Evaluating Inquiry Learning in LLM-Based Agents: Hypothesizing, Reasoning, and Exploration

Marta Knežević; Seyed Parsa Neshaei; Jibril Frej; Vinitra Swamy; Tanja Käser

cs.AIOct 15, 2026

Evaluating Inquiry Learning in LLM-Based Agents: Hypothesizing, Reasoning, and Exploration

Authors: Marta Knežević, Seyed Parsa Neshaei, Jibril Frej, Vinitra Swamy, Tanja Käser

Organizations: EPFL

Abstract

Scientific inquiry involves iterative cycles of exploration, hypothesis generation, and reasoning over observations to uncover relationships in complex systems. Large language models (LLMs) have demonstrated strong capabilities in several components of this process, including inductive reasoning, hypothesis generation, and data analysis. However, prior work typically evaluates these abilities in isolation, leaving open how models integrate them across a full inquiry cycle. In this work, we introduce a framework for evaluating LLMs' inquiry capabilities in a unified, interactive setting. We extend the Countdown task to a mathematical environment where an agent probes the system by manipulating variables, collecting observations, and inferring relationships between them. This setup enables analysis of exploration strategies, causal discovery, and hypothesis refinement during inquiry. Across seven LLMs and multiple prompting strategies, our experiments reveal limited inherent inquiry capabilities and low success rates in discovering the underlying expressions. However, structured guidance inspired by educational scaffolding significantly improves performance. Our findings highlight current limitations of LLMs in strategic exploration and iterative hypothesis refinement, and show how simple guidance strategies developed for human learners in inquiry learning can support more effective inquiry behavior.

Figures & tables

Figure 1: The agent explores the environment by collecting datapoints and engages in iterative hypothesizing to infer the underlying mathematical model.

IL Phase	Question	Label	Description
Exploring	Are IL exploration	Strategic	Only one dependent variable changed
Exploring	strategies followed?	Non-strategic	Modifying multiple variables or a repeat data point
Hypothesizing	Do data interpretations	Repeated	The agent repeats a previous hypothesis
	confirm prior beliefs?	Numerical Modification	Agent adapts numerical values in the equation (e.g. scaling)
		Term Modification	Agent adapts equation with a term expressed in variables (e.g. add new term)
Reasoning		Quantitative and Qualitative	The agent discovered a both qualitative and quantitative relationship

Table 1: Evaluation metrics for assessing inquiry behavior over agents’ trajectories.

Figure 2: Accuracy of models across equation complexity indicated by the number of independent variables (3, 4 or 5) in 0-shot and 3-shot settings.

Shots	Model	IL	AO	AOT	AOT-control	IL-ver	GIL	GIL-step	GIL-strategy	GIL-reasoning
0-shot	Llama-8B	0.006	0.011	0.011	0.023	0.011	0.063	0.069	0.075	0.080
	Vicuna-13B	0.011	0.011	0.011	0.017	0.011	0.006	0.011	0.011	0.011
	Qwen-14B	0.092	0.063	0.023	0.092	0.109	0.155	0.029	0.086	0.052
	Gemma-27B	0.040	0.057	0.046	0.086	0.046	0.098	0.034	0.086	0.075
	Qwen-32B	0.063	0.040	0.046	0.103	0.086	0.201	0.115	0.201	0.086
	Llama-70B	0.126	0.086	0.149	0.149	0.132	0.247	0.149	0.195	0.155

Table 2: Proportion of correctly induced equations across IL, GIL, and ablation settings.

Figure 3: Number of Exploration, Hypothesizing and Reasoning steps in IL and GIL across models for 0-shot (left) and 3-shot (right) settings.

Setting	Model	Support	Repeated hypothesis	Numerical modification	Term modification
0-shot IL	Qwen-14B	0.67	0.31 $\pm$ 0.12	0.38 $\pm$ 0.12	0.12 $\pm$ 0.09
	Qwen-32B	0.67	0.44 $\pm$ 0.13	0.38 $\pm$ 0.12	0.31 $\pm$ 0.12
	Llama-70B	0.88	0.19 $\pm$ 0.09	0.24 $\pm$ 0.10	0.48 $\pm$ 0.11
0-shot GIL	Qwen-14B	0.88	0.29 $\pm$ 0.10	0.43 $\pm$ 0.11	0.10 $\pm$ 0.07
	Qwen-32B	0.75	0.22 $\pm$ 0.10	0.56 $\pm$ 0.12	0.06 $\pm$ 0.06
	Llama-70B	0.67	0.12 $\pm$ 0.09	0.00 $\pm$ 0.00	0.31 $\pm$ 0.12

Table 3: Hypothesis behavior metrics (Mean

\pm

SEM) showing the average ratio of different types of hypothesis modifications.

