Precedent-Informed Reasoning: Mitigating Overthinking in Large Reasoning Models via Test-Time Precedent Learning

Qianyue Wang; Jinwu Hu; Huanxiang Lin; Bolin Chen; Zhiquan Wen; Yaofo Chen; Yu Rong; Mingkui Tan

cs.AIFeb 16, 2026

Precedent-Informed Reasoning: Mitigating Overthinking in Large Reasoning Models via Test-Time Precedent Learning

Authors: Qianyue Wang, Jinwu Hu, Huanxiang Lin, Bolin Chen, Zhiquan Wen, Yaofo Chen, Yu Rong, Mingkui Tan

Organizations: South China University of Technology · Pazhou Laboratory · DAMO Academy, Alibaba Group

Abstract

Reasoning in Large Language Models (LLMs) often suffers from inefficient long chain-of-thought traces with redundant self-exploration and validation, which inflate computational costs and even degrade performance. Inspired by human reasoning patterns where people solve new problems by leveraging past related cases to constrain search spaces and reduce trial-and-error, we propose Precedent Informed Reasoning (PIR) transforming LRMs'reasoning paradigm from exhaustive self-exploration to guided learning from precedents. PIR addresses two key challenges: what precedents to adopt and how to utilize them. First, Adaptive Precedent Selection (APS) constructs, for each question and LRM, a compact set of precedents that are both semantically related and informative for the model. It ranks examples by a joint score with semantic similarity and model perplexity, then adapts the amount of precedents to maximize perplexity reduction. Second, Test-time Experience Internalization (TEI) is treated as the test-time learning on precedent-informed instruction, updating lightweight adapters to internalize solution patterns and use them as a prior during subsequent reasoning. Experiments across mathematical reasoning, scientific QA, and code generation demonstrate that PIR consistently shortens reasoning traces while maintaining or improving final accuracy across LLMs, yielding outstanding accuracy-efficiency trade-offs.

Figures & tables

Figure 1: The illustration of different reasoning paradigms. Unlike normal reasoning that relies on self-exploration, precedent-informed reasoning leverages precedent experience to reduce the search space, improving reasoning efficiency.

Panel of Figure 2 — Figure 2: The accuracy and length on DeepSeek-R1-Qwen2.5-7B/32B and QwQ-32B as incrementally vary the number of $RS$ -filtered precedents in the reasoning prompt. Best accuracy gains are achieved within the given reference budget. We evaluate 100 randomly sampled instances per dataset. Markers denote the best result for each model-dataset pair: ${\color[rgb]{0.122,0.467,0.706}\bullet}$ as MATH500, ${\color[rgb]{0.839,0.153,0.157}\blacksquare}$ as GPQA Diamond, ${\color[rgb]{0.173,0.616,0.173}\blacktriangle}$ as LiveCode Bench. See Appendix B for details.

Method	GSM8K		MATH500		AMC AIME		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$
DeepSeek-R1-7B	92.60	380.24	87.00	2576.49	58.33	3858.16	22.80	5020.86	32.68	5775.04
DeepSeek-R1-14B	92.60	265.91	86.00	2408.36	57.76	3523.09	24.66	4411.01	36.57	5432.53
DeepSeek-R1-32B	94.20	263.04	86.80	2269.37	59.92	3661.52	36.30	5028.59	41.02	5224.52
QwQ-32B Team (2025)	93.60	290.32	88.00	3318.15	63.00	4600.75	37.42	5585.19	42.99	5575.36
prompt to concise Wei et al. (2022)	94.00	182.42	90.50	2161.51	54.50	3286.95	31.98	4120.47	45.50	5611.31

Table 1: Accuracy (

\mathbf{acc.}

, %) and average thinking length (

\mathbf{token.}

) across methods and datasets. Best and second-best results are in bold and underlined . All methods including PIR use DeepSeek-R1-32B as the backbone model.

Dataset	PIR (w/o TLM)	PIR (full)
GSM8k	0.00	1.08
MATH500	0.18	2.64
AMC AIME	0.11	5.38
GPQA Diamond	0.57	5.81
LiveCodeBench	0.04	8.19

Table 2: Statistics of the occurrence of precedent reference behaviors before and after applying TEI . Details of the behavior detection are in Appendix G .

Method	GSM8K		MATH500		AMC_AIME		GPQA Diamond		LiveCodeBench
	$\mathbf{HT.}$	$\mathbf{HS.}$	$\mathbf{HT.}$	$\mathbf{HS.}$	$\mathbf{HT.}$	$\mathbf{HS.}$	$\mathbf{HT.}$	$\mathbf{HS.}$	$\mathbf{HT.}$	$\mathbf{HS.}$
DeepSeek-R1-32B	65.81	65.03	26.83	30.86	19.17	22.56	14.11	18.57	11.82	18.44
l1-max	60.20	64.90	41.97	37.78	23.06	28.00	36.96	37.20	33.63	29.17
s1-32B	73.97	69.22	59.92	39.18	32.15	33.64	42.46	40.65	34.79	35.56
DEER	77.00	71.80	59.10	41.18	39.62	44.97	40.08	38.46	34.39	30.42
SEAL	77.46	76.07	53.01	41.91	44.22	44.97	37.02	39.46	34.73	31.72

Table 3: The statistical results of attention score above average in one reasoning path in token (

\mathbf{HT.}

) and segment (

\mathbf{HS.}

) level. Best results are in bold . More calculation details are in Appendix H .

