hypotheses and fail—but a calibration analysis of the LLM likelihoods would make the case stronger.

Who this is for: people building socially aware agents or working on hybrid LLM+Bayesian models. It deserves a serious referee. My recommendation: engage with it and ask for sensitivity analyses, a corrected update equation, and full experimental details on MMToM-QA before the claims about open-ended prediction and MMToM-QA superiority are accepted.

Referee Report

4 major / 6 minor

Summary. The paper proposes LAIP, a hybrid architecture that uses LLMs to generate candidate hypotheses about an agent's preferences and to produce action-likelihood estimates, which are then combined with Bayesian inverse planning to compute posterior distributions over those hypotheses. The authors evaluate LAIP in three settings: a controlled restaurant task with a single trajectory (Study 1), a ten-trajectory comparison against a hand-specified Bayes-optimal model across seven LLMs (Study 2), an open-ended scenario using cosine-similarity-based observation likelihoods (Study 3), and the MMToM-QA benchmark. The headline findings are that the full LAIP model produces posterior distributions that correlate significantly with the optimal model for all seven LLMs and that it outperforms LLM-only baselines, with the largest gains for smaller models. The paper also claims that LAIP can predict mental states in open-ended tasks.

Significance. If the central claim holds, this is a valuable contribution to machine Theory of Mind: it offers a practical way to scale Bayesian inverse planning by replacing manually constructed hypothesis spaces with LLM-generated ones, and the Study 2 results are consistent across a diverse set of LLM sizes, including smaller models that benefit most from the decomposition. The algorithmic sketch and the detailed prompts in the appendix are strengths for reproducibility, and the comparison across seven LLMs gives the empirical claim unusual breadth. However, the evaluation gold standard (the 'optimal model') and two of the formal equations need to be pinned down before the results can be taken at face value. The reported correlations and the abstract's claim of 'closely matching optimal results' depend on the mapping between the 20-hypothesis LLM space and the six-hierarchy optimal model, which is not described.

major comments (4)

[Algorithm 1 (Appendix A.1), line 15] The update rule stated as P(H|O) ∝ P(A|O)P(A|H)P(H) is not a proper Bayes update: the factor P(A|O) is not defined, and the correct likelihood of the observation O (the chosen action) is P(O|H), not a product of conditional action probabilities. As written, the equation is dimensionally inconsistent. Please state the precise generative model used for the update, e.g., P(H|O) ∝ P(O|H)P(H), and clarify how P(O|H) is derived from the LLM-generated action likelihoods.
[Section 4.5, unconstrained action spaces] The equation P(H|O) = softmax(S(O,A_i))P(A|H)P(H) cannot be correct as written: the softmax term is a distribution over generated actions and does not depend on H, the product is not normalized over H, and no sum over A_i appears. The reported posterior probabilities (Table 6) therefore cannot be reproduced from this equation. Please specify a proper observation likelihood, e.g., P(O|H) ∝ Σ_i softmax(S(O,A_i)) P(A_i|H), and describe how the observed string O is aligned with the generated action set.
[Section 4.3.1 (Optimal Model) and Tables 2–3] The optimal model is described with two fixed parameters (ε=0.01, P(open)=0.95) but no sensitivity analysis is provided. Since the abstract claims LAIP 'closely matches optimal results' without qualification, please report how the correlations and JSD values in Tables 2–5 vary as these parameters are perturbed over a plausible range. In addition, Figure 6 suggests the optimal model produces posteriors over six preference hierarchies, while the LLM models output 20 hypotheses; the mapping used to compute the correlations in Tables 2–3 is not stated and must be described.
[Section 4.3.2, Correlations] The Pearson and Spearman correlations are computed over all hypotheses and all trajectories pooled together (per the Table 2 caption), which treats 200 probability values that are not independent (they sum to 1 within each trajectory) as independent observations. This likely inflates the significance of the reported p-values. Please report per-trajectory correlations with appropriate error bars, or use a bootstrap/permutation procedure that respects trajectory boundaries.

minor comments (6)

[Section 4.2.2] The text says 'three measures of similarity' but only Hellinger distance and Jensen-Shannon divergence are reported; please correct or add the third measure.
[Appendix A.3] Only the hypothesis-generation prompt is provided; the prompt used to elicit P(A|H) likelihoods is essential for reproducibility and should be included.
[Table 1] MMToM-QA results are reported without any measure of variability or number of runs; please add confidence intervals or repeated runs.
[Section 4.2.1] The text references 'Appendix ??' for LLM-generated prior beliefs; the appendix reference is missing.
[General] There are several typos, e.g., 'occured' (Section 4.2.2), 'm odels' (Related Work), 'the the agent's state' (Section 4.3.1), and 'perceives' (Section 4.5); a careful proofread is needed.
[Section 4.3.2] The definition of 'options that correspond to the options considered most probable by the optimal model' (Figure 4) is informal; please specify exactly which hypotheses count as correct for each trajectory.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: LAIP's posterior is computed by Bayes' rule from LLM-generated likelihoods, and the central comparison to the optimal model is an independent benchmark, not an input to the model.

