State of Thought Enables Endogenous Reasoning
Organizations: College of Computing and Data Science, Nanyang Technological University, Singapore · Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore · Information Science & Engineering, KTH Royal Institute of Technology, Sweden · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
Abstract
Test-time compute has emerged as a major approach to improving the capabilities of Large Language Models (LLMs). However, existing test-time reasoning paradigms rely heavily on externally imposed control, either through fixed reasoning programs or through costly expansion in constrained search spaces, limiting both generalization and efficiency. We propose State of Thought (SoT), a new reasoning paradigm that enables endogenous reasoning in LLMs, with the model's internal reasoning state governing how reasoning unfolds. Concretely, SoT extracts a compact dynamics-geometric state from the model's internal information transfer and uses a 582-parameter controller on frozen backbones to selectively activate historical reasoning support useful under the current reasoning state, framing reasoning as a state-conditioned process over evidence rather than an externally prescribed token chain. Across quantitative (1.34x), general (1.62x), symbolic-and-code (1.76x), and long-context (2.51x) reasoning on 3 LLMs and 16 datasets, SoT consistently improves mean-baseline accuracy while reducing generated tokens by 62.6% and end-to-end latency by 44.6%. Across 2 VLM scales and 3 reasoning tasks, it improves mean accuracy by 3.8 points over reasoning baselines, with 74.9% fewer completion tokens and 73.5% lower latency than search-based methods. Under constrained access, SoT retains 38.2%/36.5% mean accuracy gains in training-free/embedding-only settings, while trajectory-only judging reaches 84.1% agreement across 3 API models. Together, endogenous state-driven reasoning provides a generalizable and efficient alternative.
Figures & tables
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Greedy | Vanilla | 79.0 | 58.2 | 6.2 | 53.9 | 29.6 | 26.0 | 26.0 | 25.0 | 55.2 | 33.0 |
| Reasoning Paradigm | CoT | 80.8 | 64.2 | 1.7 | 55.5 | 4.9 | 24.5 | 70.0 | 25.0 | 51.6 | 31.2 |
| PS | 71.2 | 40.0 | 1.4 | 43.4 | 4.9 | 15.2 | 55.0 | 10.0 | 22.0 | 17.6 | |
| SR | 75.8 | 44.8 | 15.6 | 50.4 | 32.5 | 31.0 | 46.0 | 25.0 | 36.4 | 32.9 | |
| SC | 83.6 | 54.0 | 1.6 | 53.2 | 16.8 | 28.5 | 52.0 | 10.0 | 35.2 | 27.3 | |
