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REVIEW 4 major objections 5 minor 35 references

Belief Attribution as Mental Explanation: The Role of Accuracy, Informativity, and Causality

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read People attribute beliefs that causally explain actions, not merely true ones.

desk verdict A clean, small-scale experiment showing causal relevance predicts belief attribution best, but the headline correlation is an in-sample fit that needs out-of-sample confirmation. read the letter →

arxiv 2505.19376 v1 pith:RTQA2Z3J submitted 2025-05-26 cs.CL

Lance Ying , Almog Hillel , Ryan Truong , Vikash K. Mansinghka , Joshua B. Tenenbaum , Tan Zhi-Xuan This is my paper
classification cs.CL
keywords theoryofmindbeliefattributioncausalrelevancementalexplanationBayesiantheory-of-mindepistemiclanguageselectionhumanexperiment
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

This paper asks why, among the many beliefs an agent holds, people single out particular ones when explaining behavior. It proposes that belief attributions work as mental explanations, scored by three factors drawn from a probabilistic generative model of rational action: accuracy, informativity, and causal relevance to observed actions. In an experiment where participants ranked natural-language statements about a character searching for keys, the causal-relevance factor alone matched human rankings at $r=0.81$, substantially higher than accuracy ($r=0.36$), informativity ($r=0.43$), or the combination of accuracy and informativity ($r=0.68$). The paper concludes that people preferentially attribute beliefs that are causally necessary and sufficient for the actions they observed, even when those beliefs are neither the most probable nor the most informative available.

What carries the argument

The load-bearing machinery is a language-augmented Bayesian theory-of-mind model: a probabilistic generative model in which an agent with known goals updates beliefs about key locations and chooses actions by Boltzmann-rational planning. Candidate belief statements are represented as epistemic-logic formulas that evaluate to Boolean truth at each time step given the agent's belief state and environment. From this, the model computes three explanatory factors: accuracy as the posterior probability that the statement is true; informativity as the Kullback-Leibler divergence a statement would provide to a listener; and causal relevance as a normality-weighted product of causal necessity (the probability that the observed actions would not have occurred if the belief were intervened to be false at the last moment $t_c$ when beliefs changed) and causal sufficiency (the probability the actions would occur if the belief were intervened true), with atypical causes weighted more heavily.

What would settle it

A direct experiment could pit a highly accurate and informative but causally inert belief against a less accurate but causally necessary belief in scenarios where the two factor rankings diverge. If participants consistently rank the accurate-and-informative statement above the causally relevant one, the central claim would fail; conversely, the paper predicts they should prefer the belief whose falsity would have changed the agent's observed path.

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Extended reading notes

Core claim

The central discovery is that causal relevance, not truth or informativeness, best explains which belief statements people choose to attribute to another agent. The model computes causal relevance from a generative model of belief-driven action by evaluating what would have happened under hypothetical interventions on the belief: a statement scores highly when setting the belief false would have prevented the observed actions and setting it true would have produced them, with unusual causes weighted more heavily. This causal score predicted average human rankings of three candidate belief statements per scenario at $r=0.81$, beating every other single factor and matching the fit of the full three-factor model ($r=0.82$). The paper also shows that accuracy and informativity together do reasonably well ($r=0.68$) and correlate with causal relevance, but qualitative cases reveal divergences where humans side with causal relevance over mere accuracy plus informativity.

Load-bearing premise

The central claim rests on the assumption that people evaluate a belief statement by simulating a hypothetical intervention at the precise moment the agent's beliefs last changed and judging only the subsequent actions, with the agent's action choices treated as Boltzmann-rational noise.

Editorial extensions

If this is right

  • If causal relevance is the dominant factor, then models of belief attribution should prioritize interventions on mental states over posterior beliefs, which suggests new prediction targets for theory-of-mind models.
  • Accuracy and informativity alone are insufficient predictors of human belief attribution, so communicative accounts of explanation need to be supplemented with causal structure rather than replaced by it.
  • The fact that a full three-factor model only marginally improves on causal relevance alone indicates that causal relevance already captures much of what accuracy and informativity contribute in these scenarios.
  • The model's formalism extends naturally to richer natural-language belief statements, including knowledge claims and compositional beliefs, because it computes factors from a grounded epistemic semantics.
  • The findings open a path toward unifying causal and communicative accounts of explanation: a causally relevant belief is often the most useful thing to tell a listener, even without an explicit communicative context.

