To Reason but Not to Stop: Understanding and Recovering Pruned Large Reasoning Models

Minh-Anh Nguyen; Nguyen T. Ha Lan; Xiyan Fu; Dung D. Le; Wei Lu

cs.CLOct 14, 2026

To Reason but Not to Stop: Understanding and Recovering Pruned Large Reasoning Models

Authors: Minh-Anh Nguyen, Nguyen T. Ha Lan, Xiyan Fu, Dung D. Le, Wei Lu

Organizations: Nanyang Technological University, Singapore · VinUniversity, Vietnam

Abstract

Weight pruning can degrade the accuracy of large reasoning models (LRMs), yet it remains unclear whether it damages reasoning itself. We find that much of this degradation stems from a failure to stop rather than to reason. As sparsity increases, pruned LRMs increasingly fail to terminate within the token budget, often after the correct answer has appeared in their reasoning, instead falling into repetitive loops, even though they still recognize where the dense model would stop. We further find that the hidden-state difference between terminating and looping continuations is consistent across pruned checkpoints, suggesting a shared direction associated with committing to an answer. Building on this, we propose Termination-Guided Activation Steering (TGAS), a training-free method that adds this direction to the residual stream at inference time. Across six LRMs, three pruning pipelines, and math and code benchmarks, TGAS improves termination and overall accuracy while reducing repetitive reasoning and generation length, showing that this failure is actionable.

Figures & tables

Figure 1: Accuracy (left) and non-termination rate (right) on AIME-25 across pruning settings (SparseGPT with OBC calibration, 16,384-token budget, averaged over 4 runs). Accuracy decreases as non-termination becomes more frequent.

Figure 2: Gold answers in non-terminating reasoning traces of DeepSeek models on MATH-500. Left: an example of reasoning divergence, where the pruned model continues reasoning after reaching the correct answer. Right: the fraction of traces containing the gold answer and the median position of its first occurrence.

n

denotes the number of non-terminating samples.

Model	Ckpt	Kept	No-Term.	Wrong	Kept $\mid$ term
DS-Qwen -7B	obc_50	91.7 $\pm$ 0.8	3.8 $\pm$ 0.3	4.5 $\pm$ 0.6	95.3 $\pm$ 0.6
DS-Qwen -7B	obc_60	77.8 $\pm$ 0.7	16.8 $\pm$ 0.1	5.4 $\pm$ 0.6	93.5 $\pm$ 0.7
DS-Qwen -14B	obc_50	89.2 $\pm$ 0.6	2.4 $\pm$ 1.5	8.4 $\pm$ 0.9	91.4 $\pm$ 0.8
DS-Qwen -14B	obc_60	74.3 $\pm$ 2.8	16.4 $\pm$ 1.9	9.3 $\pm$ 0.9	88.9 $\pm$ 1.4
OT3-7B	obc_50	79.3 $\pm$ 2.9	13.1 $\pm$ 2.4	7.6 $\pm$ 1.9	91.3 $\pm$ 2.2
OT3-7B	obc_60	63.6 $\pm$ 3.4	29.8 $\pm$ 3.3	6.6 $\pm$ 1.8	90.6 $\pm$ 2.5

Table 1: Accuracy on MATH-500 problems correctly solved by the dense model. Kept : correct; No-Term. : reasoning fails to terminate; Wrong : terminated but incorrect; Kept

\mid

term : accuracy among terminated generations. From 50% to 60% sparsity, non-termination grows sharply while the terminated-but-wrong rate stays nearly flat, so accuracy among terminated generations remains high.

Figure 3: Non-termination rate and accuracy of DeepSeek models on AIME-25 under 16K- and 65K-token budgets.

		DS-Qwen-7B			DS-Qwen-14B
		obc_50	obc_60	obc_70	obc_50	obc_60	obc_70
AIME-25	$p(\texttt{</think>}{})$	0.998	0.957	0.036	0.995	0.854	0.073
AIME-25	Med. rank	0	0	5.5	0	0	2
MATH-500	$p(\texttt{</think>}{})$	0.996	0.924	0.040	0.998	0.907	0.130
MATH-500	Med. rank	0	0	7	0	0	3

Table 2: Teacher-forced stopping signal at the dense model’s STOP position: probability of </think> and its median rank (0 means </think> is the top prediction).

	DS-Qwen-7B				OT3-7B
	dense	obc_50	obc_60	obc_70	dense	obc_50	obc_60	obc_70
$n$	794	788	796	782	800	800	796	790
$\Delta_{\mathrm{cyc}}$	$-15.3$	$-11.9$	$-9.6$	$-5.0$	$-23.1$	$-15.8$	$-13.2$	$-5.6$
Entropy	1.55	1.51	1.41	1.44	1.03	1.22	1.33	1.60

Table 3: Log-probability ratio between cyclic and progressive continuations at decision points on AIME-25.

n

: number of decision points; Entropy : predictive entropy at the decision points. Less negative (larger)

\Delta_{\mathrm{cyc}}

values indicate a stronger preference for the repetitive continuation.

Figure 4: Progress and Cyclic behaviors illustration.

	DS-Qwen-7B				DS-Qwen-14B
	dense	obc_50	obc_60	obc_70	dense	obc_50	obc_60	obc_70
$P$ (cyc $\mid$ cyc)	0.029	0.283	0.327	0.307	0.000	0.203	0.271	0.324
$P$ (cyc $\mid$ prog)	0.026	0.043	0.064	0.085	0.029	0.033	0.059	0.081
Count (k)	1.3	51.5	85.7	113.4	0.8	47.3	68.3	136.8

Table 4: Transition dynamics between Cyclic and Progress paragraphs on AIME-25 from shared branch points.

P(\mathrm{cyc}\mid\mathrm{cyc})

measures loop persistence, while

P(\mathrm{cyc}\mid\mathrm{prog})

measures loop entry; Count : number of adjacent paragraph pairs, in thousands; dense rows have fewer pairs due to early termination, while pruned checkpoints retain reasoning divergence despite using dense correct traces.

