Speak vs. Know: Balancing Behavior and Knowledge Distributions of Large Language Models

Yang Liu; Masahiro Kaneko; Chenhui Chu

cs.CLOct 20, 2026

Speak vs. Know: Balancing Behavior and Knowledge Distributions of Large Language Models

Authors: Yang Liu, Masahiro Kaneko, Chenhui Chu

Organizations: Kyoto University · MBZUAI

Abstract

Recent work reports that the distribution verbalized directly in the output text aligns far better with human opinion distributions than the next-token log-probability distribution of LLMs. However, the verbalized distribution reflects what LLMs know about a group's opinions (knowledge distribution), while what they actually output at deployment is governed by their log-probability distribution (behavior distribution). We find that when prompting LLMs to predict the opinion of a specific group, the most likely answer under the verbalized distribution differs from that under the log-probability distribution for 37% of World Values Survey questions, averaged over three LLMs. Thus, LLMs' knowledge does not match their behavior. This matters for evaluation: a verbalized distribution can score well against a group while its most likely answer is one the model never outputs, so the score no longer describes the model. The alignment scores for these two distributions reflect only the model's behavior or its knowledge, separately. We therefore propose a learnable combination of the two distributions that follows the most likely answer of the behavior distribution while preserving the shape of the knowledge distribution, with a single hyperparameter trading off behavioral fidelity against distribution quality. Our experiments on three opinion survey datasets and six models show that the balanced distribution improves behavioral consistency over the verbalized distribution from 71.6% to 95.6% on average, while the total variation distance to the human opinion distributions rises only slightly from 28.8% to 33.8%, and it remains effective under temperature scaling and cross-dataset settings.

Figures & tables

Figure 1: The alignment score depends on the shape of the target. Mongolia ranks second among the 66 countries and regions of the WVS in alignment with OLMo-3.1-32B-Instruct’s verbalized distribution, under no steering, because its opinion distribution is nearly uniform;

\circ

marks the alignment of each shown country and region’s opinion distribution with the uniform distribution.

Figure 2: For each survey question, the LLM exposes a behavior distribution (log-probability) whose most likely answer reflects what the model actually outputs, and a knowledge distribution (verbalized) whose shape is closer to the human opinion distribution. We learn a combination of the two that keeps the most likely answer of the behavior distribution while preserving the shape of the knowledge distribution, yielding the balanced distribution.

Model	Alignment score		Soft accuracy
Model	Behav.	Knowl.	Behav.	Knowl.
Qwen2.5-72B	0.765	0.875	0.799	0.809
Llama-3.1-70B	0.804	0.865	0.813	0.791
OLMo-3.1-32B	0.779	0.843	0.748	0.765

Table 1: The alignment score of the behavior (Behav.) and knowledge (Knowl.) distributions with the 66 WVS countries and regions under persona steering, and the soft accuracy of their most likely answers.

Model	No steering	Persona steering
Qwen2.5-72B	68.1%	64.9%
Llama-3.1-70B	61.1%	62.5%
OLMo-3.1-32B	56.2%	60.5%

Table 2: The behavioral consistency on the WVS: the percentage of questions on which the most likely answer of the knowledge distribution matches that of the behavior distribution.

Figure 3: Trade-offs between TV and BC under different

\lambda

. Average results across six models and three datasets, under persona steering.

Qwen2.5-72B-Instruct (open-source)
Method	OpinionQA	NYT Books	GOQA
LogProb	0.4791	0.3489	0.5002
Verbalized	0.4330	0.4794	0.4479
Ours	0.6375	0.6196	0.6432
GPT-4.1 (closed-source)
LogProb	0.4475	0.3008	0.5240

Table 3: The comparison of net utility NU of each distribution when prompting the models using persona steering across three datasets.

Figure 4: The comparison of net utility between the balanced distribution and the temperature-scaled log-probability distribution at different temperatures. The shadows indicate the standard deviation of the 5-fold cross-validation.