Reading between the lines

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

  • An unstated implication is that people may attribute beliefs the way scientists select causes: as the minimal intervention that would change the observed outcome, which suggests belief attribution could track counterfactual dependence over whole trajectories, not just the last belief change.
  • If tested across different mental states, the same causal-relevance logic might predict which desires, intentions, or emotions people cite as explanations, since those states also drive action in a generative model.
  • A testable extension is to vary the time at which beliefs change: the model's intervention point is fixed at $t_c$, so scenarios with multiple belief changes or delayed belief updates could distinguish this measure from a full counterfactual simulation account.
  • The residual error cases point toward bounded rationality and ambiguous statement readings as the next limiting factors, so incorporating suboptimal sub-goal selection and multiple readings of disjunctive statements may raise the ceiling beyond $r=0.81$.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper asks which belief statements people prefer to attribute to other agents, and proposes that people select beliefs that function as good mental explanations. Building on the LaBToM framework, the authors define three explanatory factors: accuracy (posterior probability of the belief statement given actions and observations), informativity (KL information gain of the statement relative to a listener), and causal relevance (a combination of causal necessity, causal sufficiency, and normality). The model is evaluated with an online experiment in which 41 participants watch gridworld agents collect keys and rank three belief statements for each of 18 scenarios. The α weights in the scoring function are fitted by grid search to maximize Pearson correlation with averaged human rankings. The paper reports that causal relevance is the single best predictor (r = 0.81), outperforming accuracy plus informativity (r = 0.68), accuracy alone (r = 0.36), and informativity alone (r = 0.43). The central claim is that people gravitate toward causally relevant beliefs when attributing mental states.

Significance. The paper addresses a genuine gap by connecting belief attribution with computational accounts of explanation. A notable strength is that the explanatory factor scores are computed from a generative theory-of-mind model that is independent of the human ranking data; only the α combination weights are fitted. If the causal-relevance advantage survives proper model comparison, the result would be an important contribution to both theory-of-mind research and computational pragmatics. However, the current evidence for the headline model comparison is not yet conclusive: the α weights are fitted to the same data used to compute the reported correlations, no complexity-penalized or out-of-sample comparison is reported, and the scenarios are acknowledged by the authors to only weakly disambiguate the competing accounts. The framework and stimuli are nevertheless a promising foundation for stronger tests.