Figure 5: Cosine similarity between termination-guided directions constructed from pruned DeepSeek models on MATH-500. We compare only checkpoints with sufficient positive-terminated and negative non-terminating samples; for example, all 1.5B checkpoints have at least 50 samples in each class. Directions constructed from different pruned checkpoints exhibit high cosine similarity.

			MATH-500		AIME-25		LiveCodeBench		Avg
Model	Ckpt	Method	Acc $\uparrow$	Term $\uparrow$	Acc $\uparrow$	Term $\uparrow$	Acc $\uparrow$	Term $\uparrow$	Acc $\uparrow$
OT3-1.5B	dense	Base	80.2 $\pm$ 1.6	87.2 $\pm$ 1.9	32.5 $\pm$ 1.7	39.2 $\pm$ 3.2	43.2 $\pm$ 2.9	57.4 $\pm$ 3.3	52.0
	obc_10	Base	79.6 $\pm$ 1.3	87.0 $\pm$ 0.5	34.2 $\pm$ 8.3	40.0 $\pm$ 2.7	43.4 $\pm$ 2.3	57.1 $\pm$ 2.6	52.4
		No-Repeat	79.2 $\pm$ 1.9	86.6 $\pm$ 2.2	35.0 $\pm$ 6.9	41.7 $\pm$ 6.9	38.9 $\pm$ 2.6	55.5 $\pm$ 1.6	51.0
		Forced-Answer	77.3 $\pm$ 3.0	—	29.2 $\pm$ 6.3	—	40.8 $\pm$ 2.6	—	49.1
		SEAL	77.1 $\pm$ 1.9	87.0 $\pm$ 2.0	41.7 $\pm$ 5.8	52.5 $\pm$ 5.7	38.7 $\pm$ 2.0	61.3 $\pm$ 5.8	52.5

Table 5: Training-free remedies for SparseGPT-pruned LRMs with OBC calibration. Acc is accuracy (%) and Term is the percentage of generations that terminate before the 16,384 token cap. For each checkpoint, the best accuracy is in bold and the second best is underlined . TGAS rows are shaded; the

\uparrow

subscript in Avg denotes its gain over the best competitor.

(a) RAC (SparseGPT)
		AIME-25		LiveCodeBench
Ckpt	Method	Acc	Term	Acc	Term
rac_10	Base	35.8 $\pm$ 5.0	79.2 $\pm$ 4.2	56.3 $\pm$ 1.8	85.0 $\pm$ 3.8
	No-Repeat	38.3 $\pm$ 5.8	80.0 $\pm$ 5.4	47.4 $\pm$ 3.1	85.8 $\pm$ 1.1
	Forced-Answer	33.3 $\pm$ 4.7	—	53.7 $\pm$ 1.2	—
	TGAS	39.2 $\pm$ 3.2	85.0 $\pm$ 6.9	58.7 $\pm$ 2.6	89.7 $\pm$ 3.0

Table 6: Training-free remedies for checkpoints pruned with (a) RAC and (b) C4-calibrated Wanda on DS-Qwen-7B. Acc is accuracy (%) and Term the share of generations that terminated (%).

		$\Delta_{\mathrm{cyc}}$ at decisions		DPs/1k
Model	Ckpt	U	S	U	S
DS-Qwen -7B	obc_50	$-15.3$ $\pm$ 0.5	$-17.1$ $\pm$ 0.5	9.0	5.4
DS-Qwen -7B	obc_60	$-12.0$ $\pm$ 0.4	$-15.4$ $\pm$ 0.5	12.3	5.8
DS-Qwen -14B	obc_50	$-14.7$ $\pm$ 0.4	$-17.9$ $\pm$ 0.5	7.2	5.5
DS-Qwen -14B	obc_60	$-12.7$ $\pm$ 0.4	$-14.0$ $\pm$ 0.4	11.5	6.8

Table 7:

\Delta_{\mathrm{cyc}}

at decision points, defined in Section 3.2 , on MATH-500, unsteered ( U ) vs. steered with TGAS ( S ). DPs/1k : decision points per 1,000 tokens.

Appendix figures & tables29 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Gold answers appearing in reasoning traces graded incorrect for DeepSeek-R1-Distill-Qwen models. Explicit and Conclusive denote gold-answer presence under nested detection rules.

comparison	$n$	agreement	$\kappa$
Conclusive vs judge	250	96.0%	0.898
Explicit vs judge	250	84.8%	0.782

Appendix

Table 9: Agreement between our automated measurements and the independent Gemini-2.5-Flash judge.

Panel of Figure 8 — Figure 8: Prompt used to independently validate whether a reasoning trace asserts the reference answer as its own result.

		MATH-500 L4–5					AIME-25					OpenR1-Math
Model	Ckpt	Prob.	BP	POS	NEG	Len	Prob.	BP	POS	NEG	Len	Prob.	BP	POS	NEG	Len
Deepseek-R1-Distill -Qwen-1.5B	obc_40	$91$	$91$	$2780$	$132$	$1742$	$8$	$14$	$439$	$9$	$1515$	$112$	$120$	$3433$	$407$	$2585$
	obc_50			$2545$	$367$	$1575$			$410$	$38$	$1347$			$2948$	$892$	$2484$
	obc_60			$953$	$1959$	$2695$			$260$	$188$	$2076$			$1034$	$2806$	$3392$
	obc_70			$0$	$2912$	—			$0$	$448$	—			$0$	$960$	—
Deepseek-R1-Distill -Qwen-7B	obc_40	$80$	$80$	$2554$	$6$	$1577$	$8$	$13$	$415$	$1$	$1822$	$72$	$103$	$3229$	$67$	$2729$

Appendix

Table 10: Branch points and continuation outcomes across pruning ratios. Prob. denotes problems with at least one branch point; BP , the number of branch points; POS / NEG , self-terminating/non-terminating continuations; and Len , median positive-continuation length. Despite sharing prefixes from dense traces sufficient for correct answers, higher-pruned checkpoints produce more negative continuations and longer median continuation lengths.

