GLOBE: Geometry-Led Online Behavioral Early Exit via Unit-Sphere Trajectories

Xinyue Peng; Zhenlin Liang; Meng Cai; Hua Wang

cs.AIOct 19, 2026

GLOBE: Geometry-Led Online Behavioral Early Exit via Unit-Sphere Trajectories

Authors: Xinyue Peng, Zhenlin Liang, Meng Cai, Hua Wang

Organizations: Moore Threads

Abstract

Chain-of-thought (CoT) reasoning can improve problem solving, but models often keep generating after the correct answer is already reachable; the extra steps raise serving costs and may replace a correct intermediate result with an incorrect one. We propose GLOBE (Geometry-Led Online Behavioral Early Exit), an online, training-free algorithm that terminates the model's CoT process early. GLOBE embeds each completed reasoning segment as a point on a unit sphere and reads the shape of the resulting semantic trajectory. GLOBE first applies a trial phase that generates short trial answers in a separate branch, stopping the main stream on an accepted trial after checking confidence against a threshold. If generation continues, a trajectory phase stops the stream once this path repeatedly reverses direction with little net progress. On five benchmarks including mathematical reasoning, tool calling, and agent memory, GLOBE cuts output tokens by 49.7% and active end-to-end wall time (E2E) by 51.0% across two models, and achieves a five-task average of 80.58%, comparable to Full CoT.

Figures & tables

Figure 1: Two mechanisms for triggering an early exit: a trial answer at a candidate signal (a) and a cut of the reasoning stream (b).

Figure 2: Overview of GLOBE, a training-free online algorithm over a single reasoning stream, in three steps. The example is a tool-calling irrelevance case, as the persona permits only science questions and the weather tool should not be called. In the trial phase, a get_weather trial answer at Wait is rejected for low confidence. In the trajectory phase, the reasoning wavers over calling the tool. Once reversals, marked by the red arrows, accumulate with little net displacement, further reasoning is redundant, so the trajectory stop ends the stream and the final answer declines the request.

Method	CSQA			Character-LLM			GSM8K			BFCL v4 Live			Agent Memory			Avg.
Method	Acc $\uparrow$	Tok $\downarrow$	E2E $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	E2E $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	E2E $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	E2E $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	E2E $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	E2E $\downarrow$
Qwen3.6-35B-A3B
Nothink	83.8	601	1062	90.8	124	1323	96.3	189	575	77.9	103	1015	34.5	763	1556	76.66	356	1106
Full CoT	84.7	2065	5376	94.4	1368	7775	96.7	1761	3475	81.3	962	4888	55.0	9549	16304	82.42	3141	7564
DEER	81.4	1584	3090	95.2	1233	9515	96.1	1240	2631	77.3	581	4964	55.4	6839	14434	81.08	2295	6927
ThinkBrake	82.6	2044	5719	94.4	355	6458	96.1	1779	5539	79.6	789	4818	52.9	7417	13673	81.12	2477	7241

Table 1: Main results. Acc. (%), Tok. (average output tokens), and E2E (s) per task. Agent Memory Acc. averages KV, Vector, and Recursive Sum, and its E2E is their sum. Bold: best Acc., and lowest Tok/E2E among thinking methods.

Qwen3.6-35B-A3B
Method	GSM8K		BFCL v4 Live		Agent Memory		Average
Method	Accuracy $\uparrow$	Avg Token $\downarrow$	Accuracy $\uparrow$	Avg Token $\downarrow$	Accuracy $\uparrow$	Avg Token $\downarrow$	Accuracy $\uparrow$	Avg Token $\downarrow$
GLOBE (ours)	96.5	784	80.0	371	58.0	2040	78.2	1.00 $\times$
w/o trajectory stop	96.1 ( $-0.5$ )	1529 ( $+95$ %)	80.0 ( $+0.0$ )	757 ( $+104$ %)	46.9 ( $-11.1$ )	9181 ( $+350$ %)	74.3 ( $-3.8$ )	2.62 $\times$
w/o phase switch	96.3 ( $-0.2$ )	676 ( $-14$ %)	79.5 ( $-0.4$ )	336 ( $-9$ %)	50.1 ( $-7.9$ )	2551 ( $+25$ %)	75.3 ( $-2.9$ )	0.99 $\times$
w/o trial answers	95.8 ( $-0.8$ )	959 ( $+22$ %)	79.7 ( $-0.3$ )	412 ( $+11$ %)	56.1 ( $-1.9$ )	2518 ( $+23$ %)	77.2 ( $-1.0$ )	1.19 $\times$

