Diagnosing the Explicit-to-Applied Theory of Mind Gap in LLMs

Prajvi Saxena; Sabine Janzen; Wolfgang Maass

cs.AIOct 22, 2026

Diagnosing the Explicit-to-Applied Theory of Mind Gap in LLMs

Authors: Prajvi Saxena, Sabine Janzen, Wolfgang Maass

Organizations: German Research Center for Artificial Intelligence (DFKI) · Saarland University

Abstract

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.

Figures & tables

Figure 1: The explicit-to-applied Theory of Mind gap on SimpleToM Each scenario generates three matched questions: mental-state recognition ( explicit ), behavior prediction ( applied ), and judgment ( applied ).

Benchmark	Explicit ( $\mathcal{B}_{\mathrm{E}}$ )	Applied ( $\mathcal{B}_{\mathrm{A}}$ )	$C$	$\|\mathcal{B}\|$	Regime	$\|\mathcal{S}\|$
SimpleToM	Mental-state	Behavior, Judgment	2	3,441	Static, 1 st -order	1
DynToM	Understand (A)	Transform (C,D)	7–8	3,000	Temporal, multi-step	$\leq$ 4
Hi-ToM	(indirect)	Recursive belief, location	15	1,200	Static, higher-order	$\leq$ 4
OpenToM	Attitude	Multihop first-order	3–6	2,000	Static, multi-agent	$\leq$ 4

Table 1: Each benchmark decomposes into explicit (mental-state recognition) and applied (behavioral inference) subsets. Hi-ToM provides a complementary test of higher-order reasoning recovery without a paired explicit subset. (

|\mathcal{B}|

: Total number of questions;

C

= number of answer choices;

|\mathcal{S}|

: support set size per episode.)

Method	Adapts $\theta$ ?	Prompt	Objective	What it tests
Frozen baselines
Frozen	✗	Vanilla	—	Baseline gap
CoT	✗	Step-by-step	—	Reasoning elicitation
Structured prompting
Scratchpad	✗	Belief scaffold	—	Externalizing tracking
SimToM	✗	2-stage perspective	—	Perspective filtering

Table 2: Method configurations and their diagnostic purpose. See Table 6 for benchmark-specific instantiations

Model	Condition	SimpleToM	Hi-ToM	OpenToM	DynToM
Llama-3.1-8B	Frozen	51.5	41.4	42.5	19.7
	Best prompt	65.5 h	47.5 b	48.8 b	24.5 g
	BSTTT-AR	54.2	54.4	43.1	20.7
	Matched ICL	59.8	60.3	56.4	32.6
	Best BSTTT	67.7 i	55.3 d	50.0 d	22.2 c
	$\Delta_{\mathrm{best}}$	+16.2	+18.9	+13.9	+12.9

Table 3: Cross-model summary. Accuracy (%). “Best prompt” selects the strongest prompting method without demonstrations or weight updates; “Best BSTTT” selects the strongest BSTTT configuration, including prompting compositions. Bold indicates the highest listed accuracy per model and benchmark.

\Delta_{\mathrm{best}}

is the highest listed accuracy minus Frozen, in percentage points. All accuracies are averaged over three seeds. Run-specific settings are reported in Appendix D .

Figure 2: Explicit-to-applied gap and recovery across benchmarks Bars show accuracy pooled over applied questions; diamonds indicate frozen explicit accuracy. Their difference from the frozen bars gives the baseline gap. Hi-ToM shows overall accuracy without an explicit reference.“Best BSTTT” shows the applied accuracy of the configuration selected by overall accuracy in Table 3 . Intervention gains are measured relative to the frozen bars; evaluation settings follow Table 3 .

Model	Benchmark	Frozen	BSTTT-NTL	BSTTT-AR	$\boldsymbol{\Delta}$ (AR $-$ NTL)
Llama-8B	SimpleToM	51.5	51.7	54.2	+2.5
	Hi-ToM	41.4	41.4	54.4	+13.0
	OpenToM	42.5	42.7	43.1	+0.4
	DynToM	19.7	19.9	20.7	+0.8
Qwen-7B	SimpleToM	69.4	69.0	70.8	+1.8
	Hi-ToM	40.7	40.7	40.7	0.0

Table 4: AR vs. NTL: the diagnostic contrast. Both conditions use identical LoRA configuration, support data, and gradient budget.

\Delta

(AR

-

NTL) reports the accuracy difference between answer-supervised adaptation and narrative modeling. All accuracies are averaged over three seeds.