full rationale

The paper's derivation chain is self-contained and does not reduce to its inputs by construction. LAIP computes posteriors via Bayes' rule using LLM-generated hypotheses, likelihoods, and priors (Algorithm 1), while the Study 2 'optimal model' is an independent analytic Bayesian model with fixed parameters (epsilon = 0.01, P(open) = 0.95) that shares only the hypothesis list, not the likelihood functions or the inference mechanism. No parameter is fitted to the optimal model's outputs or to the human-labeled target hypotheses, so the high correlations in Table 2 are not forced by construction. The MMToM-QA evaluation (Section 4.4) is against an external benchmark and external baselines, so no self-citation chain is load-bearing. The only mild self-reference is that the candidate hypotheses are themselves LLM-generated, which could in principle create shared support between LAIP and the optimal model, but this is a shared hypothesis space rather than an equivalence between the predicted posterior and any fitted input. The arbitrary choice of optimal-model parameters is a correctness and robustness concern, not a circularity concern. Accordingly, no specific circular step can be quoted, and the circularity score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim depends on standard Bayesian inverse planning assumptions and on the untested validity of LLM-generated likelihoods. The hand-set parameters belong mostly to the reference optimal model. No new entities are introduced.

free parameters (4)

Number of hypotheses K=20 = 20
Fixed by the authors for all studies; not fitted to data, but an ad hoc choice that constrains the hypothesis space and could affect results.
Number of candidate actions N=6 = 6
Hand-set in the open-ended Study 4; the choice of action candidates affects the cosine-similarity likelihood computation.
P(open)=0.95 in Optimal Model = 0.95
Hand-set prior for restaurant openness in the reference optimal model; it is an input to the gold-standard comparator, not to LAIP itself.
Epsilon=0.01 in Optimal Model = 0.01
Hand-set noise probability for random actions in the reference optimal model; it affects the benchmark posteriors that LAIP is compared against.

assumptions (4)

domain assumption Theory of mind can be modeled as Bayesian inverse planning, inverting an optimal policy to infer beliefs and desires (Baker et al., 2011).
The entire LAIP framework rests on this cognitive-science premise, invoked in Sections 2 and 3 without independent proof.
domain assumption Agents act approximately rationally, choosing actions that maximize expected utility with some noise.
Used in the likelihood model and in the optimal model's generative assumptions, described in Section 4.3.1.
ad hoc to paper LLM-generated likelihoods P(A|H) are valid probability estimates of a rational agent's actions under each hypothesis.
Central to Algorithm 1 lines 9-12; no calibration or validity check is provided, and the unconstrained study shows this premise can be violated by an incoherent update formula.
ad hoc to paper Cosine-similarity softmax values can serve as observation likelihoods in open-ended scenarios.
Equation in Section 4.5: P(H|O) = softmax(S(O,A_i))P(A|H)P(H) is dimensionally inconsistent and not a proper likelihood; this assumption is not defended.

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Cite this review

Pith. "Pith review of Towards Machine Theory of Mind with Large Language Model-Augmented Inverse Planning." pith.science (2026). https://pith.science/paper/5T6H6E2J

@misc{pith2026250703682,
  author       = {Pith},
  title        = {Pith review of: Towards Machine Theory of Mind with Large Language Model-Augmented Inverse Planning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5T6H6E2J}},
  note         = {Machine review of arXiv:2507.03682}
}

read the original abstract

We propose a hybrid approach to machine Theory of Mind (ToM) that uses large language models (LLMs) as a mechanism for generating hypotheses and likelihood functions with a Bayesian inverse planning model that computes posterior probabilities for an agent's likely mental states given its actions. Bayesian inverse planning models can accurately predict human reasoning on a variety of ToM tasks, but these models are constrained in their ability to scale these predictions to scenarios with a large number of possible hypotheses and actions. Conversely, LLM-based approaches have recently demonstrated promise in solving ToM benchmarks, but can exhibit brittleness and failures on reasoning tasks even when they pass otherwise structurally identical versions. By combining these two methods, this approach leverages the strengths of each component, closely matching optimal results on a task inspired by prior inverse planning models and improving performance relative to models that utilize LLMs alone or with chain-of-thought prompting, even with smaller LLMs that typically perform poorly on ToM tasks. We also exhibit the model's potential to predict mental states on open-ended tasks, offering a promising direction for future development of ToM models and the creation of socially intelligent generative agents.

Figures

Figures reproduced from arXiv: 2507.03682 by the authors.

**Figure 2.** Schematic of task design and observed trajectory for Study 1. The observed actor moves [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Posterior probabilities for hypotheses after the final timestep when the Japanese restaurant is open or closed. Darker colours indicate higher posterior probability of hypotheses (columns). When the Japanese restaurant is closed (odd rows), only the LAIP model infers that the agent’s actions are most consistent with a preference for the Japanese restaurant, followed by the Chinese restaurant, followed by the Mexi… view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Empirical results for LLMs using each model configuration, averaged across Trajectories [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Posterior probabilities for hypotheses for the LAIP (left) and zeroshot baseline (right) models after the final timestep. Darker colours indicate higher posterior probability of hypotheses (columns). LAIP, but not the baseline model, places the highest probabilit…

**Figure 6.** Figure 6: Ideal model results for Trajectories 1 through 10. [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Study 1: Results with generated prior beliefs. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

**Figure 8.** Figure 8: Hypothesis generation prompt for Study 1. [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]

**Figure 9.** Figure 9: Correlations between optimal model and LLMs, by study and condition. [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]

**Figure 10.** Figure 10: Situation prompt for Unconstrained Action Space scenario [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

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Forward citations

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