Model	LogProb	Verb.	Ours
Llama-3.1-70B	0.286	0.080	0.045
Qwen2.5-72B	0.554	0.116	0.006
OLMo-3.1-32B	0.361	0.081	0.062
GPT-4o	0.458	0.113	0.022
GPT-4.1	0.665	0.076	0.006
DeepSeek-V4-F.	0.253	0.103	0.008

Table 4: Absolute difference between each distribution’s normalized entropy and the human entropy (

0.751

), under persona steering, averaged over the three datasets (smaller means closer to the human opinion distribution). Ours is the closest to the human opinion distribution for every model. All open-source models are instruct models. F. indicates Flash.

Figure 5: The cross-dataset validation of the fitted weights

w

\lambda^{*}

for Qwen2.5-72B-Instruct and GPT-4.1. The weights fitted on one dataset still outperform all baseline distributions on another dataset. Blue bars use the

\lambda^{*}

of each model; green bars use the average

\lambda^{*}

of all six models.

Largest Falls			Largest Rises
Country	Rank	$\Delta$	Country	Rank	$\Delta$
Mongolia	14.0	$\downarrow$ 11.3	Netherlands	36.0	$\uparrow$ 15.2
Mexico	27.3	$\downarrow$ 9.0	Germany	28.2	$\uparrow$ 12.2
Thailand	18.8	$\downarrow$ 7.3	New Zealand	17.5	$\uparrow$ 9.7
Serbia	35.2	$\downarrow$ 6.7	Philippines	45.0	$\uparrow$ 8.0
Slovakia	8.5	$\downarrow$ 6.3	Malaysia	37.7	$\uparrow$ 6.5

Table 5: The change in the country’s ranking among the 66 countries when the balanced distribution is substituted for the verbalized distribution; this change is calculated as the average of the six models. Rank is the country’s average ranking under the verbalized distribution, and

\Delta

is the number of places the country falls (

\downarrow

) or rises (

\uparrow

	MCQ			Short-Answer
Model	LogProb	Verb.	Bal.	LogProb	Verb.	Bal.
Llama-3.1-70B	.622	.621	.634	.753	.666	.759
Qwen2.5-72B	.648	.596	.667	.718	.731	.791
OLMo-3.1-32B	.781	.738	.787	.863	.796	.864
GPT-4o	.525	.508	.494	.657	.597	.615
GPT-4.1	.500	.552	.546	.589	.620	.621

Table 6: The Pearson’s

r

between a country’s BLEnD accuracy and its alignment score across the 11 overlapping countries, under the log-probability (LogProb), verbalized (Verb.), and balanced (Bal.) distributions. Bold indicates the highest Pearson’s

r

of each model and task.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Behavior	Knowledge
Qwen2.5-72B-Instruct	0.765	0.875
Llama-3.1-70B-Instruct	0.804	0.866
OLMo-3.1-32B-Instruct	0.779	0.843

Appendix

Table 7: Alignment score under persona steering, averaged over the 66 WVS countries. The knowledge distribution is the strongest single expression method, consistent with Meister et al. (2025) .

Model	Mongolia	Myanmar	United States
Qwen2.5-72B-Instruct	0.879	0.783	0.905
Llama-3.1-70B-Instruct	0.875	0.772	0.906
OLMo-3.1-32B-Instruct	0.888	0.767	0.892
Uniform	0.863	0.750	0.800

Appendix

Table 8: Alignment score with Mongolia, Myanmar, and the United States under no steering, plus a uniform-distribution baseline.

Model	Behavior	Knowledge
Qwen2.5-72B-Instruct	0.168 [0.161, 0.174]	0.854 [0.848, 0.861]
Llama-3.1-70B-Instruct	0.514 [0.503, 0.525]	0.827 [0.822, 0.836]
OLMo-3.1-32B-Instruct	0.415 [0.397, 0.424]	0.871 [0.866, 0.875]
Human opinion	0.766 [0.663, 0.885]

Appendix

Table 9: The average normalized entropy of the behavior and knowledge distributions on the WVS dataset under no steering. The numbers in brackets are the minimum and maximum entropy over the 66 countries and regions.

Figure 6: Effect of the margin

m

on the normalized entropy (top) and the behavioral consistency (bottom) of the balanced distribution, averaged over the six models and three datasets under persona steering. Red:

\lambda

fixed at the value fitted at

m{=}0

; blue:

\lambda

re-optimized at each

m

. The shaded areas are the standard error across the six models.

