Knowledge acquisition from black-box large language models (LLMs) offers a practical approach to adapting smaller student models. However, many existing methods rely on predefined queries or student feedback to guide acquisition, leaving autonomous expansion of knowledge targets an important challenge. We propose MapSteal, a student-independent framework for structured recursive knowledge acquisition. Starting from a small set of initial roots, MapSteal represents acquisition targets using structured states and recursively expands them through teacher-proposed directions. Question realization, proposal admission, and deduplication constrain the acquisition process, while root-aware scheduling organizes exploration under a fixed QA budget. The resulting question--answer pairs are used to adapt student models without requiring student feedback during acquisition. Experiments with Qwen3.5 students at 2B, 4B, and 9B scales show competitive downstream performance across six medical and cybersecurity benchmarks. On the 4B medical evaluation, Full MapSteal improves average accuracy by 1.17 percentage points over a simplified recursive acquisition variant. Cross-domain evaluations show that gains depend on the domain and evaluation panel. These results demonstrate the feasibility of structured, student-independent recursive acquisition while highlighting the distinction between generating acquisition targets and obtaining useful training supervision. Our code is available at \href{https://github.com/LabRAI/Mapsteal} {https://github.com/LabRAI/Mapsteal}.
Figures & tables
Figure 1: Overview of MapSteal. Frozen domain roots initialize a structured acquisition map. Root-level FAIR scheduling selects pending states; a deterministic realizer converts non-root states into questions. A black-box teacher returns an answer, explanation, and typed child-state proposals in one successful interaction. Admitted children re-enter the frontier, while collected QA supervision is used to adapt the student only after acquisition. Map edges indicate acquisition provenance rather than verified domain relations.
Operator
O
F
C
T,D
NewObject
New
Empty
Empty
New
NewFacet
Keep
New
Keep
New
ConditionDepth
Keep
Keep
New
New
NewTarget
Keep
Keep
Keep
New
Table 1: Field updates for proposed states. “Keep” means inherit the parent’s field; “New” means use the proposed value. Transitions assign new T and D .
Medical
Cybersecurity
Student
Method
MedMCQA
MedQA
MedXpert
CyberMetric
SecEval
CTI-Bench
Qwen3.5-2B
Pristine
45.80
36.06
10.78
79.47
71.93
60.64
EvoKD
40.53±8.09
41.19±8.47
12.39±1.57
71.00±6.19
69.49±6.25
52.73±9.42
QEDKS
43.27±0.12
44.59±0.81
14.88±0.83
79.49±0.23
77.73±1.46
65.48±0.16
MapSteal (Ours)
47.87±1.03
45.59±0.16
14.65±0.19
79.70±0.14
78.68±0.56
62.41±1.07
Qwen3.5-4B
Pristine
56.60
62.14
16.73
83.63
80.60
65.71
Table 2: Main results across selected medical and cybersecurity benchmarks. Results are reported as accuracy (%).
Variant
MedMCQA
MedQA
MedXpert
Avg
Δ
Full MapSteal
62.27±0.42
66.69±0.44
17.63±0.46
48.86±0.17
–
w/o CONDITION_DEPTH
60.93±0.31
66.20±0.28
16.30±0.14
47.81±0.04
−1.05
Simplified OF
60.87±0.31
65.28±0.36
16.94±0.32
47.69±0.10
−1.17
Table 3: Ablation study of MapSteal on medical benchmarks.
Figure 2: Acquisition depth and expansion operator distributions of Simplified OF and Full MapSteal. Both methods execute 460 acquisition questions from the same 35 roots. Operator counts exclude root executions.
Roots
MedMCQA
MedQA
MedXpert
1
60.87±1.14
66.25±0.67
16.97±0.29
10
61.47±0.31
65.49±0.39
17.36±0.37
20
61.27±0.50
66.35±0.37
16.87±0.36
35
62.27±0.42
66.69±0.44
17.63±0.46
Table 4: Effect of initial acquisition root count.
Metric
OF
OFCTD
Mean trajectory depth
1.67
1.87
Distinct Object strings
231
147
Sequential novelty
0.262
0.178
Parent–child cosine
0.621
0.788
Near-duplicate rate (%)
8.5
30.8
Table 5: Descriptive acquisition statistics for Simplified OF and Full MapSteal. Semantic metrics are computed from executed acquisition questions.
Figure 3: Qualitative example of structured recursive knowledge acquisition. Starting from an acute appendicitis question, MapSteal expands into related directions involving complications, patient populations, and treatment constraints, followed by context-specific questions. The figure displays 10 selected nodes from a real 14-node executed acquisition tree. Questions are shown verbatim, and arrows represent recorded parent–child links. The complete tree is provided in Appendix C.2 .