| Variant | QS | S&C | GU | LCR | ||||||||
| acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | |
| Full SoT | 62.8 | 219.4 | 5.8 | 54.5 | 294.0 | 9.5 | 71.2 | 64.0 | 1.8 | 33.0 | 181.6 | 22.0 |
| + Threshold Tuning | 62.8 | 219.4 | 5.8 | 54.3 | 294.0 | 9.5 | 71.2 | 64.0 | 1.8 | 31.8 | 229.0 | 22.0 |
| w/o Evid. Org. | 29.6 | 469.5 | 12.9 | 44.5 | 536.2 | 16.5 | 72.4 | 193.9 | 4.9 | 26.9 | 506.5 | 14.1 |
| w/o Stopping | 60.6 | 1769.6 | 80.7 | 57.1 | 1705.1 | 110.3 | 70.2 | 4148.5 | 99.5 | 31.6 | 2937.4 | 157.3 |
| w/o Geometry | 42.5 | 68.6 | 3.3 | 46.4 | 48.0 | 2.9 | 73.0 | 25.4 | 0.9 | 24.5 | 47.2 | 2.2 |
| Method | Qwen2.5-VL-7B | Qwen2.5-VL-32B | ||||||||||||||||
| A-OKVQA | AI2D | M 3 CoT | A-OKVQA | AI2D | M 3 CoT | |||||||||||||
| acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | |
| CoT | 81.0 | 137 | 3.0 | 82.7 | 189 | 3.9 | 80.7 | 178 | 4.4 | 84.0 | 267 | 12.8 | 87.3 | 321 | 17.0 | 87.3 | 329 | 16.0 |
| PS | 84.0 | 169 | 3.5 | 82.7 | 245 | 5.9 | 81.3 | 211 | 5.8 | 80.5 | 311 | 16.9 | 72.7 | 436 | 27.1 | 78.7 | 387 | 17.9 |
| SR | 78.0 | 213 | 5.1 | 80.0 | 264 | 6.1 | 83.3 | 254 | 6.4 | 84.5 | 414 | 22.2 | 89.3 | 465 | 26.1 | 84.0 | 469 | 24.3 |
| SC | 83.5 | 691 | 15.9 | 87.3 | 955 | 19.9 | 84.0 | 909 | 21.3 | 84.0 | 1319 | 64.0 | 86.0 | 1669 | 87.6 | 87.3 | 1618 | 78.2 |
| Quantitative Reasoning | Symbolic and Code | |||||||||
| GSM8K | MATH | DROP | avg. | FOLIO | PW | BBH-T | HE | MBPP | avg. | |
| Top-3 Baseline avg. | 81.9 | 61.5 | 16.2 | 53.2 | 40.6 | 37.6 | 60.0 | 30.0 | 52.0 | 44.0 |
| SoT-Training-free | 81.8 | 60.5 | 34.6 | 59.0 | 43.4 | 30.2 | 77.0 | 53.0 | 50.8 | 50.1 |
| SoT-Embedding | 82.8 | 61.8 | 32.3 | 59.0 | 33.8 | 30.5 | 74.0 | 57.9 | 52.8 | 49.8 |
Appendix figures & tables25 assets
Supplementary material from the paper’s appendix.
Appendix
| Category | Dataset | Task type | Train | Test | Metric |
| Quantitative Reasoning (QS) | GSM8K | Math QA | — | 500 | EM |
| MATH | Competition math | — | 400 | EM | |
| DROP | Discrete reasoning QA | — | 300 | F1 | |
| General Understanding (GU) | CommonsenseQA (CSQA) | Multiple choice QA | 52 | 400 | EM |
| StrategyQA (StrQA) | Binary QA | 52 | 400 | EM | |
| BoolQ | Boolean QA | — | 400 | EM |
| Parameter | Value | Notes |
| Context budget | 1536 | Active evidence budget |
| Maximum reasoning steps | 32 | Safety cap only |
| Observation window | 4096 | Visible context span |