Table 18

Figure 9: Cosine similarity between termination-guided directions from DeepSeek-R1-Distill-Qwen checkpoints. We include only checkpoints with sufficient positive and negative samples.

		AIME25		LCB		MATH-500 L4–5
family	level	$n$ kept	kept	$n$ kept	kept	$n$ kept	kept
DeepSeek-R1-Distill-Qwen-1.5B (OBC)	dense	27.0 $\pm$ 0.0	100	133.0 $\pm$ 2.8	100	197.0 $\pm$ 1.4	100
	sparse10	19.5 $\pm$ 0.7	72.2 $\pm$ 2.6%	107.5 $\pm$ 3.5	80.8 $\pm$ 0.9%	175.0 $\pm$ 2.8	88.8 $\pm$ 2.1%
	sparse50	15.0 $\pm$ 1.4	55.6 $\pm$ 5.2%	51.0 $\pm$ 4.2	38.3 $\pm$ 2.4%	133.5 $\pm$ 6.4	67.8 $\pm$ 2.7%
	sparse60	1.5 $\pm$ 0.7	5.6 $\pm$ 2.6%	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0%	39.5 $\pm$ 9.2	20.0 $\pm$ 4.5%
DeepSeek-R1-Distill-Qwen-7B (OBC)	dense	47.0 $\pm$ 5.7	100	223.5 $\pm$ 2.1	100	223.0 $\pm$ 2.8	100

Appendix

Table 13: Dense-correct generations retained by the pruned model.

n

kept : correct for both models; kept : fraction of dense-correct generations also solved by the pruned model. Values are mean

\pm

std.

		AIME25				LCB				MATH-500 L4–5
family	level	(a)	(b)	(c)	kept $\mid$ term.	(a)	(b)	(c)	kept $\mid$ term.	(a)	(b)	(c)	kept $\mid$ term.
DeepSeek-R1-Distill-Qwen-1.5B (OBC)	sparse10	19.5 (72)	2.5 (9)	5.0 (19)	79.7 $\pm$ 5.2%	107.5 (81)	4.5 (3)	21.0 (16)	83.7 $\pm$ 0.5%	175.0 (89)	5.5 (3)	16.5 (8)	91.4 $\pm$ 0.5%
	sparse50	15.0 (56)	6.5 (24)	5.5 (20)	73.1 $\pm$ 4.4%	51.0 (38)	50.5 (38)	31.5 (24)	61.8 $\pm$ 1.4%	133.5 (68)	38.0 (19)	25.5 (13)	83.9 $\pm$ 3.3%
	sparse60	1.5 (6)	22.5 (83)	3.0 (11)	35.0 $\pm$ 21.2%	0.0 (0)	132.5 (100)	0.5 (0)	0.0%	39.5 (20)	142.5 (72)	15.0 (8)	72.0 $\pm$ 8.5%
DeepSeek-R1-Distill-Qwen-7B (OBC)	sparse10	33.0 (71)	4.0 (9)	10.0 (21)	77.5 $\pm$ 9.5%	198.0 (89)	4.5 (2)	21.0 (9)	90.4 $\pm$ 1.3%	208.0 (93)	3.0 (1)	12.0 (5)	94.5 $\pm$ 1.3%
	sparse50	30.0 (64)	8.5 (18)	8.5 (18)	78.1 $\pm$ 3.5%	145.0 (65)	25.5 (11)	53.0 (24)	73.2 $\pm$ 1.0%	204.5 (92)	8.5 (4)	10.0 (4)	95.3 $\pm$ 0.6%

Appendix

Table 14: Breakdown of dense-correct generations under pruning. Each generation is (a) correct , (b) reasoning divergence (no </think> ), or (c) terminated-wrong ( </think> emitted but the final answer is incorrect). Values show mean count per run with the corresponding percentage in parentheses. Kept

\mid

term. denotes accuracy among terminated generations. Italics indicate fewer than 30 terminated dense-correct items.

Model	Level	Token Limit	Non-termination Rate	Accuracy	Accuracy $\mid$ Terminated	Recovered Traces	Recovered Correct
7B	dense	16,384	20.0%	42.5%	53.1%	—	—
7B	dense	65,536	3.3%	42.5%	44.0%	20 / 24 (83.3%)	0
7B	obc_10	16,384	20.0%	31.7%	39.6%	—	—
7B	obc_10	65,536	2.5%	31.7%	32.5%	21 / 24 (87.5%)	0
7B	obc_50	16,384	42.5%	30.0%	52.2%	—	—
7B	obc_50	65,536	12.5%	30.8%	35.2%	36 / 51 (70.6%)	2

Appendix

Table 15: Effect of increasing the generation budget from 16,384 to 65,536 tokens on the DeepSeek-R1-Distill-Qwen 7B and 14B models on AIME-25. A 65,536 row continues each generation non-termination at 16,384 from its own tokens; recovered = non-termination at 16,384 and terminated by 65,536.