Figure 7: Training loss (left) and the fitted verbalized weight $w_{vb}$ (right) at every one of the 1,000 Adam steps, for all values of $\lambda$ in the training grid (color: $\lambda$ on a log scale) and three model and dataset pairs under persona steering. Both the loss and the weight are flat long before the step budget ends.

Model	Dataset	Log-prob	Verbalized	Ours
Llama-3.1-70B	OpinionQA	0.6323	0.4420	0.6495
	NYT Books	0.4675	0.3254	0.5649
	GOQA	0.5980	0.4604	0.6222
Qwen2.5-72B	OpinionQA	0.4791	0.4330	0.6375
	NYT Books	0.3489	0.4794	0.6196
	GOQA	0.5002	0.4479	0.6432

Appendix

Table 10: Net utility

\mathrm{NU}=\mathrm{BC}-\mathrm{TV}

of each distribution expression method under persona steering, for all six models.

Model	Dataset	Log-prob	Verbalized	Ours
Llama-3.1-70B	OpinionQA	0.5631	0.3925	0.6304
	NYT Books	0.4855	0.3458	0.6870
	GOQA	0.6116	0.4105	0.6193
Qwen2.5-72B	OpinionQA	0.4492	0.4326	0.6401
	NYT Books	0.3805	0.3201	0.7096
	GOQA	0.5316	0.4404	0.6349

Appendix

Table 11: Net utility

\mathrm{NU}=\mathrm{BC}-\mathrm{TV}

of each distribution expression method under few-shot steering, for all six models.

Model	Dataset	$\lambda^{*}$	Log-prob	Verbalized	Ours
Llama-3.1-70B	OpinionQA	59	0.8327	0.5734	0.8300
	NYT Books		0.6690	0.4181	0.6941
	GlobalOpinionQA		0.8269	0.6156	0.8241
Qwen2.5-72B	OpinionQA	18	0.7859	0.5772	0.8230
	NYT Books		0.6650	0.5688	0.7641
	GlobalOpinionQA		0.7991	0.6179	0.8354

Appendix

Table 12: Net utility

\mathrm{NU}=\mathrm{BC}-\mathrm{NWD}

of each distribution expression method under persona steering, for all six models, when the total variation is replaced by the normalized Wasserstein distance

\mathrm{NWD}=1-\mathcal{A}

. The balanced distribution is re-fitted with the Wasserstein loss and

\lambda^{*}

is re-selected per model under the same rule.

Model	Dataset	$\lambda^{*}$	Log-prob	Verbalized	Ours
Llama-3.1-70B	OpinionQA	24	0.8158	0.5247	0.8207
	NYT Books		0.7542	0.4370	0.8181
	GlobalOpinionQA		0.8385	0.5719	0.8323
Qwen2.5-72B	OpinionQA	47	0.7800	0.5761	0.8321
	NYT Books		0.7174	0.4091	0.8280
	GlobalOpinionQA		0.8104	0.6062	0.8365

Appendix

Table 13: Net utility

\mathrm{NU}=\mathrm{BC}-\mathrm{NWD}

of each distribution expression method under few-shot steering, for all six models, when the total variation is replaced by the normalized Wasserstein distance

\mathrm{NWD}=1-\mathcal{A}

. The balanced distribution is re-fitted with the Wasserstein loss and

\lambda^{*}

is re-selected per model under the same rule.

Figure 8: The comparison of net utility between the balanced distribution and the temperature-scaled log-probability distribution at different temperatures. The shadows indicate the standard deviation of the 5-fold cross-validation.