| Final answer budget | 512 | Answer generation cap |
| Stop threshold | 0.5 | Default stop rule |
| Gate threshold | 0.5 | Default keep rule |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 94.4 | 77.5 | 1.9 | 65.6 | 0.0 | 55.5 | 84.0 | 75.0 | 66.0 | 49.9 |
| PS | 88.0 | 51.5 | 2.1 | 54.4 | 0.5 | 65.5 | 92.0 | 50.0 | 47.2 | 49.6 | |
| SR | 92.0 | 68.2 | 17.6 | 65.5 | 61.1 | 83.4 | 79.0 | 60.0 | 50.4 | 68.1 | |
| SC | 92.8 | 61.0 | 1.9 | 59.5 | 0.5 | 59.5 | 87.0 | 55.0 | 48.8 | 47.2 | |
| CB | 60.0 | 41.2 | 30.8 | 46.4 | 62.1 | 85.0 | 51.0 | 50.0 | 60.8 | 69.8 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 64.8 | 41.5 | 9.9 | 43.3 | 23.2 | 43.0 | 47.0 | 20.0 | 40.4 | 38.1 |
| PS | 60.6 | 35.8 | 10.6 | 39.8 | 12.8 | 38.2 | 52.0 | 25.0 | 42.4 | 35.1 | |
| SR | 49.2 | 37.8 | 9.7 | 35.5 | 27.6 | 54.5 | 51.0 | 15.0 | 32.0 | 41.9 | |
| SC | 69.8 | 43.0 | 9.8 | 45.9 | 25.6 | 45.2 | 56.0 | 20.0 | 37.2 | 39.7 | |
| CB | 50.0 | 30.2 | 10.1 | 33.4 | 48.3 | 60.5 | 39.0 | 10.0 | 34.4 | 48.0 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 230.1 | 381.5 | 194.1 | 271.6 | 342.9 | 332.0 | 264.4 | 490.1 | 415.4 | 369.8 |
| PS | 311.0 | 358.9 | 259.9 | 314.2 | 369.9 | 354.4 | 346.0 | 404.6 | 391.4 | 372.1 | |
| SR | 346.5 | 441.6 | 307.6 | 368.5 | 337.8 | 330.4 | 336.4 | 517.6 | 473.0 | 391.7 | |
| SC | 678.4 | 928.6 | 578.2 | 736.8 | 913.0 | 875.4 | 798.1 | 1135.3 | 1056.2 | 953.9 | |
| CB | 441.8 | 521.0 | 264.5 | 423.9 | 325.8 | 324.6 | 290.0 | 424.8 | 447.3 | 363.9 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 12.1 | 25.6 | 15.7 | 17.5 | 24.0 | 23.9 | 18.9 | 41.3 | 30.4 | 27.5 |
| PS | 18.7 | 22.1 | 22.3 | 20.7 | 26.2 | 24.4 | 27.7 | 32.3 | 27.3 | 26.8 | |
| SR | 21.6 | 30.3 | 27.2 | 25.9 | 22.6 | 21.6 | 26.2 | 45.1 | 35.5 | 28.8 | |
| SC | 34.8 | 51.8 | 45.5 | 43.1 | 58.9 | 55.7 | 57.4 | 85.1 | 68.1 | 63.5 | |
| CB | 20.9 | 25.6 | 19.2 | 22.0 | 16.5 | 16.2 | 17.9 | 26.3 | 23.0 | 19.4 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 399.4 | 521.3 | 544.5 | 476.3 | 503.3 | 416.7 | 456.0 | 644.4 | 597.8 | 490.0 |
| PS | 653.4 | 698.4 | 1021.3 | 760.4 | 639.7 | 633.2 | 896.3 | 935.2 | 829.9 | 718.3 | |
| SR | 1326.7 | 1454.9 | 1804.9 | 1489.0 | 1496.6 | 1528.6 | 1601.1 | 1891.5 | 1717.5 | 1625.0 | |
| SC | 1188.4 | 1366.3 | 1646.3 | 1362.2 | 1430.4 | 1227.5 | 1433.2 | 1798.6 | 1614.9 | 1402.2 | |