Model	Benchmark	$\boldsymbol{P}$	$\boldsymbol{B}$	$\boldsymbol{B{+}P}$	$\boldsymbol{\Delta(B{+}P-P)}$	$\boldsymbol{\Delta(B{+}P-B)}$
Llama-8B	SimpleToM a	65.5	54.2	67.7	+2.2	+13.5
	Hi-ToM b	47.5	54.4	55.3	+7.8	+0.9
	OpenToM b	48.8	43.1	50.0	+1.2	+6.9
	DynToM c	20.8	20.7	22.2	+1.4	+1.5
Qwen-7B	SimpleToM a	77.0	70.8	82.5	+5.5	+11.7
	Hi-ToM c	43.8	40.7	53.7	+9.9	+13.0

Table 5: Component comparison for prompting compositions. Accuracy (%) averaged over three seeds.

P

: the selected prompting method;

B

: BSTTT-AR.

\Delta(B{+}P-P)

: additional gain from adaptation over prompting alone.

\Delta(B{+}P-B)

: additional gain from prompting over adaptation alone. Differences are reported in percentage points.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Benchmark	Fixed-weight methods and controls	Adaptation and composed methods
SimpleToM	Vanilla, CoT, MS-Reminder, matched ICL	BSTTT-NTL, BSTTT-AR, MS-Reminder+BSTTT
Hi-ToM / OpenToM	Vanilla, CoT, Scratchpad, SimToM, SymbolicToM, matched ICL	BSTTT-NTL, BSTTT-AR, Scratchpad+BSTTT, SimToM+BSTTT, SymbolicToM+BSTTT
DynToM	Frozen, CoT, Scratchpad-Frozen, matched ICL, Scratchpad-Oracle	BSTTT-NTL, BSTTT-AR, Scratchpad-TTT, Hierarchical-TTT

Appendix

Table 6: Benchmark-specific method map. Fixed-weight methods modify the input without updating model parameters. Adaptation methods use BSTTT alone or in combination with prompting. Scratchpad-Oracle supplies annotated mental states as a separate control.

Parameter	Value
LoRA rank ( $r$ )	8
LoRA alpha ( $\alpha$ )	16
LoRA dropout	0.0
Target modules	All attention and MLP projections in
top 25% of layers
Gradient steps ( $K$ )	3

Appendix

Table 7: BSTTT hyperparameters. Fixed across all AR vs. NTL comparisons.

Benchmark	Frozen	BSTTT-AR	ICL	GPU
SimpleToM	6	25	3.9	A100
Hi-ToM	2	8	9.9	H100
OpenToM	4	15	3.4	H100
DynToM	6	22	54.5	A100

Appendix

Table 8: Evaluation time in minutes for one seed. Frozen and BSTTT-AR values are estimates for an 8B-class model on one B200 GPU, with

K{=}3

adaptation steps for BSTTT-AR. ICL values are recorded Llama-3.1-8B runtimes. GPU identifies the hardware used for ICL.

Model	Method	Mental-State	Behavior	Judgment
Qwen-7B	Frozen	83.4 [81.3, 85.6]	50.7 [47.9, 53.6]	74.0 [71.5, 76.5]
	CoT	84.7 [82.6, 86.8]	46.6 [43.8, 49.4]	74.4 [71.8, 76.8]
	MS-Reminder	83.6 [81.4, 85.8]	62.0 [59.4, 64.8]	85.4 [83.3, 87.4]
	Matched ICL	81.2 [78.9, 83.4]	60.5 [57.6, 63.5]	45.4 [42.5, 48.4]
	BSTTT-AR	83.0 [80.8, 85.2]	55.0 [52.1, 57.8]	74.5 [71.9, 77.0]
	MS-Rem.+BSTTT	94.7 [93.4, 95.9]	66.4 [63.8, 69.0]	86.4 [84.3, 88.3]

Appendix

Table 9: SimpleToM per-question-type accuracy (%) with 95% bootstrap CIs (

n{=}1{,}147

items per question type, 2,000 resamples).

Benchmark	Method	Accuracy (%)	95% CI
Hi-ToM	Frozen	32.6	[30.0, 35.1]
	CoT	32.7	[30.0, 35.2]
	Scratchpad	34.8	[32.2, 37.4]
	BSTTT-NTL	31.6	[28.9, 34.1]
	BSTTT-AR	47.3	[46.3, 48.3]
	Matched ICL	39.5	[36.7, 42.2]

Appendix

Table 10: Hi-ToM and OpenToM accuracy (%) with 95% bootstrap confidence intervals. Results for GPT-oss-20B, using 2,000 resamples. Hi-ToM contains 1,200 evaluation items and OpenToM contains 2,000.

Model	SimpleToM	Hi-ToM	OpenToM	DynToM
Llama-3.1-8B	57.37	42.50	48.50	30.41
Qwen2.5-7B	59.46	48.17	42.26	39.20
GPT-OSS-20B	71.87	29.33	27.80	13.60

Appendix

Table 11: Cross-scenario ICL results across models. Accuracy (%) with answered supports drawn from other scenario families or trials.

