Unmatched Does Not Mean False: Incomplete Reference Sets Can Reverse Calibration Rankings in Open-Ended Theory-of-Mind Tracking

Long reasoning traces need reliability estimates before final answers are known. We study prefix-conditioned eventual-success estimation, $P(y=1 \mid o_{1:t})$, using prefix-safe observations. Sequential Bayesian Belief Tracking (SBBT) calibrates observation likelihoods and recursively updates a two-state belief, providing a common tracker for scalar scores, text and self-verification markers, hidden clusters, token-pooling probes, and latent-trajectory features. Across generated open-weight traces on MATH-500, GSM8K, AIME 2025, and RIMO-N, probability quality and ranking separate: score-only SBBT often improves Brier, while AUROC gains require structure-aware evidence beyond strong prefix-safe baselines. In the strongest hard math setting, structure-aware observations reach +0.110 AUROC against standard prefix-safe baselines. Under a same-prefix classifier audit, MATH-500 text markers and RIMO-N self-verification signals remain positive. Together, these findings support SBBT as a calibration-aware online inference framework and expose an evidence regime: scalar scores mainly support probability quality, while structure-aware prefix signals support ranking only when strong prefix-safe baselines have not already absorbed the rank evidence.

As large language models are deployed in high-stakes roles such as therapy, education, and personal assistance, their social cognition must be assessed reliably. Current Theory of Mind (ToM) benchmarks report aggregate scores that conflate two distinct competencies: explicit ToM (recognizing what someone believes) and applied ToM (using that belief to predict behavior). Building on this distinction, we investigate the gap and its recoverability using four structurally diverse benchmarks. Aggregate reporting obscures uneven competence: on SimpleToM, Llama-3.1-8B scores 51.5 percent overall while recognizing mental states at 99.4 percent and predicting behavior at only 28.9 percent. To assess recovery, we compare structured prompting, matched in-context learning, and our proposed Belief-State Test-Time Training (BSTTT), which adapts lightweight parameters on answered support questions through action reconstruction. Across Qwen2.5-7B, Llama-3.1-8B, and GPT-oss-20B, recovery depends on the model, task, and intervention. On SimpleToM, reminders combined with BSTTT improve Llama's behavior prediction by 40.8 percentage points; reminders account for most of the overall improvement, with BSTTT adding 1.3 to 5.5 points beyond reminders across models. Contextual examples often outperform weight updates, while BSTTT remains stronger in specific model-benchmark settings. Temporal belief tracking remains difficult despite partial recovery. These findings show that aggregate ToM scores can overstate applied competence while hiding performance recoverable through targeted assistance. We recommend decomposed reporting of explicit and applied accuracy alongside intervention comparisons that establish which failures are recoverable and under what conditions.

Theory of Mind (ToM), the ability to infer others' beliefs, goals, and intentions, is a cornerstone of social intelligence. Multimodal ToM requires inferring an agent's mental state from evidence that is available to that agent, rather than from the complete episode observed by the solver. Existing LLM-based and Bayesian model-based approaches reconstruct global event traces, yet they do not explicitly distinguish objective events from agent-admissible evidence during hypothesis evaluation. Consequently, agent-inaccessible events or semantically misaligned actions and utterances may influence the inferred belief, goal, or social intention, leading to perspective leakage and source or route confusion. We formulate this limitation as an evidence-admissibility problem: evidence should contribute to a mental-state hypothesis only when it is accessible to the relevant agent, preserves its information source, and is diagnostic of the queried mental-state variable. To operationalize this principle, we propose PIP-ToM, an evidence-admissibility interface that constructs agent-specific evidence stores, aligns them with structured mental-state claims, and calibrates model-based hypothesis scores while preserving the underlying Bayesian inference process. PIP-ToM with GPT-4o outperforms existing ToM methods across MuMA-ToM, MMToM-QA, and Hi-ToM, achieving average accuracies of 92.56%, 95.00%, and 95.00%, respectively.