		AIME-25						MATH-500 L4–5
Model	Ckpt	p( </think> )	Med. rank	logp STOP	logp </think> OTHER	$\Delta_{\text{close}}$	$\Delta_{\text{stop}}$	p( </think> )	Med. rank	logp STOP	logp </think> OTHER	$\Delta_{\text{close}}$	$\Delta_{\text{stop}}$
Deepseek-R1-Distill -Qwen-1.5B	obc_10	0.9999	0	$-0.000$	$-22.71$	$+22.71$	$+0.377$	0.9999	0	$-0.000$	$-23.11$	$+23.11$	$+0.374$
	obc_50	0.9804	0	$-0.020$	$-27.28$	$+27.26$	$+0.400$	0.9918	0	$-0.008$	$-26.51$	$+26.50$	$+0.428$
	obc_60	0.7273	0	$-0.379$	$-26.56$	$+26.18$	$+0.134$	0.6301	0	$-0.771$	$-26.06$	$+25.29$	$-0.226$
	obc_70	0.0351	44	$-9.192$	$-24.19$	$+14.99$	$-8.431$	0.0154	157.5	$-11.076$	$-23.84$	$+12.76$	$-10.229$
Deepseek-R1-Distill -Qwen-7B	obc_10	1.0000	0	$-0.000$	$-23.30$	$+23.30$	$+0.361$	0.9999	0	$-0.000$	$-24.15$	$+24.15$	$+0.349$

Appendix

Table 16: Teacher-forced evaluation of the stopping signal at the dense model’s </think> position. STOP denotes the position whose next token is the dense </think> , while OTHER includes all trace positions more than 50 tokens before STOP. Logp STOP is the mean log-probability of </think> at STOP. Logp </think> OTHER is the mean log-probability of </think> over OTHER positions, and

\Delta_{\text{close}}

= logp STOP

-

logp </think> OTHER.

\Delta_{\text{stop}}

= logp STOP

-

the mean log-probability of the token the dense model actually generated at OTHER positions. Rank 0 indicates that </think> is the model’s top prediction at STOP. All quantities are computed by teacher-forcing dense-model traces through each checkpoint.

		AIME-25					LCB					MATH-500 L4–5
Model	Ckpt	$n_{\mathrm{dec}}$	$n_{\mathrm{ctrl}}$	Dec.	Ctrl.	Ent.	$n_{\mathrm{dec}}$	$n_{\mathrm{ctrl}}$	Dec.	Ctrl.	Ent.	$n_{\mathrm{dec}}$	$n_{\mathrm{ctrl}}$	Dec.	Ctrl.	Ent.
DS-Qwen 1.5B	dense	796	200	$-13.0$	$-13.2$	1.60	720	200	$-16.7$	$-15.5$	1.46	684	200	$-14.9$	$-21.9$	1.55
	obc_10	794	200	$-13.4$	$-13.4$	1.62	734	200	$-16.0$	$-12.5$	1.44	690	200	$-15.3$	$-23.3$	1.57
	obc_50	786	194	$-8.4$	$-11.7$	1.32	788	192	$-8.2$	$-5.3$	1.48	686	200	$-10.2$	$-15.3$	1.35
	obc_60	762	182	$-3.8$	$-4.5$	1.33	756	172	$-2.7$	$-3.2$	1.33	762	198	$-5.6$	$-6.8$	1.32
	obc_70	524	154	$1.6$	$-1.2$	1.48	556	158	$2.2$	$-0.9$	1.60	506	160	$1.0$	$-0.8$	1.54

Appendix

Table 17: Log-probability ratio between cyclic and progressive continuations on AIME-25, LCB and MATH-500.

\Delta_{\mathrm{cyc}}=\log P(\mathrm{CYCLIC})-\log P(\mathrm{PROGRESS})

, scored over the next 32 tokens. Dec. is measured at decision points, Ctrl. at randomly sampled paragraph in the same traces; Ent. is the predictive entropy at the decision points.

n_{\mathrm{dec}}

is the number of decision points and

n_{\mathrm{ctrl}}

the number of control points. More negative means the model prefers the progressive continuation more strongly.

		MATH-500 L4–5			AIME-25
Model	Ckpt	$P$ (cyc $\mid$ cyc)	$P$ (cyc $\mid$ prog)	Count	$P$ (cyc $\mid$ cyc)	$P$ (cyc $\mid$ prog)	Count
DeepSeek-R1-Distill-Qwen 7B	dense	0.157	0.025	$4094$	0.029	0.026	$1296$
	obc_40	0.206	0.027	$155830$	0.230	0.031	$38947$
	obc_50	0.257	0.047	$207714$	0.283	0.043	$51479$
	obc_60	0.325	0.086	$434020$	0.327	0.064	$85675$
	obc_70	0.307	0.105	$596073$	0.307	0.085	$113353$

Appendix

Table 18: Transition dynamics between cyclic and progressive states on MATH-500 Levels 4–5 and AIME-25, measured on continuations from a shared dense branch point.

P(\mathrm{cyc}\mid\mathrm{cyc})

and

P(\mathrm{cyc}\mid\mathrm{prog})

measure loop persistence and loop entry over adjacent paragraph pairs; Count is the number of such pairs.

Table 26

(a) OpenR1-Math
Model	Levels	Transfer	Own	Shuffled	$p$
DS-Qwen-1.5B	40 $\to$ 50	0.973	0.976	0.839 / 0.950	0.005
DS-Qwen-1.5B	40 $\to$ 60	0.974	0.977	0.848 / 0.945	0.005
DS-Qwen-1.5B	50 $\to$ 40	0.971	0.970	0.833 / 0.940	0.005
DS-Qwen-1.5B	50 $\to$ 60	0.977	0.977	0.851 / 0.956	0.005
DS-Qwen-1.5B	60 $\to$ 40	0.960	0.970	0.827 / 0.933	0.010

Appendix

Table 21: Held-out ROC AUC for separating terminating from non-terminating continuations when a direction constructed at one sparsity level (%) is applied to another. Transfer : AUC of the source direction on the target’s held-out continuations; Own : AUC of the target’s own direction; Shuffled : mean / 95th percentile of the transfer AUC when the source labels are permuted (200 permutations), with permutation

p

-value

p

Figure 10: PCA of continuation representations at the steering layer on OpenR1-Math. For each model, PCA is fitted jointly on the continuations of all sparsity levels. Terminating continuations form a compact cluster, while non-terminating ones spread widely along the same PC1 at every sparsity level.

