CORE: Conflict-Oriented Reasoning Elimination for Verifiable Language-Model Search

Siyu Song; Rui Xu; Jia Lin; Kai Liu; Weifang Wang

cs.CLSep 30, 2026

CORE: Conflict-Oriented Reasoning Elimination for Verifiable Language-Model Search

Authors: Siyu Song, Rui Xu, Jia Lin, Kai Liu, Weifang Wang

Organizations: School of Computer Science and Technology, School of Computer Science and Engineering · School of Information Science and Engineering, Sun Yat-sen University · College of Computer Science, College of Computer Science

Abstract

Test-time reasoning systems often respond to failure by restarting or revising the latest step, even when an earlier decision caused the error. We introduce CORE, a search controller that requests a certified conflict core from a verifier, backjumps to the latest decision in that core, and caches the conflict to avoid repeating it. Under sound verification, finite branching and depth, and exhaustive proposals, the uncapped search is complete and never prunes a valid solution. On 2,000 planted graph-coloring instances with matched proposals and an exact verifier, CORE reduces median verifier calls by 39.8% at 30 variables and 35.0% at 36 variables relative to chronological repair; caching further improves on backjumping alone. Across five reasoning tasks, CORE achieves 75.9% mean success with Qwen2.5-7B-Instruct and 84.2% with Qwen3-8B, compared with 72.5% and 81.8% for Tree of Thoughts. It also uses fewer verifier calls and generated tokens on both backbones. These results show the value of using certified failure explanations to direct language-model search.

Figures & tables

Panel of Figure 1 — Figure 1: Illustration of Core . A proposer extends a decision trajectory and an external verifier checks it. The highlighted decisions $d_{2}$ and $d_{5}$ form a conflict core, while gray decisions are irrelevant to this failure. The controller learns the core, backjumps to $d_{5}$ , and rejects future candidates that contain both conflicting decisions.

Panel of Figure 2 — Figure 2: The same failure under matched decision order. Chronological repair retreats through $d_{4}$ and $d_{3}$ before reconsidering $d_{2}$ . Core uses $C=\{d_{1},d_{2}\}$ to jump directly to $d_{2}$ and caches the conflict to prune its supersets. Gray decisions are absent from the core.

Figure 3: Median verifier calls over 500 paired instances per size. All methods use the same proposal order and exact verifier.

$n$	Chron.	CORE-BJ	Core	$\Delta$
18	32.0	31.0	31.0	$-3.1\%$
24	95.0	70.0	69.0	$-27.4\%$
30	223.5	147.0	134.5	$-39.8\%$
36	267.0	189.0	173.5	$-35.0\%$

Table 1: Median verifier calls.

\Delta

compares Core with chronological repair. Every method solved every main-test instance within budget.

Qwen2.5-7B-Instruct
Method	GSM8K (500)	MATH-500 (500)	24-Game (200)	Blocks (200)	HumanEval (164)	Mean	Verifier calls	Tokens (k)
Direct CoT	72.4	42.8	61.0	41.0	58.5	55.1	1.0	1.3
Self-Consistency-8	80.6	51.2	78.0	48.0	64.0	64.4	8.0	9.6
Self-Refine-4	78.1	49.6	75.0	55.0	67.7	65.1	3.2	4.9
Tree of Thoughts	82.0	55.4	88.0	67.0	70.1	72.5	18.6	14.2
Core	83.8	58.6	92.0	73.0	72.0	75.9	10.9	9.1

Table 2: End-to-end task success rates (%) for both backbones. Calls and generated tokens are per-problem means. Mean success averages the five task columns; sample counts are shown in the headers.

Figure 4: End-to-end results. Left: mean task success against mean verifier calls for both backbones. Right: Qwen2.5-7B-Instruct ablations of core memory, backjumping, and conflict precision.

Variant	Success	Calls	Core size	Jump
Core	75.9	10.9	2.7	3.8
No core memory	73.8	12.7	2.7	3.6
No backjumping	72.9	15.4	2.8	1.0
Full-prefix conflicts	71.8	16.1	8.9	1.2
Soft heuristic cores	74.9	14.3	3.4	2.9

Table 3: Qwen2.5-7B-Instruct ablations. Success is mean task accuracy (%); other columns are per-problem means. “Jump” is the number of decision levels removed per repair.

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CORE: Contrastive Reflection Enables Rapid Improvements in Reasoning

Linas Nasvytis, Simon Jerome Han, Ben Prystawski, Satchel Grant+2

Stanford University

LLM Self-Refinement Efficient Language Model Reasoning Language Model Self-Improvement LLM Reasoning Reasoning Trace Analysis

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Language models can use verifiable rewards to improve at a wide variety of reasoning tasks. However, both parametric (e.g. RLVR) and non-parametric (e.g. prompt optimization) approaches to doing so typically require hundreds of training samples and thousands of model rollouts, making them expensive in the best case and intractable in the worst. To address this challenge, we introduce Contrastive Reflection (CORE), a non-parametric learning algorithm that compares past reasoning traces to generate insights: short natural-language descriptions of reasoning strategies and constraints that capture differences between successful and unsuccessful problem attempts. Across four reasoning tasks, we demonstrate that CORE enables more rapid improvement than both parametric (GRPO) and non-parametric (GEPA, episodic RAG, and MemRL) methods, while using fewer rollouts. Under fixed rollout budgets with as few as five training samples, CORE achieves the strongest performance in most task-data regimes. Finally, we highlight how CORE is substantially more context-efficient than non-parametric baselines, requiring fewer prompt tokens while storing learned knowledge as compact, interpretable natural-language insights. Our results therefore suggest that distilling contrasts between successful and unsuccessful reasoning traces into abstract and useful insights can provide a more efficient and interpretable route to model self-improvement than weight updates, prompt optimization, or direct reuse of stored reasoning traces.

Abstract

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