Table 2: Component ablation: accuracy (%) and average output tokens, reporting changes against GLOBE (Table 1 ). Parentheses give accuracy differences in points and relative token changes (%), computed before rounding. The Average token column gives the geometric mean of the token ratios. red is worse than GLOBE, green better, and gray a tie.

Figure 3: Stop reliability on separate analysis runs. (a) Harm and rescue of GLOBE early stops versus Full CoT on GSM8K, BFCL v4 Live, and Agent Memory. (b) Stop outcomes per controller: stopped and correct (green), stopped and wrong (orange), and natural close (grey).

Figure 4: Operating-point evidence. (a) Diagnostic trial and cut evidence used to locate the phase switch. (b) Selection of

\tau_{Q}

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Benchmark	Items	Metric	Budget	Conc.	GLOBE (Qwen)	GLOBE (Gemma)
CSQA	1,221	accuracy	8K	8	$(4,8,0.14)$	$(4,8,0.14)$
GSM8K	1,319	strict EM	8K	8	$(4,8,0.14)$	$(4,8,0.14)$
BFCL v4 Live	2,251	All-live acc.	16K	4	$(4,8,0.14)$	$(4,8,0.14)$
Agent Memory	$3\times 155$	agent acc.	16K/step	4	$(4,8,0.14)$	$(4,8,0.14)$
Character-LLM	857	NAS	2K	1	$(n_{\min}{=}3,8,0.14)$	$(n_{\min}{=}10,8,0.14)$

Appendix

Table 3: Task contracts and GLOBE settings. Budget is the retained-token budget of a request; Conc. is the number of concurrent items, held fixed across all methods within each task. GLOBE thresholds are

(K_{\mathrm{phase}},K_{\mathrm{osc}},\tau_{Q})

; Character-LLM has no trial phase, and its first entry

n_{\min}

is the number of completed segments before the trajectory stop is armed.

Model	Task	$\Delta$ Acc (points)	Tok. reduction	E2E reduction	Speed-up
Qwen	CSQA	$+1.7$	$74.6\%$	$76.0\%$	$4.17\times$
	Character-LLM	$+0.1$	$31.8\%$	$30.7\%$	$1.44\times$
	GSM8K	$-0.2$	$55.5\%$	$43.3\%$	$1.76\times$
	BFCL v4 Live	$-1.3$	$61.4\%$	$37.2\%$	$1.59\times$
	Agent Memory	$+3.0$	$78.6\%$	$64.9\%$	$2.85\times$
Gemma	CSQA	$-1.0$	$64.5\%$	$59.4\%$	$2.46\times$

Appendix

Table 4: GLOBE against Full CoT on each model–task pair of Table 1 .

\Delta

Acc is the score difference in points (NAS for Character-LLM); token and E2E reductions are relative to Full CoT; the speed-up is the ratio of the two E2E times. The ten-pair mean gives the figures quoted in the abstract; the final row excludes Qwen BFCL v4 Live.

	CSQA	GSM8K	BFCL v4 Live
Trials launched per item	$0.05$	$0.92$	$1.36$
Trial acceptance rate (%)	$41.3$	$24.2$	$20.4$
Discarded trial tokens per item	$0.2$	$4.1$	$20.0$
Requests per item	$2.04$	$2.91$	$3.06$
Embedding requests per item	$4.82$	$5.74$	$2.80$
Embedding time share of item wall time (%)	$13.6$	$10.1$	$10.5$

Appendix

Table 5: What the controller costs, per item, for the Qwen runs behind Figure 3 b. Requests count the main stream, trials, and the continuation. The embedding share is the embedding time divided by the item’s wall time; because the observer runs alongside the main stream, it bounds the latency the observer can add.