| CB | 3868.3 | 3866.0 | 4187.8 | 3947.4 | 3846.2 | 3823.3 | 4166.9 | 3991.8 | 4045.2 | 3923.9 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 25.0 | 47.4 | 26.6 | 32.9 | 39.2 | 25.8 | 23.0 | 60.7 | 56.7 | 36.9 |
| PS | 27.9 | 36.7 | 32.2 | 31.9 | 22.4 | 19.6 | 38.0 | 50.1 | 46.1 | 29.5 | |
| SR | 37.8 | 56.3 | 43.5 | 45.4 | 41.1 | 49.8 | 39.6 | 87.1 | 80.4 | 59.6 | |
| SC | 73.0 | 100.4 | 81.7 | 84.3 | 107.6 | 72.8 | 79.9 | 149.6 | 129.4 | 96.9 | |
| CB | 40.6 | 43.1 | 39.0 | 41.0 | 35.0 | 33.0 | 40.1 | 49.8 | 52.6 | 39.5 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 348.8 | 439.0 | 534.7 | 425.3 | 394.8 | 353.3 | 471.7 | 617.2 | 574.4 | 436.3 |
| PS | 665.9 | 703.1 | 1094.4 | 785.4 | 801.5 | 728.8 | 944.9 | 1000.4 | 868.1 | 807.6 | |
| SR | 1222.4 | 1336.4 | 1779.2 | 1399.6 | 1403.3 | 1283.2 | 1782.4 | 1970.0 | 1709.8 | 1483.3 | |
| SC | 1038.6 | 1205.6 | 1612.7 | 1237.8 | 1168.6 | 1070.2 | 1408.3 | 1817.2 | 1588.2 | 1273.9 | |
| CB | 3872.7 | 3857.2 | 4205.3 | 3950.7 | 3913.1 | 3867.3 | 4130.2 | 4221.4 | 4093.7 | 3969.3 | |
| Category | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM | MATH | DROP | avg. | FOL | PW | BBH | HE | MBPP | avg. | ||
| Reasoning Paradigm | CoT | 26.7 | 40.5 | 18.0 | 29.1 | 28.6 | 19.3 | 27.0 | 49.7 | 46.7 | 29.7 |
| PS | 31.2 | 41.1 | 23.8 | 32.6 | 36.3 | 25.1 | 37.1 | 46.7 | 42.7 | 33.6 | |
| SR | 44.6 | 52.2 | 29.9 | 43.5 | 51.7 | 39.0 | 54.1 | 72.8 | 64.1 | 50.4 | |
| SC | 76.4 | 130.4 | 56.5 | 89.4 | 70.8 | 66.0 | 72.4 | 132.9 | 123.9 | 83.9 | |
| CB | 63.2 | 65.4 | 35.5 | 57.0 | 56.1 | 53.8 | 52.1 | 71.5 | 72.0 | 59.1 | |
| Variant | QS | S&C | GU | LCR | ||||||||
| acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | |
| Full SoT | 66.1 | 545.8 | 16.8 | 76.8 | 408.4 | 19.0 | 81.3 | 133.2 | 5.8 | 25.2 | 254.0 | 23.4 |
| + Threshold Tuning | 66.1 | 545.8 | 16.8 | 76.8 | 408.4 | 19.0 | 81.3 | 133.2 | 5.8 | 25.2 | 254.0 | 23.4 |
| w/o Evid. Org. | 30.0 | 532.1 | 21.5 | 28.4 | 556.1 | 21.7 | 72.4 | 234.7 | 9.4 | 26.5 | 489.4 | 14.3 |
| w/o Stopping | 76.0 | 1401.9 | 37.4 | 32.4 | 2326.2 | 59.6 | 70.2 | 4175.0 | 100.9 | 31.7 | 2815.8 | 72.8 |
| w/o Geometry | 56.5 | 77.9 | 3.9 | 23.1 | 45.8 | 2.5 | 73.0 | 25.4 | 0.9 | 21.2 | 48.2 | 2.2 |
| Variant | QS | S&C | GU | LCR | ||||||||
| acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | |
| Full SoT | 46.3 | 248.2 | 43.8 | 51.7 | 329.8 | 62.6 | 72.5 | 143.6 | 28.0 | 23.5 | 260.6 | 62.8 |
| + Threshold Tuning | 46.3 | 248.2 | 43.8 | 51.7 | 329.8 | 62.6 | 72.5 | 143.6 | 28.0 | 23.5 | 260.6 | 62.8 |