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
LoRA rank
16
LoRA alpha
32
LoRA dropout
0.05
Target modules
gate, up, down projections
Learning rate
3×10−4
Training epochs
2
Appendix
Table 6: LoRA hyperparameters used for MapSteal Student adaptation.
Stage
Runs
Time (h)
MapSteal LoRA training
18
6.3
QEDKS LoRA training
18
6.6
QEDKS acquisition
18
∼ 36.0
EvoKD online acquisition/training
18
∼ 54.0
Final evaluation (all methods)
54
22.4
Appendix
Table 7: Recorded GPU time for the final experiments. Acquisition and online-training durations include Teacher API waiting time. LoRA training required 15–19 minutes per seed for 2B, 20–26 minutes for 4B, and 20–25 minutes for 9B Students. Final evaluation covered all 54 adapters, requiring 7.3, 7.7, and 7.4 GPU-hours for MapSteal, QEDKS-Adapted, and EvoKD-Adapted, respectively.
Figure 4: Acquisition depth and expansion operator distributions under different initial root counts. Each configuration contains 460 executed acquisition nodes. Depth statistics include the acquisition roots but exclude the shared cold-start QA pairs.
Metric
R1
R10
R20
R35
Recursive nodes
459
450
440
425
Mean depth
5.27
2.86
2.37
1.87
Max depth
6
5
5
4
CONDITION_DEPTH
100
133
113
108
Non-empty Condition (%)
37.8
42.8
33.0
29.1
Training QA after QC
500
498
496
495
Appendix
Table 8: Acquisition statistics under different initial root counts. All configurations use 460 successful Teacher acquisition queries.
Figure 5: Extended QA budget scaling of MapSteal on Qwen3.5-4B for Medicine, under the LoRA recipe (learning rate 2×10−4 , three epochs, all seven LoRA target modules). The y -axis shows accuracy gain over the pristine Student in percentage points. Results show mean ± sample standard deviation over three training seeds using one fixed nested acquisition trajectory. The budget counts successfully acquired QA supervision, including the 40-example seed set, rather than API requests. B0 is the pristine Student without an adapter, and the dashed horizontal line marks zero gain.
Figure 6: Complete acquisition forests of Simplified OF (left) and Full MapSteal (right). Both methods execute 460 acquisition questions from the same 35 roots. Nodes are colored by depth, and edges indicate recorded parent–child relationships.
Figure 7: Complete executed acquisition tree for an acute appendicitis root in Full MapSteal. All 14 executed nodes are shown with their original questions and recorded parent–child links. The selected nodes displayed in the main-text qualitative example are part of this tree.
Figure 8: Condition transitions in a real acquisition lineage rooted in multiple sclerosis. CONDITION_DEPTH introduces and later replaces the condition, while NEW_TARGET preserves the existing condition. A separate NEW_FACET branch explores another facet. All displayed nodes and edges are taken from the executed acquisition trajectory.
Domain
Roots
Admit/call
Novelty
Δacq
95% CI
Seeds
Panel
Medicine
35
2.57
0.179
+1.59
[+0.37,+2.82]
3
Medical3
CS
46
1.97
0.250
−0.57
–
3
MMLU-CS
Law
48
1.72
0.257
−2.35
[−3.57,−1.14]
3
LawMacro
Biology
42
2.39
0.213
+0.35
–
1
MMLU-Bio
Business
64
–
–
−0.20
[−2.31,+1.89]
1
MMLU-Business
Chemistry
48
2.18
0.257
+0.99
[−0.55,+2.47]
3
Broad3
Appendix
Table 9: Cross-domain results with Qwen3.5-4B. Δacq measures the accuracy difference over the matched root-only baseline, except for Medicine, which uses Seed40-only. Acquisition statistics are computed over the first 460 successful executions, including initial roots. Confidence intervals are reported in percentage points.
Domain
Student
Primary Δ [95% CI]
Independent2 Δ [95% CI]
Chemistry
2B
−0.89[−2.62,+0.81]
−0.36[−1.19,+0.47]
4B
+0.99[−0.55,+2.47]
−0.36[−1.20,+0.47]
9B
+1.79[+0.04,+3.49]
−0.77[−1.69,+0.12]
Cybersecurity
2B
+1.51[+0.78,+2.24]
–
4B
+0.88[+0.27,+1.49]
–
9B
+1.13[+0.56,+1.70]
–
Appendix
Table 10: Incremental acquisition gains across Student scales (B500 minus root-only, pp). Primary evaluation uses Broad3 for Chemistry and CyberMacro for Cybersecurity. Independent2 is an additional Chemistry evaluation averaging ChemBench MCQ and SuperGPQA Chemistry.
Medicine
Run
MedMCQA
MedQA
MedXpert
Seed 42
31.20
31.42
10.69
Seed 43
44.80
45.56
12.69
Seed 44
45.60
46.58
13.80
40.53±8.09
41.19±8.47
12.39±1.57
Cybersecurity
Appendix
Table 11: Individual EvoKD runs with Qwen3.5-2B. Results are accuracy (%); the final row reports mean ± sample SD over three independent runs.