Setting	Model	Cause-Effect Ratio	Statement	Qual. only	Qual. + Quant.
0-shot IL	Qwen-14B	$0.39\pm 0.05$	$0.53\pm 0.09$	$0.13\pm 0.05$	$0.09\pm 0.04$
	Qwen-32B	$0.29\pm 0.04$	$0.08\pm 0.04$	$0.48\pm 0.08$	$0.17\pm 0.06$
	Llama-70B	$0.34\pm 0.05$	$0.41\pm 0.07$	$0.20\pm 0.05$	$0.03\pm 0.03$
0-shot GIL	Qwen-14B	$1.00\pm 0.00$	$0.06\pm 0.01$	$0.41\pm 0.08$	$0.38\pm 0.08$
	Qwen-32B	$1.00\pm 0.00$	$0.08\pm 0.01$	$0.41\pm 0.08$	$0.36\pm 0.08$
	Llama-70B	$1.00\pm 0.00$	$0.05\pm 0.01$	$0.69\pm 0.08$	$0.14\pm 0.06$

Table 4: Reasoning behavior metrics (Mean

\pm

SEM) showing the proportion of cause–effect relations and identified information types during data collection.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Without Context		With Context
	Abstract	Acronym	Abstract	Acronym
Llama-8B	0.077	0.000	0.077	0.154
Vicuna-13B	0.077	0.308	0.231	0.692
Qwen-14B	0.308	0.654	0.500	1.000
Gemma-27B	0.231	0.577	0.538	0.769
Qwen-32B	0.538	0.769	0.731	0.923

Appendix

Table 5: Percentage of correctly induced mathematical models for different LLMs, depending on whether the variables use abstract names (e.g., A, B, C) or acronyms, and whether the full variable name is provided as context (w/ context) or not (w/o context).

Figure 4: The distribution of steps across models and settings. The color denotes the approach (blue: IL, red: GIL), the shading the number of examples (0-shot, 1-shot, 3-shot), and the pattern the type of step (Action, Thought, Hypothesis)

# shots	Model	IL	IL-ver	GIL-step	GIL-reasoning	GIL-strategy	GIL
0-shot	Llama-8B	0.00 $\pm$ 0.00	0.00 $\pm$ 0.00	1.97 $\pm$ 0.03	1.98 $\pm$ 0.03	1.95 $\pm$ 0.02	1.95 $\pm$ 0.02
	Vicuna-13B	0.00 $\pm$ 0.00	0.00 $\pm$ 0.00	0.13 $\pm$ 0.04	0.01 $\pm$ 0.01	0.13 $\pm$ 0.03	0.09 $\pm$ 0.03
	Qwen-14B	3.43 $\pm$ 0.32	11.76 $\pm$ 0.68	0.74 $\pm$ 0.08	1.90 $\pm$ 0.04	1.74 $\pm$ 0.05	1.90 $\pm$ 0.04
	Gemma-27B	3.70 $\pm$ 0.27	5.18 $\pm$ 0.21	0.29 $\pm$ 0.05	1.20 $\pm$ 0.07	1.99 $\pm$ 0.04	1.94 $\pm$ 0.02
	Qwen-32B	3.28 $\pm$ 0.33	13.74 $\pm$ 0.69	0.61 $\pm$ 0.07	1.26 $\pm$ 0.08	1.79 $\pm$ 0.03	1.81 $\pm$ 0.03
	Llama-70B	3.06 $\pm$ 0.10	3.80 $\pm$ 0.12	2.06 $\pm$ 0.04	1.99 $\pm$ 0.03	1.99 $\pm$ 0.04	1.82 $\pm$ 0.03

Appendix

Table 6: Number of hypotheses proposed in the model trajectories during the exploration phase for each model, method, and their ablations. All values are shown with 2 decimal points.

		IL		GIL		GIL-Extended
Model	# Shots	Coeff.	Int.	Coeff.	Int.	Coeff.	Int.
Qwen-14B	0	0.09	0.14	0.02	0.02	0.05	0.05
	1	0.02	0.02	0.00	0.00	0.00	0.02
	3	0.03	0.09	0.00	0.05	0.00	0.02
Qwen-32B	0	0.10	0.09	0.00	0.03	0.03	0.05
	1	0.05	0.10	0.05	0.05	0.07	0.03

Appendix

Table 7: Results across models and few-shot settings, reported separately for coefficients and intercepts under IL, GIL, and GIL-Extended that allows for longer exploration across the inquiry cycles. Coeff. and Int. stands for equations with both coefficients and intercept, and equations with intercept term only.

