IDEA: An Interpretable and Editable Decision-Making Framework for LLMs via Verbal-to-Numeric Calibration

Yanji He; Yuxin Jiang; Yiwen Wu; Bo Huang; Jiaheng Wei; Wei Wang

cs.AIApr 14, 2026

IDEA: An Interpretable and Editable Decision-Making Framework for LLMs via Verbal-to-Numeric Calibration

Authors: Yanji He, Yuxin Jiang, Yiwen Wu, Bo Huang, Jiaheng Wei, Wei Wang

Organizations: The Hong Kong University of Science and Technology (Guangzhou) · Huawei Technologies Co.,Ltd · The Hong Kong University of Science and Technology

Abstract

Large Language Models are increasingly deployed for decision-making, yet their adoption in high-stakes domains remains limited by miscalibrated probabilities, unfaithful explanations, and inability to incorporate expert knowledge precisely. We propose IDEA, a framework that extracts LLM decision knowledge into an interpretable parametric model over semantically meaningful factors. Through joint learning of verbal-to-numerical mappings and decision parameters via EM, correlated sampling that preserves factor dependencies, and direct parameter editing with mathematical guarantees, IDEA produces calibrated probabilities while enabling quantitative human-AI collaboration. Experiments across five datasets show IDEA with Qwen-3-32B (78.6%) outperforms DeepSeek R1 (68.1%) and GPT-5.2 (77.9%), achieving perfect factor exclusion and exact calibration -- precision unattainable through prompting alone. The implementation is publicly available at https://github.com/leonbig/IDEA.

Figures & tables

Figure 1: Three manifestations of the trust deficit in LLM-based decision making, stemming from a common root: internal-external misalignment. (a) Uncalibrated probabilities : ranking and scoring yield inconsistent orderings for the same options. (b) Unfaithful explanations : generated rationales diverge from the latent reasoning that actually determines outputs. (c) Uncontrollable interventions : natural language instructions fail to guarantee behavioral compliance—factor X continues to influence predictions despite explicit exclusion instructions.

Figure 2: The IDEA framework illustrated on a loan approval task. Given applicant conditions $C$ , the framework extracts binary factor values, handles uncertainty via Monte Carlo sampling, and produces calibrated probabilities through a learned decision model $P_{\bm{\theta}}(O=1\mid\mathbf{f})$ with interpretable coefficients. The offline phase (bottom left) jointly learns model parameters and verbal-to-numerical mappings via EM. Expert intervention (bottom right) enables precise, auditable parameter edits—e.g., excluding credit history by setting $\beta_{3}=0$ shifts approval probability from 21.6% to 52.3%.

Model	Method	BIG	Crd	C2S	PLS	TOD	Avg	F1 $C_{1}$	F1 $C_{2}$	F1 Eq	Avg
N/A	Random	50.0	50.0	50.0	50.0	50.0	50.0	0.333	0.333	0.333	0.333
DeepSeek R1	CoT	51.8	57.0	88.7	75.4	67.7	68.1	0.318	0.335	0.205	0.286
GPT-5.2	CoT	67.8	68.2	95.0	82.9	75.8	77.9	0.455	0.438	0.295	0.402
Qwen-3-4B	CoT	51.4	57.5	94.2	75.1	68.1	69.3	0.352	0.325	0.261	0.313
	Logit	52.4	54.9	88.8	75.6	70.2	68.4	0.281	0.292	0.238	0.270
	Vanilla	56.7	56.1	91.7	82.0	70.4	71.4	0.392	0.361	0.284	0.346

Table 1: Main results across two evaluation paradigms. Left (Experiment I): Binary decision accuracy (%) on five benchmarks spanning complex real-world decisions (BIGDATA22, German Credit) and commonsense reasoning (COMMON2SENSE, PLASMA, TODAY). Right (Experiment II): Macro F1 for three-way probability ranking on paired COMMON2SENSE queries, measuring whether models correctly identify which condition provides stronger evidential support. F1 scores are reported separately for cases where

C_{1}

dominates,

C_{2}

dominates, or neither (Equal). Shaded rows denote IDEA variants; best results per model size in bold .

Model	Category	Method	Factor Exclusion		Quantitative Calibration
Model	Category	Method	ERR ( $\uparrow$ )	$p$ -value ( $\uparrow$ )	Relative Error ( $\downarrow$ )
Qwen-3-4B	Prompting	CoT	0.12	0.021	0.88
		Vanilla	0.33	0.004	0.71
		Logit	0.27	0.009	0.79
	Editing	IDEA	1.00	N/A	0.00
Qwen-3-8B	Prompting	CoT	0.36	0.013	0.66

Table 2: Results of user-edited factor intervention. We categorize CoT, Vanilla, and Logit as generic Prompting methods, distinct from IDEA. Note: Under IDEA factor exclusion, the decision model removes

F_{X}

by setting

\beta_{X}{=}0

and dropping all interactions involving

F_{X}

, so

\Delta P\equiv 0

and the paired

t

-test is undefined (reported as N/A). IDEA enforces

|\mathrm{AME}_{j}-\rho\,\mathrm{AME}_{i}|\leq 10^{-6}

, so the relative error rounds to

0.00

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

	Expert	LLM	Overlap
German Credit	9	7	6 (85.7%)

Appendix

Table 3: Factor set comparison with domain experts.

Dataset	$\max(\Delta_{j})$	$\text{mean}(\Delta_{j})$	$\min(\Delta_{j})$
German Credit	8.4	3.2	0.3
TODAY	5.1	1.8	0.1
COMMON2SENSE	3.9	1.4	0.2

Appendix

Table 4: Accuracy degradation (%) under single-factor removal.