Method	Qwen-2.5-7B	Llama-3.1-8B	GPT-oss-20B
Frozen	69.4	51.5	57.6
CoT	68.5	57.0	59.9
MS-Reminder	77.0	65.5	64.1
Matched ICL	62.4	59.8	66.7
BSTTT-NTL	69.0	51.7	56.9
BSTTT-AR	70.8	54.2	58.9

Appendix

Table 12: SimpleToM results across models. Overall accuracy (%) across 3,441 evaluation episodes, with 1,147 per question type. Bold identifies the best result for each model; underlining identifies the best result without parameter updates. MS-Reminder+BSTTT-AR combines the mental-state reminder with AR adaptation (Appendix C.3 ).

Method	Qwen-2.5-7B	Llama-3.1-8B	GPT-oss-20B
Frozen	40.7	41.4	32.6
CoT	42.6	38.8	32.7
Scratchpad	43.8	43.0	34.8
SimToM	38.8	41.8	31.7
SymbolicToM	43.0	47.5	25.7
Matched ICL	60.6	60.3	39.5

Appendix

Table 13: Hi-ToM results across models. Accuracy (%) on 1,200 evaluation items over three seeds. Bold identifies the best result for each model; underlining identifies the best result without parameter updates. Hi-ToM evaluates factual and recursive belief questions without a paired explicit–applied decomposition (Appendix B.2 ).

Method	Qwen-2.5-7B	Llama-3.1-8B	GPT-oss-20B
Frozen	40.5	42.5	35.6
CoT	41.0	41.6	31.5
Scratchpad	40.4	45.8	35.8
SimToM	45.6	48.1	34.4
SymbolicToM	42.7	48.8	28.9
Matched ICL	60.4	56.4	28.85

Appendix

Table 14: OpenToM results across models. Accuracy (%) on 2,000 evaluation items over three-seed averages. Bold identifies the best result for each model; underlining identifies the best result without parameter updates.

Method	Qwen-2.5-7B	Llama-3.1-8B	GPT-oss-20B
Frozen	35.7	19.7	13.0
CoT	35.7	24.5	14.4
Scratchpad-Frozen	38.4	20.8	14.3
Matched ICL	39.9	32.6	13.3
BSTTT-NTL	35.7	19.9	13.2
BSTTT-AR	35.4	20.7	13.2

Appendix

Table 15: DynToM results across models. Accuracy (%) on 3,000 evaluation items report three-seed averages. Bold identifies the best result for each model; underlining identifies the best result without parameter updates, excluding the oracle control. Scratchpad-Oracle supplies annotated mental-state tables and is reported separately.

Model	Method	Mental-state	Behavior	Judgment
Qwen-2.5-7B	Frozen	83.4	50.7	74.0
	Matched ICL	81.2	60.5	45.4
	MS-Reminder+BSTTT-AR	94.7	66.4	86.4
Llama-3.1-8B	Frozen	99.4	28.9	26.2
	Matched ICL	99.4	66.0	14.0
	MS-Reminder+BSTTT-AR	99.8	69.7	33.7

Appendix

Table 16: SimpleToM accuracy (%) by question type. Results are averaged over three seeds. MS-Reminder+BSTTT-AR combines mental-state prompting with parameter adaptation. The decomposition distinguishes improvements in behavior prediction from changes in recognition and judgment.

Benchmark	Model	Frozen	Frozen	BSTTT-AR	ICL	Best BSTTT	$\boldsymbol{\Delta_{\mathrm{gap}}}$
		Explicit	Applied
SimpleToM	Qwen-2.5-7B	83.4	62.4	64.7	53.0	76.4	21.0
	Llama-3.1-8B	99.4	27.5	31.8	40.0	51.7	71.9
	GPT-oss-20B	100.0	36.4	38.4	50.1	48.0	63.6
OpenToM	Qwen-2.5-7B	46.5	38.0	35.7	66.5	47.4	8.5
	Llama-3.1-8B	46.1	40.9	41.0	61.5	51.8	5.2

Appendix

Table 17: Values underlying Figure 2 . Accuracy (%) on the explicit and applied subsets. Explicit accuracy is reported under frozen inference; applied accuracy pools the applied question types. “Best BSTTT” denotes the BSTTT configuration selected by overall benchmark accuracy.

\Delta_{\mathrm{gap}}

is frozen explicit accuracy minus frozen applied accuracy, in percentage points. Hi-ToM reports overall accuracy because it lacks a paired explicit–applied decomposition. Intervention gains are obtained by subtracting the corresponding frozen accuracy.

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