Method	GSM8K		MATH500		AMC AIME		GPQA Diamond		LiveCodeBench
	Time	GPU	Time	GPU	Time	GPU	Time	GPU	Time	GPU
DeepSeek-R1-32B	18.06	72.00	114.40	72.00	174.35	72.00	224.00	72.00	246.72	72.00
QwQ-32B	59.35	72.00	145.67	72.00	211.96	72.00	253.27	72.00	253.06	72.00
prompt to concise	27.43	72.00	104.15	72.00	142.28	72.00	161.92	72.00	242.33	72.00
s1-32B	140.48	72.00	206.75	72.00	226.54	72.00	49.05	72.00	191.75	72.00
l1-max	23.19	40.00	51.15	40.00	49.30	40.00	58.34	40.00	62.07	40.00

Table 4: Time (seconds) and GPU memory (GB) cost of different methods across datasets. Within an A800, PIR is the second-fastest method in most case, with latency close to DEER (best) and substantially faster than the base model. With accuracy improvements over DEER (Table 1 ), PIR offers a favorable accuracy–efficient trade-off.

Method	GSM8K		MATH500		AMC AIME		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$
DeepSeek-R1-32B	94.20	263.04	86.80	2269.37	59.92	3661.52	36.30	5028.59	41.02	5224.52
w/o APS	94.60	253.22	88.80	1819.20	61.80	3472.31	55.15	4219.80	45.02	5045.93
w/o TEI	95.40	281.37	90.60	3725.20	63.60	3933.19	56.88	5169.49	46.46	5383.76
PIR (Ours)	95.60	197.03	93.20	1485.36	67.40	2935.83	65.22	3024.81	57.11	4023.37

Table 5: Ablation results. w/o reference example removes reference examples from input context. w/o instruction adaptation disables test-time adaption and uses only precedent informed prompting for reasoning.

Panel of Figure 3 — Figure 3: Scalability of PIR across different reasoning models, with average accuracy (%) and reasoning tokens on different models reported for each dataset.

Sampling	MATH500		GPQA Diamond		LiveCodeBench
Strategy	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$
e=0	88.80	1819.20	36.15	4219.80	40.02	5224.52
e=1	87.00	2517.10	37.21	3291.51	36.54	5193.00
e=2	89.00	2239.31	49.30	3968.34	40.38	5840.62
e=3	94.00	2345.72	32.79	4186.22	38.46	4991.40
e=4	90.00	2154.91	35.88	4173.04	42.31	4919.39

Table 6: Comparison of example selection strategies under the same test-time experience internalization setting. We isolate the effect of PIR’s dual-dimension, adaptive selection by contrasting it with fixed-size (

e=n

) and single-dimension strategies (random, semantic-only, perplexity-only and SIFT Hübotter et al. (2025) ). See Appendix J.2 for details of settings.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

	MATH500		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$
e=0	87.00	2576.49	41.86	5482.81	21.15	25058.90
e=1	88.00	2019.90	40.00	4411.38	19.23	25189.14
e=2	82.00	1754.70	42.00	4110.14	28.84	22101.56
e=3	82.00	1655.82	46.00	3943.48	36.53	23313.76
e=4	86.00	2109.38	48.00	4069.18	30.76	24710.72

Appendix

Table 7: The result of pre-experiment for DeepSeek-R1-Distilled-Qwen2.5-7B.

e=k

means there are k examples provided in the input prompt.

	MATH500		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{len.}$	$\mathbf{acc.}$	$\mathbf{len.}$	$\mathbf{acc.}$	$\mathbf{len.}$
e=0	91.00	3055.53	63.95	9243.30	55.76	19482.96
e=1	92.00	2285.34	46.51	8706.31	53.84	16686.50
e=2	88.00	3101.46	66.67	6267.77	57.69	14190.69
e=3	94.00	2660.18	55.81	4466.50	50.00	14973.87
e=4	88.00	3766.13	68.60	3482.04	48.07	13135.62

Appendix

Table 8: The result of pre-experiment for DeepSeek-R1-Distilled-Qwen2.5-32B.

e=k

means there are k examples provided in the input prompt.