Domain
Method
QA Rows
Input (K)
Output (K)
Cost ($)
Medicine
MapSteal
495
1278.6
318.3
5.10
EvoKD
504
132.3±24.8
54.8±8.3
0.70±0.12
QEDKS
500
439.8±6.4
53.9±1.5
1.31±0.02
Cybersecurity
MapSteal
500
1268.9
294.1
4.89
EvoKD
504
119.6±2.4
50.3±0.3
0.64±0.01
QEDKS
500
241.6±0.2
55.1±0.2
0.92±0.00
Appendix
Table 12: Recorded Teacher token usage and estimated acquisition costs under the nominal B500 supervision budget. Token counts are reported in thousands (K). Costs are reconstructed from archived usage records rather than verified invoices. Some EvoKD records have incomplete Teacher-call accounting.
Metric
Count
Rate
Initially incorrect
195
–
Excluded cases
16
–
Evaluated errors
179
100.0%
Errors persisted
50
27.9%
Correct after reformulation
129
72.1%
Appendix
Table 13: Error persistence under question reformulation in a preliminary Medicine diagnostic.
Fine-tuning large language models (LLMs) with high-quality knowledge has been shown to enhance their performance effectively. However, there is a paucity of research on the depth of domain-specific knowledge comprehension by LLMs and the application of targeted active learning to improve their expertise. To address this gap, we introduce the Knowledge-Aware Active Learning (KA2L) framework. This framework assesses LLMs' mastery of specific knowledge points to aid in constructing unanswerable or unknowable questions through latent space analysis. This active learning strategy enhances training efficiency by focusing on knowledge the model has yet to master, thereby minimizing redundancy in learning already acquired information. This study innovatively employs a knowledge distribution probing technique to examine the hidden states of specific Transformer layers and identify the distribution of known and unknown knowledge within the LLM. Additionally, a hidden-state decoding method is proposed to generate numerous unknown questions in natural language from the latent knowledge space. In our experiments, we selected nine open-source LLMs to validate the effectiveness of the proposed framework. Results indicate that KA2L not only significantly reduces 50% annotation and computation costs across two open-domain and one vertical-domain dataset but also achieves better performance, offering valuable insights into active learning strategies for LLMs. The code is available at https://github.com/greenjerry/KA2L.
Haoxuan Yin, Chen Tang, Yangfan Wang +2
Faculty of Computing, Harbin Institute of Technology, Harbin, 150001, China · Institute for Advanced Algorithms Research, Shanghai, 201306, China · National Key Laboratory of Smart Farm Technologies and Systems, Harbin, 150001, China
Knowledge distillation from large language models (LLMs) assumes that the teacher's output distribution is a high-quality training signal. On reasoning tasks, this assumption is frequently violated. A model's intermediate representations may encode the correct answer, yet this information is lost or distorted through the vocabulary projection, where prompt formatting and answer-token choices creates brittle, noisy outputs. We introduce \method{}, a distillation framework that bypasses this bottleneck by training lightweight probes on frozen teacher hidden states and using the probe's predictions, rather than output logits, as supervision for student training. This simple change yields consistent improvements across four reasoning benchmarks (AQuA-RAT, ARC Easy/Challenge, and MMLU), with gains most pronounced under limited data. Probes trained on intermediate representations provide cleaner labels than the teacher's own outputs, effectively denoising the distillation signal. \method{} requires no architectural changes to student or teacher, is architecture-agnostic, and adds minimal compute since probe training is cheap and teacher representations can be cached. By exploiting internal representations, \method{} enables practitioners to extract more value from large teacher models without additional training data or architectural complexity.
Ryan Brown, Chris Russell
Oxford Internet Institute, University of Oxford, Oxford, United Kingdom.
Modern language models are trained on heterogeneous web-scale text corpora. Consequently, studying knowledge and skill acquisition is difficult, as prior exposure to related content is hard to characterize. To address this challenge, we introduce LittleCurriculum, a curated 88B-token pretraining corpus tailored to U.S. elementary school material, explicitly excluding concepts, facts, and vocabulary taught above Grade 5. Training a 5B-parameter LLM from scratch on LittleCurriculum yields LittleLearner, a model with sufficient language competence for open-ended evaluation, yet with clear knowledge and capability boundaries mapped to interpretable curriculum guidelines. We release LittleCurriculum and LittleLearner as a developmentally restricted sandbox to study how models acquire, represent, and use data under a well-defined training scope. We illustrate the sandbox's utility in a first suite of experiments on injecting new knowledge through post-training and in-context learning. These methods let LittleLearner better utilize existing knowledge, but do not raise out-of-scope capabilities. Our findings underscore the value of this controlled environment for future investigations.