major comments (4)
  1. [Model Fitting and Table 1] The α coefficients are fit by maximizing Pearson's correlation on the same averaged human rankings used to compute the reported r values. This makes the correlations in Table 1 in-sample fits, and the reported 95% confidence intervals do not account for the parameter fitting. The central claim that Causal (r = 0.81) outperforms Acc+Info (r = 0.68) rests on this comparison, so the authors should report leave-one-scenario-out or leave-one-statement-out cross-validated correlations, or a penalized model-comparison statistic such as AIC, BIC, or WAIC, for each factor combination.
  2. [Table 1] Several fitted coefficients sit at the upper boundary of the grid search range [0,10], most notably αCSucc = 10.00 for the Causal model and αAcc = 10.00 for Acc+Info and other combinations. Boundary solutions suggest the grid may truncate the optimum and that the data do not strongly constrain the parameters. A sensitivity analysis over a wider range, or a continuous optimizer with reported standard errors, is needed before the parameter values can be interpreted as meaningful and before the Causal advantage can be attributed to the model rather than to the chosen grid.
  3. [Results and Discussion] The authors themselves state in the Discussion that the stimuli 'do not strongly disambiguate' causal relevance from the combined accuracy and informativity account, and the Results report a high correlation (r = 0.81) between the Acc+Info and Causal models. With only 18 scenarios and 54 statement-level data points, the 0.13 correlation advantage of Causal over Acc+Info is fragile. The paper should report per-scenario correlations or the proportion of scenarios in which Causal ranks the human-preferred statement more accurately than Acc+Info, along with a leave-one-scenario-out analysis, to show that the aggregate advantage is not driven by a few scenarios.
  4. [Causal Relevance equations] The causal relevance measure intervenes at the most recent time step tc at which the agent's beliefs changed and evaluates only subsequent actions (CNecc and CSuff equations). This is a strong structural assumption about how people perform causal reasoning about beliefs. Because the paper's central claim depends on this specific formalization, the authors should compare at least one alternative (e.g., intervening at the current time, or counterfactual reasoning over the entire trajectory) or provide quantitative evidence that the model rankings are robust to this choice. The Discussion mentions that hypothetical and counterfactual interventions 'do not come apart significantly' in this experiment, but no such comparison is shown.
minor comments (5)
  1. [Experiment Design] The manuscript states that there are 18 scenarios (6 maps × 3 key allocations), but the Experiment Design paragraph says 'Each participant completed all 21 scenarios in a randomized order.' This inconsistency should be corrected.
  2. [Figure 3] The caption contains a typo: 'enivonment' should be 'environment'; in addition, the text at the end of the Qualitative Analysis section refers to 'Acc+sfInfo', which should be 'Acc+Info'.
  3. [Results section] There are minor typos in the text: 'lister' should be 'listener' and 'casual intuitions' in the Discussion should be 'causal intuitions'.
  4. [Probabilistic Attribution of Belief Statements] The Score equation is written as a linear combination of logarithms 'except for Info, which is in log-space.' This wording is confusing because Info is already a KL divergence; please clarify whether the model uses log(Info) in the sum and why this choice was made.
  5. [Model Fitting] The computation of the 95% confidence intervals in Table 1 is not described. Please state whether these are bootstrap intervals, and if so, whether the bootstrap resamples participants, scenarios, or statements, and whether the α parameters were refit during resampling.

Circularity Check

1 steps flagged · score 4.0 of 10

The reported correlations are optimized in-sample fits, so the Causal advantage is a goodness-of-fit claim rather than an independent prediction.

  1. fitted input called prediction [Model Fitting / Results (Correlation Analysis); Table 1]
    "We then fit the coefficients α f for each explanatory factor by maximizing the Pearson’s correlation between the average predicted ranks and the average human-provided ranks for each statement. ... Our results indicate that the causal relevance factor (Causal) was the single factor that best explained human rankings over belief attributions, with a correlation of r = 0.81."

    The model parameters α_f are fitted by maximizing exactly the Pearson correlation that is then reported as evidence for the central claim. With no held-out data, cross-validation, or model-comparison statistic, the r values in Table 1 are optimized in-sample goodness-of-fit values, not predictions. The comparison of Causal (r=0.81) against Acc+Info (r=0.68) is therefore a comparison of fitted correlations on the same 54 averaged statement ranks used as the fitting target. This is reinforced by α_CSucc=10.00 sitting at the upper boundary of the grid-search range.

full rationale

The explanatory factors — accuracy, informativity, and causal relevance — are computed from the generative model via probabilistic, information-theoretic, and interventionist quantities that do not use the human ranking data. That part of the derivation is self-contained. The central circularity concern is that the α weights in the probabilistic attribution model are fitted to the very same averaged human rankings that are later correlated with model rankings, and no cross-validation or held-out evaluation is reported. Thus the reported r values, including the 0.81 vs 0.68 advantage of Causal over Acc+Info, are optimized in-sample fits rather than predictive validations. This does not reduce the central claim to a definitional tautology, because the factor scores themselves are not derived from the human data and the fitted correlations are not guaranteed to order the models in the observed way; but the statistical evidence for the headline claim is weaker than presented. The paper's self-citations to LaBToM and ELoT are used as modeling infrastructure, not as a substitute for evidence, so they are not load-bearing circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The model rests on the LaBToM framework (from the authors' own prior work) and on several behavioral assumptions about rational action and belief update. The fitted linear weights are free parameters tuned to the same data used for evaluation.

