RESCUE: Repairing Language Model Errors to Sparse Circuits via Reinforcement Learning

Chuanpu Liu; Miao Yu; Yikai Cai; Yuanhe Zhang; Zhenhong Zhou; Li Sun; Zuming Jiang; Yufei Guo

cs.LGSep 29, 2026

RESCUE: Repairing Language Model Errors to Sparse Circuits via Reinforcement Learning

Authors: Chuanpu Liu, Miao Yu, Yikai Cai, Yuanhe Zhang, Zhenhong Zhou, Li Sun, Zuming Jiang, Yufei Guo

Organizations: Beijing University of Posts and Telecommunications · University of Hong Kong · Nanyang Technological University · China Aerospace Science and Industry Corporation

Abstract

Large language models (LLMs) exhibit strong general capabilities that mechanistic interpretability has attributed to sparse computational circuits. However, existing circuit studies emphasize preserving functionality or explaining safety, leaving the mechanisms underlying failures across a broader range of tasks largely unexplored. Extending circuit analysis from abilities to errors, we explore the perspective that such failures may likewise arise from erroneous internal computations and that targeted tuning of the corresponding parameters can correct such errors while largely preserving other capabilities. Motivated by this insight, we introduce RESCUE (Reasoning-Error Sparse-Circuit Uncovering and Editing), a framework that localizes error-associated circuits and surgically repairs them for performance enhancement. General tasks typically involve multi-step reasoning and long-form generation, where early deviations can cause prefixes to drift from supervised references, leading SFT-based mask optimization to overlook circuits involved in generation-time errors. RESCUE therefore refines these masks through reinforcement learning with multiple masked-model rollouts, improving their relevance to observed task failures. Finally, RESCUE introduces a pruning technique and precisely fine-tunes error circuits to correct task failures, thereby translating error localization into a sparse and targeted model update. We validate RESCUE on heterogeneous repair sets across two domains: (1) mathematical reasoning, identifying a math error circuit of 1.40% density whose repair raises accuracy from 6.0% to 75.5%; and (2) medical QA, where a similarly compact 1.44% circuit improves repair-set accuracy from 0% to 81%. Our code is available at: https://github.com/chuanpupig/RESCUE.

Figures & tables

Figure 1: Overview of RESCUE , with complementary repair and preservation signals ( Left ), the sparse-circuit localization and tuning framework ( Middle ), and targeted repair generations ( Right ).

Figure 2: Post-tuning accuracy after heterogeneous GSM8K repair; Aggregate Evaluation is the macro-average over the eight non-target benchmarks in Section 5.1 . The panels use different truncated y-axis ranges for readability, with exact percentages shown above each bar.

Model	Error Pattern	Base (Acc.)	RESCUE Abl. (Acc.)	$\Delta$ (pp)	Circuit
Qwen3-8B	Misleading Premise Back-solving	2%	93%	+91	0.32%
	Dynamic State Tracking	1%	91%	+90	0.31%
	Dropped-lowest Average	4%	94%	+90	0.26%
	Declining Group Accumulation	2%	76%	+74	0.44%
	Multiplicative Increment Back-solving	0%	91%	+91	0.39%
Llama-3.1-8B- Instruct	Cumulative Target Gap	1%	95%	+94	0.62%

Table 1: Pattern-specific circuit ablation. Circuit denotes the proportion of selected MLP rows.

Model	Error Pattern	Rephrased(Acc.)	Ablation (Acc.)	$\Delta$ (pp)
Qwen3-8B	Misleading Premise Back-solving	28%	42%	+14
	Dynamic State Tracking	17%	25%	+8
	Dropped-lowest Average	3%	16%	+13
	Declining Group Accumulation	1%	18%	+17
	Multiplicative Increment Back-solving	0%	23%	+23
Llama-3.1-8B- Instruct	Cumulative Target Gap	25%	60%	+35

Table 2: Cross-rephrase transfer of pattern-specific error circuits. Accuracy is measured over 100 rephrased examples before and after ablating the circuit localized from the original formulation.

Figure 3: Density-matched random-circuit controls. Pale-blue lines denote their means, while orange dashed and red solid lines denote Base and RESCUE, respectively.

Figure 4: Full-set ablation accuracy (%) during sequential repair for (a) Qwen3-8B and (b) Llama-3.1-8B-Instruct. AR1–AR5 denote repair stages; pattern order follows Table 1.

Model	Method	Repair-set (Acc.)	Circuit	MedMCQA	Aggregate Eval.
		Targeted Repair		Post-tuning Evaluation
Qwen3-8B	Base	3.0%	–	59%	66.63%
	LoRA	65.0%	–	60%	64.75%
	RESCUE	78.5%	1.47%	60%	66.75%
Llama-3.1-8B-Instruct	Base	0.0%	–	59%	62.38%
	LoRA	65.5%	–	57%	58.88%

Table 3: Cross-domain repair results on MedMCQA. Repair-set accuracy is measured after RESCUE and after LoRA. Aggregate Eval. is the mean accuracy over the eight benchmarks.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5: English translation of the prompt for generating pattern-specific GSM8K problems.