Task	Method	Stop (%)	Post-stop (%)	Yield (%)
CSQA	DEER	$58.9$ (719)	$77.7$	$45.8$
	ThinkBrake	$69.9$ (853)	$87.6$	$61.2$
	RCPD	$95.7$ (1,169)	$85.5$	$81.9$
	GLOBE (ours)	$98.6$ (1,204)	$86.2$	$\mathbf{85.0}$
GSM8K	DEER	$65.4$ (862)	$95.4$	$62.3$
	ThinkBrake	$0.0$ (0)	–	$0.0$

Appendix

Table 6: Stop coverage versus stop quality on Qwen from separate analysis runs. Stop: stopped items over

N

(count in parentheses). Post-stop: accuracy among the stopped items. Yield: stopped and correct over

N

N

1{,}221

(CSQA),

1{,}319

(GSM8K),

2{,}251

(BFCL v4 Live), and

465

(Agent Memory). On Agent Memory an item counts as stopped when the request that ends it is stopped. Bold: best yield per task.

Model	Task	Harm (%)	Rescue (%)
Qwen	GSM8K	$0.94$	$29.8$
	BFCL v4 Live	$4.17$	$9.56$
	Agent Memory	$10.8$	$24.9$
Gemma	GSM8K	$3.14$	$40.0$
Gemma	BFCL v4 Live	$4.14$	$9.75$

Appendix

Table 7: Harm and rescue of GLOBE early stops against Full CoT from separate analysis runs, joined item by item as in Figure 3 a. Harm: share of Full CoT-correct items that GLOBE stops early and answers wrong. Rescue: share of Full CoT-wrong items that GLOBE stops early and answers right.

	Qwen				Gemma
Variant	$\Delta$	$p$	Stop	Tok	$\Delta$	$p$	Stop	Tok
GLOBE (full)	–	–	$97.0\%$	$1.00\times$	–	–	$76.7\%$	$1.00\times$
w/o trial answers	$-7$	$0.38$	$97.0\%$	$1.01\times$	$+1$	$1.00$	$77.0\%$	$1.07\times$
w/o trajectory stop	$\mathbf{-127}$	$2{\times}10^{-24}$	$1.9\%$	$6.84\times$	$\mathbf{-107}$	$5{\times}10^{-11}$	$8.0\%$	$7.71\times$
w/o phase switch	$-5$	$0.60$	$96.8\%$	$0.96\times$	$+1$	$1.00$	$77.5\%$	$0.95\times$
w/o $\tau_{Q}$ gate	$+7$	$0.41$	$98.8\%$	$0.85\times$	$-16$	$0.12$	$84.0\%$	$0.93\times$

Appendix

Table 8: CSQA remove-one ablation (

N=1{,}221

). Every variant is a full run compared item by item with the full-GLOBE run of the same sweep.

\Delta

: change in correct items;

p

: exact McNemar test; Stop: share of items stopped early; Tok: retained reasoning tokens relative to the full run.

	Qwen			Gemma
Variant	$\Delta$ NAS [95% CI]	$p$	Tok	$\Delta$ NAS [95% CI]	$p$	Tok
w/o trajectory stop	$+1.49$ [ $+0.32$ , $+2.66$ ]	$0.08$	$2.78\times$	$+1.83$ [ $+0.56$ , $+3.07$ ]	$6{\times}10^{-10}$	$1.43\times$
w/o phase switch	$+0.16$ [ $-1.03$ , $+1.37$ ]	$0.97$	$1.00\times$	$-0.02$ [ $-1.20$ , $+1.18$ ]	$0.80$	$1.01\times$
w/o $\tau_{Q}$ gate	$-0.33$ [ $-1.58$ , $+0.92$ ]	$0.69$	$0.89\times$	$-2.05$ [ $-3.25$ , $-0.86$ ]	$8.5{\times}10^{-4}$	$0.88\times$

Appendix

Table 9: Character-LLM remove-one ablation (

N=857

single-turn interviews). Each variant is a full run of the role-play harness compared item by item with the full-GLOBE run of the same sweep.

