# Mathematical Reasoning on MATH500 (Pass@8/Avg@8)

Source: [Mathematical Reasoning on MATH500 (Pass@8/Avg@8)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math500-pass-at-8-avg-at-8>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-11T10:31:22.155Z

Evaluation of model performance on the MATH500 dataset for mathematical reasoning, specifically reporting results derived from 8 sampling attempts (Pass@8 and Avg@8).

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Mathematical reasoning |
| Dataset (including any stated split) | MATH500 |
| Metric | Avg Score (@8) |
| Unit | PERCENT |
| Direction | Higher is better |
| Results loaded | 18 of 18 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [Avg Score (@8)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math500-pass-at-8-avg-at-8.md?metric=Avg%20Score%20(%408)>): Higher is better; unit: PERCENT.

- [Pass@8](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math500-pass-at-8-avg-at-8.md?metric=Pass%408>): Higher is better; unit: PERCENT.

- [Average Score](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math500-pass-at-8-avg-at-8.md?metric=Average%20Score>): Higher is better; unit: PERCENT.

## Recorded results

| Method | Avg Score (@8) | Result date | Report paper |
| --- | --- | --- | --- |
| vOPDtop-k | 79.3 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| vOPDfull-V | 78.9 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPDfull-V | 78.6 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPD | 75.2 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPDtop-k | 75 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| vOPDtop-k | 64.9 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPDfull-V | 64.6 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| vOPDfull-V | 64.4 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| vOPDfull-V | 64 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| vOPDtop-k | 64 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPDfull-V | 62.8 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPD | 61.2 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPDtop-k | 58.8 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPD | 58.7 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| OPDtop-k | 58 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| Student | 51.1 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| Student | 43.1 | Not recorded | 6a0162c0dbc836b87d8233b0 |
| Student | 42.3 | Not recorded | 6a0162c0dbc836b87d8233b0 |

### vOPDtop-k

Avg Score (@8): 79.3. Result ID: 6a01aff747f34ce924e43f4a.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-4B → Qwen3-4B-Base"}. This record does not assert independent reproduction.

### vOPDfull-V

Avg Score (@8): 78.9. Result ID: 6a01aff747f34ce924e43f4b.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-4B → Qwen3-4B-Base"}. This record does not assert independent reproduction.

### OPDfull-V

Avg Score (@8): 78.6. Result ID: 6a01aff747f34ce924e43f49.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa71dd1e209131cea536d1.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-4B → Qwen3-4B-Base"}. This record does not assert independent reproduction.

### OPD

Avg Score (@8): 75.2. Result ID: 6a01aff747f34ce924e43f47.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-4B → Qwen3-4B-Base"}. This record does not assert independent reproduction.

### OPDtop-k

Avg Score (@8): 75. Result ID: 6a01aff747f34ce924e43f48.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69df1bcb7d0172140ec7bc19.md>)

[Implementation](<https://github.com/thunlp/OPD>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-4B → Qwen3-4B-Base"}. This record does not assert independent reproduction.

### vOPDtop-k

Avg Score (@8): 64.9. Result ID: 6a01aff747f34ce924e43f44.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-1.7B → Qwen3-1.7B-Base"}. This record does not assert independent reproduction.

### OPDfull-V

Avg Score (@8): 64.6. Result ID: 6a01aff747f34ce924e43f43.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa71dd1e209131cea536d1.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-1.7B → Qwen3-1.7B-Base"}. This record does not assert independent reproduction.

### vOPDfull-V

Avg Score (@8): 64.4. Result ID: 6a01aff747f34ce924e43f51.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Olmo-3-7B-Think → Olmo-3-7B-Base"}. This record does not assert independent reproduction.

### vOPDfull-V

Avg Score (@8): 64. Result ID: 6a01aff747f34ce924e43f45.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-1.7B → Qwen3-1.7B-Base"}. This record does not assert independent reproduction.

### vOPDtop-k

Avg Score (@8): 64. Result ID: 6a01aff747f34ce924e43f50.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Olmo-3-7B-Think → Olmo-3-7B-Base"}. This record does not assert independent reproduction.

### OPDfull-V

Avg Score (@8): 62.8. Result ID: 6a01aff747f34ce924e43f4f.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa71dd1e209131cea536d1.md>)

Recorded evaluation configuration: {"Model Setup":"Olmo-3-7B-Think → Olmo-3-7B-Base"}. This record does not assert independent reproduction.

### OPD

Avg Score (@8): 61.2. Result ID: 6a01aff747f34ce924e43f4d.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Olmo-3-7B-Think → Olmo-3-7B-Base"}. This record does not assert independent reproduction.

### OPDtop-k

Avg Score (@8): 58.8. Result ID: 6a01aff747f34ce924e43f4e.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69df1bcb7d0172140ec7bc19.md>)

[Implementation](<https://github.com/thunlp/OPD>)

Recorded evaluation configuration: {"Model Setup":"Olmo-3-7B-Think → Olmo-3-7B-Base"}. This record does not assert independent reproduction.

### OPD

Avg Score (@8): 58.7. Result ID: 6a01aff747f34ce924e43f41.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-1.7B → Qwen3-1.7B-Base"}. This record does not assert independent reproduction.

### OPDtop-k

Avg Score (@8): 58. Result ID: 6a01aff747f34ce924e43f42.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69df1bcb7d0172140ec7bc19.md>)

[Implementation](<https://github.com/thunlp/OPD>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-1.7B → Qwen3-1.7B-Base"}. This record does not assert independent reproduction.

### Student

Avg Score (@8): 51.1. Result ID: 6a01aff747f34ce924e43f46.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-4B → Qwen3-4B-Base"}. This record does not assert independent reproduction.

### Student

Avg Score (@8): 43.1. Result ID: 6a01aff747f34ce924e43f4c.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Olmo-3-7B-Think → Olmo-3-7B-Base"}. This record does not assert independent reproduction.

### Student

Avg Score (@8): 42.3. Result ID: 6a01aff747f34ce924e43f40.

[Reporting paper](<https://www.sota2.com/research/paper/6a0162c0dbc836b87d8233b0.md>)

Recorded evaluation configuration: {"Model Setup":"Qwen3-1.7B → Qwen3-1.7B-Base"}. This record does not assert independent reproduction.

Page 1 of 1. This is an index page, not the full collection.