			Accuracy (%)			Under TGAS (%)
Model	Ckpt	#NT	Base	Oracle	TGAS	NT $\to$ Correct	Wrong $\to$ Correct	Kept
DS-Qwen-1.5B	dense	22	75.2 $\pm$ 0.5	75.8 $\pm$ 1.4	77.1 $\pm$ 5.4	19.6 $\pm$ 4.0	43.2 $\pm$ 9.5	90.9 $\pm$ 1.5
	obc_10	22	73.3 $\pm$ 2.7	73.7 $\pm$ 2.7	76.7 $\pm$ 0.0	29.0 $\pm$ 9.5	42.5 $\pm$ 6.5	90.7 $\pm$ 4.8
	obc_50	72	54.8 $\pm$ 2.4	57.4 $\pm$ 3.0	61.8 $\pm$ 4.9	33.7 $\pm$ 1.9	42.2 $\pm$ 13.9	82.2 $\pm$ 2.3
	obc_60	204	15.5 $\pm$ 3.0	32.6 $\pm$ 3.0	30.9 $\pm$ 1.1	25.8 $\pm$ 0.3	9.2 $\pm$ 5.5	65.8 $\pm$ 3.9
DS-Qwen-7B	dense	4	85.1 $\pm$ 1.1	85.1 $\pm$ 1.1	86.3 $\pm$ 1.9	16.6 $\pm$ 23.5	44.0 $\pm$ 3.7	94.2 $\pm$ 2.5

Appendix

Table 22: Headroom and recovery on MATH-500. #NT : number of non-terminating Base generations. Oracle : Base accuracy if every non-terminating generation that already states the gold answer explicitly were counted as correct. NT

\to

Correct and Wrong

\to

Correct : share of non-terminating and terminated-wrong Base generations that become correct under TGAS. Kept : share of Base-correct generations that remain correct.

			MATH-500		AIME-25		LiveCodeBench
Model	Ckpt	Method	Acc	Term	Acc	Term	Acc	Term
Deepseek-R1-Distill -Qwen-1.5B	dense	Base	75.2 $\pm$ 0.5	91.6 $\pm$ 0.0	22.5 $\pm$ 4.2	71.7 $\pm$ 5.8	34.5 $\pm$ 1.6	76.1 $\pm$ 1.8
		No-Repeat	71.0 $\pm$ 0.0	91.2 $\pm$ 0.5	22.5 $\pm$ 4.2	74.2 $\pm$ 7.4	27.6 $\pm$ 1.6	80.8 $\pm$ 3.9
		Forced-Answer	74.2 $\pm$ 2.4	—	22.5 $\pm$ 4.2	—	35.3 $\pm$ 1.8	—
		SEAL	73.7 $\pm$ 2.1	95.8 $\pm$ 0.6	18.3 $\pm$ 1.9	76.7 $\pm$ 6.1	35.0 $\pm$ 3.7	84.7 $\pm$ 3.3
		TGAS	77.1 $\pm$ 5.4	92.4 $\pm$ 1.3	25.8 $\pm$ 4.2	75.8 $\pm$ 5.7	36.8 $\pm$ 2.6	86.3 $\pm$ 3.7

Appendix

Table 23: Training-free remedies for SparseGPT-pruned LRMs with OBC calibration DeepSeek-R1-Distill-Qwen models. Acc. and Term. denote accuracy and termination rate, respectively. Forced-Answer’s Term. is not reported, since forcing ends every generation by design.

			MATH-500		AIME-25		LiveCodeBench
Model	Ckpt	Method	Acc	Term	Acc	Term	Acc	Term
Deepseek-R1-Distill -Llama-8B	dense	Base	82.4 $\pm$ 2.7	97.9 $\pm$ 0.8	34.2 $\pm$ 5.7	70.0 $\pm$ 11.2	58.7 $\pm$ 2.5	85.5 $\pm$ 1.8
		No-Repeat	83.0 $\pm$ 0.8	97.7 $\pm$ 0.0	35.0 $\pm$ 4.3	71.7 $\pm$ 3.3	44.7 $\pm$ 3.3	85.0 $\pm$ 1.3
		Forced-Answer	81.3 $\pm$ 1.6	—	30.8 $\pm$ 1.7	—	53.2 $\pm$ 1.1	—
		SEAL	80.2 $\pm$ 1.8	97.7 $\pm$ 0.3	32.5 $\pm$ 5.7	87.5 $\pm$ 4.2	57.9 $\pm$ 2.7	91.6 $\pm$ 2.3
		TGAS	84.0 $\pm$ 2.2	97.3 $\pm$ 0.0	38.3 $\pm$ 5.8	80.8 $\pm$ 3.2	60.8 $\pm$ 2.2	87.9 $\pm$ 1.8

Appendix

Table 24: Training-free remedies for SparseGPT-pruned LRMs with OBC calibration DeepSeek-R1-Distill-Llama and OpenThinker3 models. Acc. and Term. denote accuracy and termination rate, respectively. Forced-Answer’s Term. is not reported, since forcing ends every generation by design.

			MATH-500		AIME-25		LiveCodeBench
Model	Ckpt	Method	Acc	Term	Acc	Term	Acc	Term
Deepseek-R1-Distill -Qwen-1.5B	obc_50	Base	54.8 $\pm$ 2.4	72.5 $\pm$ 0.5	13.3 $\pm$ 2.7	46.7 $\pm$ 4.7	13.4 $\pm$ 2.2	32.1 $\pm$ 4.3
		Forced-Answer	59.4 $\pm$ 3.0	—	13.3 $\pm$ 2.7	—	16.6 $\pm$ 3.1	—
		TGAS	61.8 $\pm$ 4.9	85.1 $\pm$ 1.9	15.8 $\pm$ 1.7	58.3 $\pm$ 5.8	16.1 $\pm$ 1.0	51.8 $\pm$ 6.9
		Masked-LoRA	60.3 $\pm$ 3.1	82.1 $\pm$ 1.4	11.7 $\pm$ 5.8	52.5 $\pm$ 5.7	15.3 $\pm$ 1.8	30.8 $\pm$ 4.3
	obc_60	Base	15.5 $\pm$ 3.0	21.9 $\pm$ 1.9	1.7 $\pm$ 1.9	6.7 $\pm$ 4.7	0.0 $\pm$ 0.0	0.5 $\pm$ 0.6

Appendix

Table 25: Training-free remedies vs. Masked-LoRA for SparseGPT-pruned LRMs with OBC calibration DeepSeek-R1-Distill-Qwen models. Forced-Answer’s Term is not reported, since forcing ends every generation by design.