| w/o Evid. Org. | 31.3 | 995.0 | 70.4 | 36.0 | 1002.6 | 65.8 | 63.2 | 836.8 | 51.0 | 3.0 | 921.1 | 90.7 |
| w/o Stopping | 31.3 | 995.0 | 64.0 | 36.0 | 1002.6 | 65.4 | 63.2 | 836.8 | 50.7 | 3.0 | 921.1 | 90.6 |
| w/o Geometry | 34.0 | 58.1 | 11.8 | 30.7 | 56.9 | 13.3 | 57.6 | 50.8 | 7.6 | 3.3 | 54.0 | 13.8 |
| Quantitative Reasoning | Symbolic and Code | |||||||||
| GSM8K | MATH | DROP | avg. | FOLIO | PW | BBH-T | HE | MBPP | avg. | |
| Top-3 Baseline avg. | 93.6 | 73.5 | 22.6 | 63.2 | 62.1 | 85.6 | 87.7 | 73.8 | 63.5 | 74.5 |
| SoT-Training-free | 81.8 | 60.8 | 34.6 | 59.1 | 49.5 | 30.2 | 77.0 | 53.0 | 50.4 | 52.0 |
| SoT-Embedding | 82.6 | 58.3 | 34.8 | 58.6 | 51.2 | 59.5 | 71.0 | 48.8 | 49.6 | 56.0 |
| Quantitative Reasoning | Symbolic and Code | |||||||||
| GSM8K | MATH | DROP | avg. | FOLIO | PW | BBH-T | HE | MBPP | avg. | |
| Top-3 Baseline avg. | 66.6 | 43.1 | 10.2 | 40.0 | 42.7 | 57.4 | 55.3 | 21.7 | 40.4 | 43.5 |
| SoT-Training-free | 75.2 | 52.2 | 34.4 | 53.9 | 31.3 | 50.5 | 63.0 | 56.1 | 49.2 | 50.0 |
| SoT-Embedding | 76.0 | 52.0 | 36.7 | 54.9 | 30.8 | 50.5 | 63.0 | 55.5 | 49.2 | 49.8 |
| Model | Method | Quantitative Reasoning | Symbolic and Code | ||||||||
| GSM8K | MATH | DROP | avg. | FOLIO | PW | BBH-T | HE | MBPP | avg. | ||
| GPT-5.4 | Self-Consistency | 92.0 | 78.0 | 5.0 | 58.3 | 69.0 | 77.0 | 86.0 | 87.0 | 77.0 | 79.2 |
| Self-Verification | 92.0 | 78.0 | 5.0 | 58.3 | 62.0 | 79.0 | 85.0 | 87.0 | 78.0 | 78.2 | |
| LLM-as-a-Judge | 92.0 | 79.0 | 4.0 | 58.3 | 70.0 | 76.0 | 86.0 | 86.0 | 78.0 | 79.2 | |
| SoT-Judge | 85.0 | 79.0 | 94.0 | 86.0 | 50.0 | 60.0 | 77.0 | 86.0 | 76.0 | 69.8 | |
| Claude 4.7 | Self-Consistency | 90.0 | 78.0 | 1.0 | 56.3 | 65.0 | 73.0 | 58.0 | 94.0 | 86.0 | 75.2 |
| Trajectory pool | QS | S&C | GU | LCR | ||||||||
| acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | acc. | tok. | lat. | |
| Full HQ pool | 70.8 | 247.9 | 6.3 | 57.1 | 324.2 | 11.1 | 75.5 | 58.0 | 1.6 | 37.3 | 121.1 | 97.5 |
| No filter | 71.3 | 931.3 | 30.0 | 57.7 | 1080.8 | 84.1 | 49.2 | 886.0 | 29.5 | 21.5 | 900.9 | 91.5 |
| Weak filter | 71.3 | 931.3 | 24.3 | 57.7 | 1080.8 | 34.5 | 49.2 | 886.0 | 17.7 | 21.3 | 900.9 | 90.7 |
| No pipeline | 71.3 | 931.3 | 26.1 | 57.7 | 1080.8 | 53.4 | 49.2 | 886.0 | 49.3 | 21.5 | 900.9 | 89.3 |
| Training-free | 72.3 | 917.4 | 26.0 | 58.3 | 1078.9 | 35.0 | 53.8 | 906.6 | 19.7 | 28.1 | 872.9 | 95.8 |