Model	$\lambda^{*}$	OpinionQA		NYT Books		GlobalOpinionQA
Model	$\lambda^{*}$	$w_{lp}$	$w_{vb}$	$w_{lp}$	$w_{vb}$	$w_{lp}$	$w_{vb}$
Llama-3.1-70B	18	0.70	0.30	0.43	0.57	0.58	0.42
Qwen2.5-72B	37	0.41	0.59	0.35	0.65	0.36	0.64
OLMo-3.1-32B	16	0.61	0.39	0.45	0.55	0.58	0.42
GPT-4o	38	0.40	0.60	0.44	0.56	0.38	0.62
GPT-4.1	16	0.24	0.76	0.20	0.80	0.23	0.77

Appendix

Table 14: The per-model

\lambda^{*}

(a single

\lambda

per model, shared across its three datasets, that maximizes the model's average net utility) and the corresponding mixing weights

w_{lp},w_{vb}

\mathcal{D}_{lp}+\mathcal{D}_{vb}

under persona steering.

Model	$\lambda^{*}$	OpinionQA		NYT Books		GlobalOpinionQA
Model	$\lambda^{*}$	$w_{lp}$	$w_{vb}$	$w_{lp}$	$w_{vb}$	$w_{lp}$	$w_{vb}$
Llama-3.1-70B	20	0.54	0.46	0.31	0.69	0.84	0.16
Qwen2.5-72B	30	0.31	0.69	0.22	0.78	0.36	0.64
OLMo-3.1-32B	12.1	0.59	0.41	0.33	0.67	0.65	0.35
GPT-4o	25	0.29	0.71	0.37	0.63	0.32	0.68
GPT-4.1	20	0.18	0.82	0.21	0.79	0.30	0.70

Appendix

Table 15: The per-model

\lambda^{*}

(a single

\lambda

per model, shared across its three datasets, that maximizes the model's average net utility) and the corresponding mixing weights

w_{lp},w_{vb}

\mathcal{D}_{lp}+\mathcal{D}_{vb}

under few-shot steering.

Figure 9: Cross-dataset transfer of the fitted weights

w

(at the per-model

\lambda^{*}

) for all six models under persona steering. Blue bars use the

\lambda^{*}

of each model; green bars use the average

\lambda^{*}

of all six models.

Figure 10: Cross-dataset transfer of the fitted weights

w

(at the per-model

\lambda^{*}

) for all six models under few-shot steering. Blue bars use the

\lambda^{*}

of each model; green bars use the average

\lambda^{*}

of all six models.

Country	Alignment Score
Country	Verbalized	Balanced
United States	0.910	0.898 $\downarrow$ .012
Canada	0.894	0.890 $\downarrow$ .004
New Zealand	0.879	0.879 $\downarrow$ .000
Hong Kong	0.883	0.867 $\downarrow$ .016
Mongolia	0.882	0.848 $\downarrow$ .034

Appendix

Table 16: The alignment scores of the verbalized and balanced distributions for seven representative countries under no steering, averaged over the six models.

Country	Llama		Qwen		OLMo		GPT-4o		GPT-4.1		DeepSeek
Country	Verb	Ours	Verb	Ours	Verb	Ours	Verb	Ours	Verb	Ours	Verb	Ours
United States	0.906 1	0.889 3	0.905 1	0.902 1	0.892 1	0.875 3	0.917 1	0.903 1	0.927 1	0.918 1	0.911 1	0.903 1
Northern Ireland	0.902 2	0.899 1	0.902 2	0.896 2	0.876 8	0.863 5	0.908 2	0.893 2	0.921 2	0.912 2	0.899 5	0.889 2
Chile	0.890 4	0.856 15	0.899 4	0.870 11	0.887 3	0.861 7	0.908 3	0.881 7	0.896 7	0.878 11	0.908 2	0.886 4
Canada	0.884 7	0.890 2	0.899 3	0.892 3	0.884 5	0.880 1	0.902 4	0.892 3	0.906 3	0.897 4	0.892 9	0.888 3
Slovakia	0.878 11	0.851 19	0.884 12	0.853 20	0.881 7	0.852 15	0.896 5	0.875 9	0.887 12	0.862 20	0.900 4	0.880 6

Appendix

Table 17: Alignment score and country ranking of the verbalized distribution (Verb) and the balanced distribution (Ours) on the 66 WVS countries and regions, under no steering. The subscript is the rank of the country among the 66 under that distribution (1 = highest alignment score). The balanced distribution uses the persona-steering weights of Table 14 , averaged over the three datasets, applied unchanged to the WVS distributions. Countries are sorted by their average verbalized rank over the six models.

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