	MATH500		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{len.}$	$\mathbf{acc.}$	$\mathbf{len.}$	$\mathbf{acc.}$	$\mathbf{len.}$
e=0	92.00	3671.68	65.11	9242.30	57.69	13973.98
e=1	91.00	2284.34	48.84	8705.31	59.61	14082.94
e=2	92.00	3100.47	66.67	6266.77	61.54	13747.86
e=3	93.00	2659.18	55.81	4465.50	50.00	13556.00
e=4	88.00	3765.13	68.60	3481.04	51.06	11775.93

Appendix

Table 9: The result of pre-experiment for QwQ-32B.

e=k

means there are k examples provided in the input prompt.

	GSM8K	MATH500	AMC AIME	GPQA Diamond	LiveCodeBench
precedent	2000	2000	2000	700	880
test	500	500	500	200	175

Appendix

Table 10: Sample Counts of Different Datasets for Precedent and Test Samples

Method	GSM8K		MATH500		AMC_AIME		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$
DeepSeek-R1-7B	92.60	440.39	88.91	4519.88	60.20	9305.71	27.45	17040.71	37.10	20331.73
DeepSeek-R1-14B	93.40	465.91	89.80	3973.30	60.20	7440.76	47.64	9678.51	47.95	16099.46
DeepSeek-R1-32B	95.00	464.54	91.00	4020.06	66.00	7312.36	53.80	11733.01	53.40	17384.53
QwQ-32B	96.20	1261.63	94.29	3875.44	66.90	6096.18	53.15	11732.34	57.32	15163.50

Appendix

Table 11: Accuracy (

\mathbf{acc.}

, %) and average reasoning length (

\mathbf{token.}

) of models under a 32k context window.

Method	GSM8K		MATH500		AMC_AIME		GPQA Diamond		LiveCodeBench
	Adapt.	Reason.	Adapt.	Reason.	Adapt.	Reason.	Adapt.	Reason.	Adapt.	Reason.
Ours (DeepSeek-R1-32B)	0.99	30.672	1.13	45.52	1.34	53.23	1.05	46.66	1.3	54.5

Appendix

Table 12: Stage time analysis.

\mathbf{Adapt.}

and

\mathbf{Reason.}

represent time adaptation and time reasoning respectively.

Method	GSM8K		MATH500		AMC_AIME		GPQA Diamond		LiveCodeBench
	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$	$\mathbf{acc.}$	$\mathbf{token.}$
QwQ-32B	92.40	1672.23	88.00	3318.15	64.45	5297.53	48.84	6132.83	30.77	6723.94
Ours(QwQ-32B)	95.80	738.24	90.00	1557.84	68.77	2126.18	55.56	4033.46	34.62	5587.40
DeepSeek-R1-7B	89.60	478.28	87.00	2576.49	62.53	2207.90	41.86	5482.81	15.38	7055.57
Ours(DeepSeek-R1-7B)	92.60	362.50	88.80	2055.53	64.40	1475.00	45.21	4862.41	19.25	6568.69
DeepSeek-R1-14B	90.80	439.25	86.00	2408.36	63.75	4223.15	31.40	5241.13	21.15	6433.59

Appendix

Table 13: The details result of scalability of PIR across different reasoning models.

Dataset	Num.
GSM8K	1.19
MATH500	1.56
AMC_AIME	2.73
GPQA Diamond	2.43
LiveCodeBench	2.23

Appendix

Table 14: Average number of dynamic precedents selected for different datasets.

Efficient Language Model Reasoning

Efficient language model reasoning studies how to improve problem-solving accuracy while reducing inference, memory, latency, and training costs.

See all 370 papers

Understanding and Mitigating Premature Confidence for Better LLM Reasoning
May 23, 2026Jingchu Gai, Guanning Zeng, Christina Baek +4Confidence Estimation in Language Models RL for Language Model Reasoning
1Carnegie Mellon University · 2Tsinghua University
Draft-Thinking: Learning Efficient Reasoning in Long Chain-of-Thought LLMs
Feb 28, 2026Jie Cao, Tianwei Lin, Juekai Lin +7Efficient Language Model Reasoning CoT Reasoning
Zhejiang University · Tencent
OS-Pruner: Pruning Chains-of-Thought of Reasoning Models via Optimal Stopping
Jul 13, 2026Mohammed Ehab, Aymane El Gadarri, Vivek F. Farias +2Efficient Language Model Reasoning Sequential Decision Making
MIT · Columbia Business School

May 23, 2026J/K move · Enter open · S save

Understanding and Mitigating Premature Confidence for Better LLM Reasoning

Jingchu Gai, Guanning Zeng, Christina Baek, Chen Wu+3

1Carnegie Mellon University · 2Tsinghua University

Confidence Estimation in Language Models RL for Language Model Reasoning LLM Uncertainty Estimation LLM Reasoning

Open paper AskPDF arXiv

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Abstract

Efficient Language Model Reasoning

Explore similar work

Understanding and Mitigating Premature Confidence for Better LLM Reasoning

Draft-Thinking: Learning Efficient Reasoning in Long Chain-of-Thought LLMs

OS-Pruner: Pruning Chains-of-Thought of Reasoning Models via Optimal Stopping