		$\Delta_{\mathrm{cyc}}$ at decisions		DPs/1k
Model	Ckpt	U	S	U	S
Deepseek-R1-Distill -Qwen-1.5B	dense	$-14.9\pm$ 0.5	$-16.4\pm$ 0.6	8.1	5.6
	obc_10	$-15.3\pm$ 0.5	$-16.5\pm$ 0.6	8.0	5.3
	obc_50	$-10.2\pm$ 0.4	$-12.7\pm$ 0.5	9.2	5.2
	obc_60	$-5.6\pm$ 0.3	$-6.3\pm$ 0.4	23.7	10.5
Deepseek-R1-Distill -Qwen-7B	dense	$-18.2\pm$ 0.6	$-20.5\pm$ 0.6	7.1	4.7

Appendix

Table 26:

\Delta_{\mathrm{cyc}}

at decision points on MATH-500 L4–5 with and without TGAS. U : unsteered traces; S : steered traces scored with the steering hook. More negative values indicate stronger preference for moving on. DPs/1k : decision points per 1,000 generated tokens.

		AIME-25				LiveCodeBench
Model	Ckpt	Base	$D$ =4096	$D$ =8192	$D$ =16384	Base	$D$ =4096	$D$ =8192
Deepseek-R1-Distill -Qwen-1.5B	dense	22.5 $\pm$ 4.2	19.2 $\pm$ 1.7	22.5 $\pm$ 4.2	22.5 $\pm$ 4.2	34.5 $\pm$ 1.6	35.0 $\pm$ 1.8	35.3 $\pm$ 1.8
	obc_10	21.7 $\pm$ 4.3	16.7 $\pm$ 4.7	21.7 $\pm$ 6.9	21.7 $\pm$ 4.3	32.9 $\pm$ 2.6	33.7 $\pm$ 1.9	33.4 $\pm$ 3.4
	obc_50	13.3 $\pm$ 2.7	12.5 $\pm$ 3.2	14.2 $\pm$ 1.7	13.3 $\pm$ 2.7	13.4 $\pm$ 2.2	19.2 $\pm$ 4.6	16.6 $\pm$ 3.1
	obc_60	1.7 $\pm$ 1.9	2.5 $\pm$ 3.2	2.5 $\pm$ 3.2	2.5 $\pm$ 3.2	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0
	obc_70	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0	0.0 $\pm$ 0.0

Appendix

Table 27: Effect of the Forced-Answer budget. Accuracy (%) after forcing an answer at

D

reasoning tokens, compared with the unforced checkpoint ( Base ). Generations finishing before

D

are kept unchanged, and at

D=16{,}384

only capped generations are forced.

AIME-25

LiveCodeBench

Base

n

n

=32

Base

n

n

=32

Model

Ckpt

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

DS-Qwen -1.5B

dense

22.5

\pm

4.2

71.7

\pm

5.8

7.5

\pm

4.2

68.3

\pm

7.9

22.5

\pm

4.2

74.2

\pm

7.4

34.5

\pm

1.6

76.1

\pm

1.8

8.9

\pm

1.4

79.7

\pm

1.0

27.6

\pm

1.6

80.8

\pm

3.9

obc_10

21.7

\pm

4.3

71.7

\pm

1.9

6.7

\pm

2.7

66.7

\pm

4.7

24.2

\pm

5.7

70.0

\pm

8.6

32.9

\pm

2.6

76.6

\pm

3.1

8.9

\pm

2.6

77.9

\pm

4.8

30.5

\pm

2.3

82.4

\pm

3.0

obc_50

13.3

\pm

2.7

46.7

\pm

4.7

3.3

\pm

0.0

46.7

\pm

9.8

17.5

\pm

5.7

51.7

\pm

7.9

13.4

\pm

2.2

32.1

\pm

4.3

1.8

\pm

1.0

40.3

\pm

5.0

9.5

\pm

2.6

40.8

\pm

6.2

obc_60

1.7

\pm

1.9

6.7

\pm

4.7

0.0

\pm

0.0

42.5

\pm

13.4

2.5

\pm

5.0

23.3

\pm

4.7

0.0

\pm

0.0

0.5

\pm

0.6

0.0

\pm

0.0

31.6

\pm

3.6

0.0

\pm

0.0

7.4

\pm

0.9

Appendix

Table 28: No-Repeat

n

-gram size. Acc is accuracy (%) and Term the share of generations that terminated (%). All three columns of a dataset come from the same evaluation pass, so Base here is that pass’s unblocked run.