Panel of Figure 6 — Figure 6: English translation of the prompt for rephrasing pattern-specific problems.

Panel of Figure 7 — Figure 7: English translation of the prompt for minimally correcting erroneous reasoning.

Panel of Figure 8 — Figure 8: Illustrative minimum-intervention correction. Colored text marks the erroneous and revised quantities; unchanged reasoning is omitted for brevity.

Model	Benchmark	Base	LoRA	Supervised-only	RESCUE
Qwen3-8B	ARC-C	56	57	57	57
	HellaSwag	75	76	75	76
	WinoGrande	68	67	68	67
	PIQA	78	77	78	77
	TruthfulQA	36	36	36	36
	MMLU-Math	50	53	55	50

Appendix

Table 4: Detailed post-tuning accuracy (%) after heterogeneous GSM8K repair; Aggregate Eval. is the macro-average over the eight non-target benchmarks.

Model	Benchmark	Base	Misleading Premise Back-solving	Dynamic State Tracking	Dropped-lowest Average	Declining Group Accumulation	Multiplicative Increment Back-solving
Qwen3-8B	GSM8K	80	80	81	80	86	82
	MATH-500	75	76	75	77	74	75
	ARC-C	56	56	56	57	55	58
	HellaSwag	75	75	75	75	75	75
	WinoGrande	68	69	68	68	67	68
	PIQA	78	77	78	77	77	77

Appendix

Table 5: Post-tuning accuracy (%) after independently repairing each pattern-specific GSM8K dataset; Aggregate Eval. is the macro-average over the eight non-target benchmarks.

Figure 9: Layer-wise enrichment of localized error-circuit rows, normalized by each circuit’s overall selection density. Curves and shading show the mean and min–max range across five pattern-specific circuits;

E=1

denotes no enrichment.

Model		Misleading Premise Back-solving	Dynamic State Tracking
Qwen3-8B	Rephrased Base	28%	17%
	Transferred Abl.	42%	25%
	Re-localized Abl.	95%	95%
	$\Delta$ vs. Base (pp)	+67	+78
	Circuit	0.68%	0.69%
Model		Cumulative Target Gap	Percentage Risk

Appendix

Table 6: Re-localization on rephrased pattern-specific datasets. Transferred Abl. applies the original circuit, whereas Re-localized Abl. uses a circuit localized on the rephrased data; the bottom panel reports post-tuning accuracy.

Figure 10: Benchmark accuracy for the base models and their final states after five sequential repairs (AR5).

Model	Benchmark	Base	LoRA	RESCUE
Qwen3-8B	MedMCQA	59	60	60
	GSM8K	80	85	86
	ARC-C	56	57	58
	HellaSwag	75	76	76
	WinoGrande	68	68	69
	PIQA	78	76	79

Appendix

Table 7: Detailed post-tuning accuracy (%) for MedMCQA repair. Aggregate Eval. averages the eight benchmarks from ARC-C through BBH and excludes GSM8K.

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Large language models (LLMs) often exhibit flawed reasoning ability that undermines reliability. Existing approaches to improving reasoning typically treat it as a general and monolithic skill, applying broad training which is inefficient and unable to target specific reasoning errors. We introduce Reasoning Editing, a paradigm for selectively modifying specific reasoning patterns in LLMs while preserving other reasoning pathways. This task presents a fundamental trade-off between Generality, the ability of an edit to generalize across different tasks sharing the same reasoning pattern, and Locality, the ability to preserve other reasoning capabilities. Through systematic investigation, we uncover the Circuit-Interference Law: Edit interference between reasoning patterns is proportional to the overlap of their neural circuits. Guided by this principle, we propose REdit, the first framework to actively reshape neural circuits before editing, thereby modulating interference between reasoning patterns and mitigating the trade-off. REdit integrates three components: (i) Contrastive Circuit Reshaping, which directly addresses the generality-locality trade-off by disentangling overlapping circuits; (ii) Meta-Contrastive Learning, which extends transferability to novel reasoning patterns; and (iii) Dual-Level Protection, which preserves preexisting abilities by constraining reshaping update directions and regularizing task-level predictions. Extensive experiments with Qwen-2.5-3B on propositional logic reasoning tasks across three difficulty levels demonstrate that REdit consistently achieves superior generality and locality compared to baselines, with additional validation in mathematics showing broader potential. Our code is available at https://github.com/LzyFischer/REdit.

Abstract

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