Removed	0%	15%	30%	40%	50%
German Credit	68.9	67.1	64.8	60.2	54.1
TODAY	75.0	73.8	71.5	68.3	63.7
COMMON2SENSE	95.1	94.2	92.6	89.1	84.5

Appendix

Table 5: Accuracy (%) under progressive factor removal.

Model	Factor Inf.	Decision Model	Margin.
Qwen-3-4B	58.4	27.2	14.4
Qwen-3-32B	31.6	42.8	25.6

Appendix

Table 6: Error distribution by pipeline stage (%).

Factor	Description	$\beta_{j}$	AME
$F_{1}$	Stable employment	+1.82	+0.284
$F_{2}$	Acceptable debt ratio	+1.67	+0.261
$F_{3}$	Positive credit history	+1.43	+0.223
$F_{4}$	Sufficient collateral	+0.89	+0.139

Appendix

Table 7: Partial Learned parameters for credit decision.

Factor	Description	$\beta_{j}$	AME
$F_{1}$	Timeline permits participation	+2.31	+0.341
$F_{2}$	Age-appropriate for competition	+1.89	+0.279
$F_{3}$	Educational timeline consistent	+0.72	+0.106

Appendix

Table 8: Learned parameters for temporal reasoning.

Model	BIG	Credit	PLASMA	Avg
Logistic (IDEA)	59.5	60.3	80.2	66.7
MLP-16	60.2	61.1	81.0	67.4
$\Delta$	+0.7	+0.8	+0.8	+0.7

Appendix

Table 9: Accuracy (%) comparison between logistic regression and MLP decision models.

Noise $\epsilon$	BIG	Crd	TOD	PLS	C2S
0.00 (baseline)	59.5	60.3	71.4	80.2	94.8
0.10	58.1	59.5	70.2	78.9	93.6
0.20	55.8	57.2	68.1	76.1	91.2
0.30	52.4	54.8	64.5	72.3	87.5

Appendix

Table 10: Decision accuracy (%) under verbal label noise.

Method	Setup (one-time)	Per Instance
Vanilla/CoT/Logit	0	1
BIRD	0	$N$
IDEA	$\sim$ 20 + $\min(2^{N},256)$	$N+T$

Appendix

Table 11: LLM query counts. For IDEA with

N=6,T=50

: setup

\approx

84 queries; inference = 56 queries/instance.

Method	Latency (s)	Accuracy (%)
Vanilla	0.8	71.7
CoT	2.1	69.2
IDEA ( $T$ =50)	18.4	73.2
IDEA ( $T$ =20)	8.2	72.4

Appendix

Table 12: Per-instance latency with sequential execution (Qwen-3-8B).

Component	Hyperparameter	Value
EM Algorithm	Precision ratio $\tau_{\theta}/\tau_{\phi}$	1.0
	Convergence threshold	$10^{-4}$
	Max iterations	100
Regularization	$\lambda_{1}$ (L1 on $\bm{\gamma}$ )	0.01
	$\lambda_{2}$ (L2 on $\bm{\gamma}$ )	0.001
	$\lambda$ (ranking loss)	0.1

Appendix

Table 13: Hyperparameter configuration for IDEA.

Samples ( $T$ )	Accuracy (%)	Std. Error
10	93.2	0.42
25	94.3	0.28
50	94.8	0.19
100	94.9	0.14

Appendix

Table 14: Effect of Monte Carlo sample size.

$\lambda_{1}$	Interaction Sparsity (%)	Accuracy (%)
0.001	12.5	94.1
0.01	45.8	94.8
0.1	87.5	93.6

Appendix

Table 15: Effect of L1 regularization strength.

Metric	Value
Fleiss’ $\kappa$	0.71
Pairwise Agreement	84.2%
Unanimous Agreement	67.3%

Appendix

Table 16: Inter-annotator agreement statistics for the 150 newly annotated instances.

Figure 3: Prompting Example: DECOMPOSE QUERY.

Figure 4: Prompting Example: GENERATE STATEMENTS.

Figure 5: Prompting Example: EXTRACT FACTORS.

Figure 6: Prompting Example: CHECK BINARY SUPPORT.

Figure 7: Prompting Example: CHECK OVERLAPPING FACTOR.

Figure 8: Prompting Example: CHECK CONDITION COVERAGRE.

Figure 9: Prompting Example: FACTOR DETERMINATION (STEP 1).

Figure 10: Prompting Example: MONTE CARLO SAMPLING (STEP 2).

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Large Language Models (LLMs) increasingly support decision-making in high-stakes domains, but they often hallucinate and express confidence that is misaligned with factual correctness. Response-level confidence is a coarse signal: a single generation can mix correct and incorrect statements, so a single number is not actionable for users that must accept, reject, or verify individual pieces of information. We study claim-level confidence calibration as a decision-relevant uncertainty signal: each response is decomposed into atomic, verifiable claims, and each claim is assigned a calibrated confidence using inference-time signals from consistency across samples and self-verification. Our framework operates in closed-box settings (no logits, no fine-tuning) and applies post-hoc calibration directly at the claim level, enabling selective intervention such as evidence retrieval or human review for low-confidence claims. Across TriviaQA and TruthfulQA we evaluate seven baselines on six recent models (Llama-3.1, Mistral, Qwen2.5, DeepSeek-R1, GPT-4, GPT-4o), and show that claim-level decomposition combined with post-hoc calibration reduces expected calibration error on factual questions while exposing failure modes on adversarial false-premise questions where decision-makers most need reliable uncertainty estimates.

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