\alpha=-2

\alpha=-1.5

\alpha=-1

\alpha=0

\alpha=+1

\alpha=+1.5

\alpha=+2

Model

Test

Ckpt

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Deepseek-R1-Distill -Qwen-7B

AIME

dense

31.7

\pm

4.3

70.0

\pm

6.1

37.5

\pm

5.0

83.3

\pm

7.2

37.5

\pm

4.2

81.7

\pm

1.9

42.5

\pm

5.7

80.0

\pm

7.2

41.7

\pm

6.9

79.2

\pm

8.8

42.5

\pm

6.9

82.5

\pm

3.2

36.7

\pm

4.2

83.3

\pm

5.0

obc_10

32.5

\pm

3.2

70.0

\pm

4.7

37.5

\pm

9.2

76.7

\pm

3.8

37.5

\pm

4.2

80.0

\pm

6.1

31.7

\pm

5.8

80.0

\pm

7.2

40.0

\pm

6.1

76.7

\pm

8.2

43.3

\pm

3.2

85.0

\pm

9.6

36.7

\pm

2.7

88.3

\pm

7.2

obc_50

27.5

\pm

6.3

33.3

\pm

7.2

25.8

\pm

5.7

45.8

\pm

10.7

30.8

\pm

6.9

55.0

\pm

4.3

30.0

\pm

4.7

57.5

\pm

7.4

30.0

\pm

4.7

63.3

\pm

4.7

25.8

\pm

4.2

64.2

\pm

4.2

25.8

\pm

3.2

72.5

\pm

4.3

obc_60

10.0

\pm

2.7

13.3

\pm

4.7

14.2

\pm

4.2

16.7

\pm

4.7

15.8

\pm

5.7

25.8

\pm

3.2

22.5

\pm

6.3

43.3

\pm

8.6

22.5

\pm

1.7

49.2

\pm

4.2

20.8

\pm

7.4

55.0

\pm

3.3

20.0

\pm

3.2

63.3

\pm

8.2

LCB

dense

55.3

\pm

2.2

73.4

\pm

2.0

57.4

\pm

2.2

80.5

\pm

3.7

55.8

\pm

2.7

81.1

\pm

1.5

59.2

\pm

3.8

83.7

\pm

1.4

59.7

\pm

2.2

89.2

\pm

3.0

59.7

\pm

1.3

90.0

\pm

3.3

56.1

\pm

1.4

91.3

\pm

1.3

Appendix

Table 29: Effect of steering strength

\alpha

on accuracy and termination. Each model is steered with its main direction scaled by

\alpha

, absolute steering coefficient;

\alpha=0

is the unsteered checkpoint and negative

\alpha

pushes against the direction. Acc is accuracy (%) and Term the share of generations that terminated (%).

			n50		n75		n100		Full
Model	Test	Ckpt	Acc	Term	Acc	Term	Acc	Term	Acc	Term
Deepseek-R1-Distill -Qwen-7B	AIME	dense	38.3 $\pm$ 6.4	82.5 $\pm$ 9.2	36.7 $\pm$ 9.0	79.2 $\pm$ 5.7	42.5 $\pm$ 4.2	80.0 $\pm$ 3.8	41.7 $\pm$ 6.9	79.2 $\pm$ 8.8
		obc_10	35.8 $\pm$ 3.2	83.3 $\pm$ 8.6	38.3 $\pm$ 4.3	80.8 $\pm$ 3.2	35.8 $\pm$ 1.7	80.8 $\pm$ 3.2	43.3 $\pm$ 4.7	80.8 $\pm$ 1.7
		obc_50	31.7 $\pm$ 4.3	69.2 $\pm$ 3.2	28.3 $\pm$ 6.4	62.5 $\pm$ 5.0	30.8 $\pm$ 8.8	69.2 $\pm$ 4.2	31.7 $\pm$ 3.3	68.3 $\pm$ 6.9
		obc_60	18.3 $\pm$ 4.3	55.0 $\pm$ 5.8	20.0 $\pm$ 3.8	57.5 $\pm$ 3.2	25.0 $\pm$ 6.4	62.5 $\pm$ 3.2	22.5 $\pm$ 3.2	54.2 $\pm$ 3.2
	LCB	dense	58.2 $\pm$ 2.3	87.4 $\pm$ 3.1	57.9 $\pm$ 2.3	86.3 $\pm$ 0.9	57.9 $\pm$ 2.3	88.4 $\pm$ 2.6	59.7 $\pm$ 2.2	89.2 $\pm$ 3.0

Appendix

Table 30: TGAS with directions built from different numbers of samples per class. Acc is accuracy (%) and Term the share of generations that terminated (%). n50 , n75 and n100 use 50, 75 and 100 samples per class; Full is the direction used in the main experiments. We use the same

\alpha

values as in the main experiments for each configuration.

Model	SEAL	Layer mean	Unit-avg
DS-Qwen-1.5B	dense	0.172	0.108
DS-Qwen-1.5B	obc_50	0.245	0.269
DS-Qwen-7B	dense	0.283	0.187
DS-Qwen-7B	obc_50	0.306	0.265
DS-Qwen-14B	dense	0.269	0.221
DS-Qwen-14B	obc_50	0.244	0.214

Appendix

Table 31: Cosine between the steering directions of SEAL and TGAS, averaged over decoder layers. Layer mean : cosine of the unnormalised layer averages; Unit-avg : each layer normalised before averaging.

				AIME-25		LiveCodeBench
Model	Pruner	Ckpt	Method	Acc	Term	Acc	Term
Deepseek-R1-Distill -Qwen-7B	RAC	10%	Base	35.8 $\pm$ 5.0	79.2 $\pm$ 4.2	56.3 $\pm$ 1.8	85.0 $\pm$ 3.8
			No-Repeat	38.3 $\pm$ 5.8	80.0 $\pm$ 5.4	47.4 $\pm$ 3.1	85.8 $\pm$ 1.1
			Forced-Answer	33.3 $\pm$ 4.7	—	53.7 $\pm$ 1.2	—
			TGAS	39.2 $\pm$ 3.2	85.0 $\pm$ 6.9	58.7 $\pm$ 2.6	89.7 $\pm$ 3.0
		50%	Base	24.2 $\pm$ 5.7	32.5 $\pm$ 5.7	32.6 $\pm$ 1.7	37.4 $\pm$ 2.2

Appendix

Table 32: Training-free remedies on checkpoints pruned with SparseGPT-pruned LRMs with RAC calibration and with C4 calibration (Wanda prune). Acc is accuracy (%) and Term the share of generations that terminated (%). Forced-Answer’s Term is not reported, since forcing ends every generation by design. Best accuracy per checkpoint and dataset in bold.

