GLOBE: Geometry-Led Online Behavioral Early Exit via Unit-Sphere Trajectories
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
| Method | CSQA | Character-LLM | GSM8K | BFCL v4 Live | Agent Memory | Avg. | ||||||||||||
| Acc | Tok | E2E | Acc | Tok | E2E | Acc | Tok | E2E | Acc | Tok | E2E | Acc | Tok | E2E | Acc | Tok | E2E | |
| 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 |
| Method | GSM8K | BFCL v4 Live | Agent Memory | Average | ||||
|---|---|---|---|---|---|---|---|---|
| Accuracy | Avg Token | Accuracy | Avg Token | Accuracy | Avg Token | Accuracy | Avg Token | |
| Qwen3.6-35B-A3B | ||||||||
| GLOBE (ours) | 96.5 | 784 | 80.0 | 371 | 58.0 | 2040 | 78.2 | 1.00 |
| w/o trajectory stop | 96.1 ( ) | 1529 ( %) | 80.0 ( ) | 757 ( %) | 46.9 ( ) | 9181 ( %) | 74.3 ( ) | 2.62 |
| w/o phase switch | 96.3 ( ) | 676 ( %) | 79.5 ( ) | 336 ( %) | 50.1 ( ) | 2551 ( %) | 75.3 ( ) | 0.99 |
| w/o trial answers | 95.8 ( ) | 959 ( %) | 79.7 ( ) | 412 ( %) | 56.1 ( ) | 2518 ( %) | 77.2 ( ) | 1.19 |
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 | ||
| GSM8K | 1,319 | strict EM | 8K | 8 | ||
| BFCL v4 Live | 2,251 | All-live acc. | 16K | 4 | ||
| Agent Memory | agent acc. | 16K/step | 4 | |||
| Character-LLM | 857 | NAS | 2K | 1 |
| Model | Task | Acc (points) | Tok. reduction | E2E reduction | Speed-up |
|---|---|---|---|---|---|
| Qwen | CSQA | ||||
| Character-LLM | |||||
| GSM8K | |||||
| BFCL v4 Live | |||||
| Agent Memory | |||||
| Gemma | CSQA |
| CSQA | GSM8K | BFCL v4 Live | |
|---|---|---|---|
| Trials launched per item | |||
| Trial acceptance rate (%) | |||
| Discarded trial tokens per item | |||
| Requests per item | |||
| Embedding requests per item | |||
| Embedding time share of item wall time (%) |
| Task | Method | Stop (%) | Post-stop (%) | Yield (%) |
|---|---|---|---|---|
| CSQA | DEER | (719) | ||
| ThinkBrake | (853) | |||
| RCPD | (1,169) | |||
| GLOBE (ours) | (1,204) | |||
| GSM8K | DEER | (862) | ||
| ThinkBrake | (0) | – |
| Model | Task | Harm (%) | Rescue (%) |
|---|---|---|---|
| Qwen | GSM8K | ||
| BFCL v4 Live | |||
| Agent Memory | |||
| Gemma | GSM8K | ||
| BFCL v4 Live |
| Qwen | Gemma | |||||||
|---|---|---|---|---|---|---|---|---|
| Variant | Stop | Tok | Stop | Tok | ||||
| GLOBE (full) | – | – | – | – | ||||
| w/o trial answers | ||||||||
| w/o trajectory stop | ||||||||
| w/o phase switch | ||||||||
| w/o gate | ||||||||
| Qwen | Gemma | |||||
|---|---|---|---|---|---|---|
| Variant | NAS [95% CI] | Tok | NAS [95% CI] | Tok | ||
| w/o trajectory stop | [ , ] | [ , ] | ||||
| w/o phase switch | [ , ] | [ , ] | ||||
| w/o gate | [ , ] | [ , ] | ||||
| Correct | Acc. (%) | Tok | E2E (s) | Traj. | |
|---|---|---|---|---|---|
| 1,798 | 3,332 | 699 | |||
| 1,786 | 3,253 | 835 | |||
| 1,790 | 3,325 | 966 | |||
| 1,783 | 3,105 | 1,019 | |||
| 1,785 | 2,878 | 1,070 |
| Task | Encoder | Dim. | Acc. (%) | Tok | E2E (s) | Traj. | Embed (s) |
|---|---|---|---|---|---|---|---|
| BFCL v4 Live | 8B | 4,096 | 3,071 | 1,067 | |||
| 4B | 2,560 | 3,081 | 1,063 | ||||
| 0.6B | 1,024 | 3,177 | 1,063 | ||||
| GSM8K | 8B | 4,096 | 1,751 | 1,032 | |||
| 4B | 2,560 | 1,893 | 1,030 | ||||
| 0.6B | 1,024 | 1,762 | 1,035 |
Efficient Language Model Reasoning
Efficient language model reasoning studies how to improve problem-solving accuracy while reducing inference, memory, latency, and training costs.
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