Learning Dynamic Belief Graphs for Theory-of-mind Reasoning
Organizations: Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD, USA · Civil and Coastal Engineering, University of Florida, Gainesville, FL, USA · School of the Environment, Society & Sustainability, University of Utah, Salt Lake City, UT, USA · Department of Psychology, University of Utah, Salt Lake City, UT, USA
Abstract
Theory of Mind (ToM) reasoning with Large Language Models (LLMs) requires inferring how people's implicit, evolving beliefs shape what they seek and how they act under uncertainty -- especially in high-stakes settings such as disaster response, emergency medicine, and human-in-the-loop autonomy. Prior approaches either prompt LLMs directly or use latent-state models that treat beliefs as static and independent, often producing incoherent mental models over time and weak reasoning in dynamic contexts. We introduce a structured cognitive trajectory model for LLM-based ToM that represents mental state as a dynamic belief graph, jointly inferring latent beliefs, learning their time-varying dependencies, and linking belief evolution to information seeking and decisions. Our model contributes (i) a novel projection from textualized probabilistic statements to consistent probabilistic graphical model updates, (ii) an energy-based factor graph representation of belief interdependencies, and (iii) an ELBO-based objective that captures belief accumulation and delayed decisions. Across multiple real-world disaster evacuation datasets, our model significantly improves action prediction and recovers interpretable belief trajectories consistent with human reasoning, providing a principled module for augmenting LLMs with ToM in high-uncertainty environment. https://anonymous.4open.science/r/ICML_submission-6373/
Figures & tables
| Benchmark | Backbone | Metric | Ours ⋆‡ | AutoToM ∘‡ | LLM Inference † | FLARE ∘† | Reconciliation ∘† | |||||
| Inter | Final | Inter | Final | Inter | Final | Inter | Final | Inter | Final | |||
| Wildfire ‡ (Six Beliefs) | Qwen3-8B | Action Acc. | 0.8443 | 0.9157 | 0.3860 | 0.6959 | 0.2796 | 0.6888 | 0.6790 | 0.7760 | 0.2427 | 0.6194 |
| Macro-F1 | 0.7960 | 0.9023 | 0.1825 | 0.5215 | 0.1629 | 0.4079 | 0.4104 | 0.7741 | 0.1522 | 0.6190 | ||
| Qwen3-32B | Action Acc. | 0.9201 | 0.9490 | 0.3833 | 0.7742 | 0.3096 | 0.6888 | 0.6607 | 0.7763 | 0.4568 | 0.7373 | |
| Macro-F1 | 0.9310 | 0.9368 | 0.1390 | 0.5330 | 0.1182 | 0.4079 | 0.4492 | 0.6556 | 0.1571 | 0.6508 | ||
| Qwen3-72B | Action Acc. | 0.8208 | 0.9005 | 0.1499 | 0.7788 | 0.3277 | 0.6888 | 0.4821 | 0.5520 | 0.4741 | 0.8341 | |
| Benchmark | Backbone | Our Model ⋆ ‡ | AutoToM ∘ ‡ | SimToM † | LLM Inference † | ||||
| Belief Acc. | Action Acc. | Belief Acc. | Action Acc. | Belief Acc. | Action Acc. | Belief Acc. | Action Acc. | ||
| SimpleToM ‡ (Single Belief) | DeepSeek-R1 | 0.917 | 0.996 | 0.942 | 0.775 | 0.610 | 0.580 | 0.860 | 0.732 |
| Llama-3-8B | 0.987 | 0.996 | 0.905 | 0.661 | 0.620 | 0.900 | 0.689 | 0.505 | |
| Llama-3-70B | 0.857 | 0.933 | 0.979 | 0.847 | 0.980 | 0.930 | 0.968 | 0.756 | |
| Qwen3-32B | 0.948 | 0.991 | 0.906 | 0.746 | 0.980 | 0.950 | 0.947 | 0.767 | |
| Qwen3-8B | 0.961 | 0.991 | 0.867 | 0.446 | 0.870 | 0.780 | 0.823 | 0.518 | |
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
| First person | Third person | Probabilistic prompting | Few-shot prompting | CoT prompting | |
| Belief 0 | 0.3311 | 0.3207 | 0.3588 | 0.3638 | 0.3495 |
| Belief 1 | 0.4099 | 0.4241 | 0.4101 | 0.4021 | 0.4055 |
| Belief 2 | 0.2952 | 0.1046 | 0.2504 | 0.2478 | 0.2396 |
| Belief 3 | 0.1848 | 0.1029 | 0.2628 | 0.1747 | 0.2083 |
| Belief 4 | 0.3757 | 0.3329 | 0.3604 | 0.3614 | 0.3223 |
| Belief 5 | 0.3824 | 0.3241 | 0.3680 | 0.3551 | 0.3327 |
| 2 beliefs | 4 beliefs | Original Setup (6 beliefs) | |
| Belief 0 | - | 0.3187 ( ) | 0.3311 ( ) |
| Belief 1 | - | 0.4067 ( ) | 0.4099 ( ) |
| Belief 2 | 0.2637 ( ) | 0.1795 ( ) | 0.2952 ( ) |
| Belief 3 | 0.3315 ( ) | 0.1100 ( ) | 0.1848 ( ) |
| Belief 4 | - | - | 0.3757 ( ) |
| Belief 5 | - | - | 0.3824 ( ) |
| Methods | Intermediate Acc | Final Acc | Inference Time (s) |
| K=6 (Exact) | 0.8443 | 0.9157 | 0.003031 |
| K=6 (MF) | 0.8240 | 0.9167 | 0.001569 |
| K=6 (MCMC) | 0.8223 | 0.9204 | 0.018991 |
| K=10 (Exact) | - | - | 0.003165 |
| K=10 (MF) | - | - | 0.001895 |
| K=10 (MCMC) | - | - | 0.031219 |
| Methods | |||
| Belief 0 | 0.3311 ( ) | 0.3395 ( ) | -0.3246 ( ) |
| Belief 1 | 0.4099 ( ) | 0.3983 ( ) | -0.3294 ( ) |
| Belief 2 | 0.2952 ( ) | -0.2590 ( ) | -0.2545 ( ) |
| Belief 3 | 0.1848 ( ) | -0.1320 ( ) | -0.2340 ( ) |