AIME-25

LiveCodeBench

SEAL (dense)

SEAL (50%)

TGAS

SEAL (dense)

SEAL (50%)

TGAS

Model

Ckpt

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

Acc

Term

DS-Qwen-1.5B

dense

18.3

\pm

1.9

76.7

\pm

6.1

19.5

\pm

2.9

75.8

\pm

8.3

25.8

\pm

4.2

75.8

\pm

5.7

35.0

\pm

3.7

84.7

\pm

3.3

35.5

\pm

2.2

86.6

\pm

3.0

36.8

\pm

2.6

86.3

\pm

3.7

obc_10

21.7

\pm

4.3

80.8

\pm

7.4

25.0

\pm

6.9

76.7

\pm

8.6

26.7

\pm

4.7

75.0

\pm

6.9

34.5

\pm

4.6

85.5

\pm

3.0

33.4

\pm

3.6

81.3

\pm

2.2

37.1

\pm

2.6

83.2

\pm

2.9

obc_50

15.8

\pm

3.2

60.0

\pm

6.7

16.7

\pm

2.7

57.5

\pm

5.7

15.8

\pm

1.7

58.3

\pm

5.8

13.2

\pm

3.5

46.3

\pm

4.0

15.3

\pm

1.8

45.8

\pm

5.0

16.1

\pm

1.0

51.8

\pm

6.9

obc_60

5.0

\pm

6.4

27.5

\pm

7.4

3.3

\pm

2.7

24.2

\pm

7.4

5.0

\pm

1.9

40.0

\pm

4.7

0.0

\pm

0.0

\pm

0.0

\pm

0.0

\pm

0.0

\pm

0.0

2.4

\pm

1.8

Appendix

Table 34: SEAL with steering vectors built on the dense model or on the 50% checkpoint, compared with TGAS. Acc : accuracy (%); Term : termination rate (%). Best accuracy per checkpoint and benchmark in bold.

		AIME-25			LiveCodeBench
Model	Sparsity	TGAS	Plan-CoT ${}_{\text{dense}}$	Plan-CoT 50%	TGAS	Plan-CoT ${}_{\text{dense}}$	Plan-CoT 50%
Accuracy (%)
DS-Qwen-7B	Dense	$\mathbf{41.7}_{\pm 6.9}$ (+1)	$37.5_{\pm 3.2}$ ( $-$ 0.2)	$39.2_{\pm 5.0}$ ( $-$ 0.2)	$59.7_{\pm 2.2}$ (+1)	$58.7_{\pm 2.8}$ ( $-$ 0.1)	$\mathbf{60.3}_{\pm 3.0}$ ( $-$ 0.2)
	10%	$\mathbf{43.3}_{\pm 4.7}$ (+1.25)	$40.0_{\pm 2.7}$ ( $-$ 0.1)	$38.3_{\pm 4.3}$ ( $-$ 0.2)	$\mathbf{60.3}_{\pm 3.4}$ (+1.25)	$\mathbf{60.3}_{\pm 2.3}$ ( $-$ 0.1)	$57.9_{\pm 3.5}$ ( $-$ 0.2)
	50%	$\mathbf{31.7}_{\pm 3.3}$ (+0.5)	$29.2_{\pm 3.2}$ ( $-$ 0.1)	$\mathbf{31.7}_{\pm 7.9}$ ( $-$ 0.2)	$\mathbf{41.8}_{\pm 2.3}$ (+0.5)	$40.3_{\pm 1.3}$ ( $-$ 0.1)	$40.0_{\pm 3.1}$ ( $-$ 0.2)
	60%	$22.5_{\pm 3.2}$ (+1.25)	$22.5_{\pm 3.2}$ ( $-$ 0.1)	$\mathbf{25.0}_{\pm 1.9}$ ( $-$ 0.1)	$\mathbf{19.5}_{\pm 3.3}$ (+1.25)	$15.5_{\pm 1.8}$ ( $-$ 0.2)	$13.7_{\pm 1.2}$ ( $-$ 0.2)

Appendix

Table 35: TGAS at its best steering strength

\alpha

(shown in parentheses) compared with Plan-CoT at best steering coefficient, using a steering vector extracted from the dense model (Plan-CoT

{}_{\text{dense}}

) or from the 50%-sparse model (Plan-CoT 50% ). Best value per row and benchmark in bold.

Repetition in Language Generation

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Jul 13, 2026J/K move · Enter open · S save

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

Mohammed Ehab, Aymane El Gadarri, Vivek F. Farias, Adam Jozefiak+1

MIT · Columbia Business School

Overthinking in Language Models Sequential Decision Making Optimal Stopping Efficient Language Model Reasoning Efficient Language Model Inference Large Reasoning Models

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Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks through Chain-of-Thought (CoT) prompting. However, these models often exhibit "computational overthinking," generating redundant reasoning steps that increase latency and cost without improving accuracy. Recent studies suggest that CoT trajectories can be significantly pruned, yet existing methods often rely on forcing a static thinking budget, heuristic filtering, sub-optimal early exit via classification, or expensive re-training. In this paper, we introduce OS-Pruner, a lightweight plug-in framework that formulates chain-of-thought pruning as an optimal stopping problem. Given a reasoning prefix, OS-Pruner learns whether further reasoning is worth its token cost by optimizing an explicit utility that trades off final-answer accuracy against generated length. Our novel formulation enables the model to dynamically assess the sufficient point of termination for a reasoning chain. OS-Pruner is designed to be lightweight during both training and inference, and to provide users with fine-grained control over the reasoning-effort vs. accuracy trade-off. On diverse reasoning benchmarks and base models, OS-Pruner achieves 20-60% reduction in generation length with minimal accuracy sacrifice.

Abstract

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