\Delta

NAS in points with a paired bootstrap

95\%

interval;

p

: exact Wilcoxon signed-rank test; Tok: retained reasoning tokens relative to the full run. The role-play harness has no trial phase (Appendix A.6 ), so there is no w/o trial answers row.

$\tau_{Q}$	Correct	Acc. (%)	Tok	E2E (s)	Traj.
$0.06$	1,798	$79.88$	$322.0$	3,332	699
$0.08$	1,786	$79.34$	$285.6$	3,253	835
$0.10$	1,790	$79.52$	$270.8$	3,325	966
$0.12$	1,783	$79.21$	$252.9$	3,105	1,019
$\mathbf{0.14}$	$\mathbf{1{,}800}$	$\mathbf{79.96}$	$\mathbf{240.9}$	$\mathbf{3{,}071}$	$\mathbf{1{,}067}$
$0.16$	1,785	$79.30$	$241.8$	2,878	1,070

Appendix

Table 10:

\tau_{Q}

sweep with

K_{\mathrm{phase}}=4

and

K_{\mathrm{osc}}=8

. Tok: retained reasoning tokens per item. Traj.: trajectory stops. Bold: the selected setting.

Task	Encoder	Dim.	Acc. (%)	Tok	E2E (s)	Traj.	Embed (s)
BFCL v4 Live	8B	4,096	$79.96$	$240.9$	3,071	1,067	$0.54$
	4B	2,560	$79.61$	$236.2$	3,081	1,063	$0.43$
	0.6B	1,024	$79.12$	$242.5$	3,177	1,063	$0.37$
GSM8K	8B	4,096	$95.91$	$358.3$	1,751	1,032	$0.95$
	4B	2,560	$96.36$	$357.3$	1,893	1,030	$0.78$
	0.6B	1,024	$95.91$	$362.7$	1,762	1,035	$0.58$

Appendix

Table 11: Sensitivity to the segment encoder (Qwen, reference configuration). The 8B rows use the default encoder; on BFCL v4 Live this is the run of Table 1 . Tok: retained reasoning tokens per item. Traj.: items closed by the trajectory stop. Embed: embedding time per item.

Figure 5: Signal-specific analysis. Top: the share of candidate signals whose short trial passes the confidence test, split by signal type. Middle: the share that passes the test and is correct. The thinking-close signal keeps improving until

400

tokens (

40\%

gate,

35\%

yield), while the two textual markers never exceed

27\%

and

17\%

; Wait peaks at

100

–

200

tokens and decays from there, and Actually is the weakest of the three throughout. Bottom, over a longer axis: the marker lane’s window. The share of passed confidence tests whose answer is correct falls from

78\%

45\%

beyond

800

tokens while the mean trial confidence stays flat at about

0.80

. Bins are

100

tokens wide and hold at least

25

events.

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</think> Doesn't Stop Reasoning: Analysis of Spurious CoT Termination

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Chain-of-thought (CoT) reasoning improves large reasoning models (LRMs) on complex tasks but often produces long, redundant traces. Recent training-free early-exit methods shorten these traces by choosing an intermediate point to stop reasoning. We study one such strategy that injects an end-of-think token (EoT, </think>) at this point to trigger the reasoning-to-answering transition, and find that the injected EoT does not always induce a clean answering phase. Answering-phase generation can continue before the model regenerates another EoT, with the span preceding this regenerated EoT scaling with the reasoning tokens saved by early exit and exhibiting continued reasoning behavior. We call this spurious CoT termination, where reasoning-like generation continues into the answering phase. We hypothesize that insufficient attention to the injected EoT contributes to spurious CoT termination and probe this hypothesis with Exit-token Attention Biasing (EAB). Across four LRMs, five benchmarks, and two early-exit methods, increasing attention to the injected EoT reduces spurious CoT termination and answering-phase length. These results reveal a limitation of controlling LRMs by externally matching their explicit think-block format. Inserting the EoT token conforms to this format but does not by itself guarantee the intended reasoning-to-answering transition. Our code is available at https://github.com/Seunghee-Koh/Spurious-CoT-Termination.

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