free parameters (6)
  • alpha_Acc = 10.00 (in All Factors model)
    Linear weight for accuracy in the overall score, fitted by grid search to maximize correlation with human rankings.
  • alpha_Info = 0.086 (in All Factors model)
    Linear weight for informativity, fitted similarly.
  • alpha_CNecc = 1.216 (in All Factors model)
    Exponent for causal necessity times abnormality, fitted by grid search.
  • alpha_CSucc = 2.432 (in All Factors model)
    Exponent for causal sufficiency times normality, fitted by grid search.
  • 50-50 prior for accuracy = 0.5 (chosen, not fitted here)
    The posterior accuracy uses a 50-50 prior over the truth of phi, chosen to avoid counting effects and improve fit, following prior work by the authors.
  • K = 3 initial belief weights = 3 (chosen)
    The initial belief prior is uniform over distributions of 3 equal weights over initial states, a modeling choice inherited from prior work.
assumptions (5)
  • domain assumption Actions are Boltzmann-rational with respect to the agent's beliefs and goal.
    The action selection model in the generative model section defines P(At | Bt; g) proportional to exp(-Q_g(Bt, At)), assuming a soft-max rational planner.
  • domain assumption Belief update is deterministic and based on consistency with observations.
    The model states the belief is updated deterministically based on consistency with what the agent observes.
  • domain assumption Uniform prior over initial environment states and over K=3 weight distributions.
    The model assumes uniform P(S0) and uniform initial belief prior over distributions of 3 weights, as stated in the Computational Model section.
  • domain assumption Each belief statement has a single valid reading.
    The model evaluates each ELoT formula under one interpretation; the Discussion lists this as a limitation.
  • domain assumption Intervention at the last belief-change time step captures causality.
    Causal necessity and sufficiency are computed by setting phi false or true at tc, the last time the agent's beliefs changed, which is a modeling choice.

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Cite this review

Pith. "Pith review of Belief Attribution as Mental Explanation: The Role of Accuracy, Informativity, and Causality." pith.science (2026). https://pith.science/paper/RTQA2Z3J

@misc{pith2026250519376,
  author       = {Pith},
  title        = {Pith review of: Belief Attribution as Mental Explanation: The Role of Accuracy, Informativity, and Causality},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RTQA2Z3J}},
  note         = {Machine review of arXiv:2505.19376}
}
read the original abstract

A key feature of human theory-of-mind is the ability to attribute beliefs to other agents as mentalistic explanations for their behavior. But given the wide variety of beliefs that agents may hold about the world and the rich language we can use to express them, which specific beliefs are people inclined to attribute to others? In this paper, we investigate the hypothesis that people prefer to attribute beliefs that are good explanations for the behavior they observe. We develop a computational model that quantifies the explanatory strength of a (natural language) statement about an agent's beliefs via three factors: accuracy, informativity, and causal relevance to actions, each of which can be computed from a probabilistic generative model of belief-driven behavior. Using this model, we study the role of each factor in how people selectively attribute beliefs to other agents. We investigate this via an experiment where participants watch an agent collect keys hidden in boxes in order to reach a goal, then rank a set of statements describing the agent's beliefs about the boxes' contents. We find that accuracy and informativity perform reasonably well at predicting these rankings when combined, but that causal relevance is the single factor that best explains participants' responses.

Figures

Figures reproduced from arXiv: 2505.19376 by the authors.

Figure 1
Figure 1. An example scenario in our belief attribution ex￾periment. An animation on the left shows a player in a trea￾sure game, who is trying to find a blue key to unlock the blue door to retrieve the gold chest. On the right, participants are asked to rank three statements about the player’s beliefs based on their likelihood of attributing each statement. belief attribution and its relationship with explanation gener￾ation… view at source ↗
Figure 2
Figure 2. Correlation plots between average human rankings (y-axis) and model rankings (x-axis) for selected combinations of explanatory factors. Among the factors shown, the Causal model best explains human judgments (r = 0.81), with Accuracy + Informativity coming second (r = 0.68) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Qualitative examples showing model and human rankings of sets of 3 belief statements. On the left of each example is the agent’s trajectory in the enivonment. On the right, we plot a continuous rank metric for each statement and model. split-half correlation among human participants was r = 0.94. Our results indicate that the causal relevance factor (Causal) was the single factor that best explained human rankings o… view at source ↗

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