| Belief 4 | 0.3757 ( ) | 0.2663 ( ) | -0.3395 ( ) |
| Belief 5 | 0.3824 ( ) | 0.3006 ( ) | -0.3221 ( ) |
| Belief interventions | Inter action flip rate | Inter action prob. change | Final action flip rate | Final action prob. change |
| Flipping extreme beliefs ( ) | 0.6508 | 0.2869 | 0.1633 | 0.2408 |
| Flipping neutral beliefs ( ) | 0.1640 | 0.0550 | 0.0306 | 0.0538 |
| Our Model | No ELBO | No ELBO, no factor graph | |
| Belief 0 | 0.3311 ( ) | 0.1605 ( ) | 0.1767 ( ) |
| Belief 1 | 0.4099 ( ) | 0.3049 ( ) | 0.2707 ( ) |
| Belief 2 | 0.2952 ( ) | 0.1826 ( ) | 0.2032 ( ) |
| Belief 3 | 0.1848 ( ) | 0.1526 ( ) | 0.1755 ( ) |
| Belief 4 | 0.3757 ( ) | 0.2921 ( ) | 0.3454 ( ) |
| Belief 5 | 0.3824 ( ) | 0.2938 ( ) | 0.2983 ( ) |
| Category | Belief ID | Belief Statement |
| Property Risk | B0 | My home would be damaged or destroyed by fire. |
| B1 | My neighborhood would be damaged or destroyed by fire. | |
| Self Safety Risk | B2 | I might become injured. |
| B3 | I might die. | |
| Others Safety Risk | B4 | Other people, pets, or livestock might become injured. |
| B5 | Other people, pets, or livestock might die. |
| Category | Survey Question |
| Observations | (1) Before you decided to evacuate (or stay), did one or more emergency officials let you know that your area was under an evacuation warning, pre-evacuation notice, or an evacuation order? |
| (2) Before you decided to evacuate (or stay), did someone you know tell you to evacuate or that an evacuation warning or order was issued for your area? | |
| (3) Before you decided to evacuate (or stay), did you see, hear, or feel flames or embers in your immediate vicinity (that is, your neighborhood)? | |
| Beliefs | (1) After first finding out from the emergency official(s), how much did you believe each of the following statements on a scale of 1 to 5? |
| (2) After first finding out from someone you know, how much did you agree with each of the following statements on a scale of 1 to 5? | |
| (3) After you first observed fire cues, how much did you believe each of the following statements on a scale of 1 to 5? |
| Task Type | Prompt Template Content |
|---|---|
| Probability of beliefs given observations | Context: You are a resident in a wildfire evacuation scenario. Based on your history provided above, analyze the current situation. Hypothetical Scenario: 1. Your Past Observation: {past_observation} 2. Your Current Observation: {observation} 3. Your Previous Belief State: {last_belief} Hypothesis to Evaluate: Target Belief: {belief} Task: Evaluate if you are likely to hold the "Target Belief" given the observation and their previous belief state. Answer with only the letter (A or B). Options: (A) Likely (B) Unlikely |
| Probability of actions given beliefs | Context: You are a resident in a wildfire evacuation scenario. Based on your history provided above, analyze the current situation. Hypothetical Scenario: 1. You hold this belief: {belief} 2. You are evaluating the Action: {action} Task: Analyze if this specific belief encourages or discourages you to take the target action. Considering your background, is the target action likely? Answer with only the letter (A or B). Options: (A) Likely (B) Unlikely |
| Describe states after actions | Context: You are a resident in a wildfire evacuation scenario. Based on your history provided above, analyze the current situation. Current Situation: {observation} Your Decision: {action} Task: Describe the IMMEDIATE consequences of this action from your first-person perspective. Focus on sensory details and safety status change. Constraints: Keep it brief (1-3 sentences); Be objective; Avoid speculation. |
| Belief Relations | Context: You are a resident in a wildfire evacuation scenario. Analyze the relationship between two beliefs held by yourself. Input: Belief 1: {belief 1} Belief 2: {belief 2} Task: Output only one number: a value between 0 and 1 indicates they weaken each other; a value greater than 1 indicates they enhance each other. Do not explain. |
| Infer belief given action and observation | Context: You are a resident in a wildfire evacuation scenario. Based on your history provided above, analyze the current situation. Hypothetical Scenario: 1. Resident’s Current Observation: {observation} 2. The resident has made this action: {action} Hypothesis to Evaluate: Target Belief: {belief} Task: Evaluate if the resident likely holds the "Target Belief" given the observation and the action they made. Answer with only the letter (A or B). Options: (A) Likely (B) Unlikely |