Model	# observations	0-shot	3-shot
Qwen-14B	4-3-3	0.328	0.362
	7-0-0	0.259	0.345
	7-3-3	0.328	0.276
	7-6-6	0.241	0.276
	10-3-3	0.293	0.345
Qwen-32B	4-3-3	0.276	0.414

Appendix

Table 8: Performance of different models with respect to the number of observations across different exploration cycles indicated in the column Steps .

Shots	Model	C1	C2	C3	C4	C5
0-shot	Qwen-14B	0.259	0.276	0.293	0.293	0.293
	Qwen-32B	0.224	0.276	0.276	0.276	0.276
	Llama-70B	0.276	0.345	0.379	0.397	0.414
3-shot	Qwen-14B	0.241	0.276	0.293	0.328	0.328
	Qwen-32B	0.241	0.328	0.362	0.397	0.397
	Llama-70B	0.345	0.362	0.414	0.414	0.431

Appendix

Table 9: Performance across number of exploration cycles (C) for different models and number of shots.

Panel of Figure 5 — Figure 5: Percentage of strategic exploration across all models and different types of IL and GIL settings.

Setting	Model	Strategic Exploration	Repeated Observation	Random Exploration
0-shot IL	Qwen-14B	0.31 $\pm$ 0.07	0.04 $\pm$ 0.02	0.65 $\pm$ 0.07
	Qwen-32B	0.08 $\pm$ 0.03	0.02 $\pm$ 0.01	0.90 $\pm$ 0.03
	Llama-70B	0.26 $\pm$ 0.04	0.02 $\pm$ 0.01	0.72 $\pm$ 0.04
0-shot GIL	Qwen-14B	0.92 $\pm$ 0.01	0.01 $\pm$ 0.01	0.07 $\pm$ 0.01
	Qwen-32B	0.91 $\pm$ 0.01	0.00 $\pm$ 0.00	0.08 $\pm$ 0.01
	Llama-70B	0.92 $\pm$ 0.01	0.00 $\pm$ 0.00	0.08 $\pm$ 0.01

Appendix

Table 10: Mean ± SEM for three types of data collection strategies, namely Strategic exploration, exploration that results with collection of the Repeated Observation , and Random Exploration that includes modifying multiple variables simultaneously.

# shots	Model	Verification	Calculation	Correct
0-shot	Qwen-14B	$0.58\pm 0.05$	$0.26\pm 0.08$	$0.66\pm 0.14$
	Qwen-32B	$0.57\pm 0.05$	$0.27\pm 0.09$	$0.84\pm 0.11$
	Llama-70B	$0.48\pm 0.05$	$0.39\pm 0.08$	$0.89\pm 0.06$
3-shot	Qwen-14B	$0.45\pm 0.05$	$0.10\pm 0.05$	$0.32\pm 0.18$
	Qwen-32B	$0.37\pm 0.04$	$0.18\pm 0.07$	$0.54\pm 0.17$
	Llama-70B	$0.26\pm 0.04$	$0.15\pm 0.06$	$0.83\pm 0.15$

Appendix

Table 11: IL-strategy verification metrics (Mean ± SEM) across models and shots. The columns indicate the ratio of Thought steps including verification ( Verification ), the ratio of verifications containing explicit calculation ( Calculation ), and the ratio of correct computation among verifications containing computations ( Correct ).

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We propose agentic automata learning to evaluate the extent to which tool-calling LLM agents can uncover hidden environments through interaction, a capability increasingly required in agentic tasks (e.g., reproducing an executable without access to its source code by interacting with it). In our setup, an agent should uncover a hidden deterministic finite automaton (DFA) by interacting with an oracle through (1) membership queries ("Does this string belong to the target language?'') and (2) equivalence queries ("Is this the target DFA?''). Agentic automata learning yields a scalable testbed with controlled task complexity, measurable interaction efficiency, and strong algorithms to compare against from the classic automata-learning literature. Evaluating state-of-the-art LLMs with a multi-turn agent scaffold, we find that while they are able to recover simple DFAs, their performance drops sharply as DFA size increases. Results improve with a more elaborate ReAct-style state-tracking scaffold, yet strong models still struggle with complex instances. Trajectory analyses reveal recurring failures in query planning, evidence integration, and hypothesis construction. These failures occur even though the models mention classic automata learning algorithms in their reasoning, and can implement and execute them when given access to a coding environment. Our results suggest that for state-of-the-art LLMs, identifying a solution to the problem is insufficient, and reliably executing the resulting plan still poses a distinct challenge.

Abstract

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