---
language:
- en
task_categories:
- text-generation
tags:
- math
- reasoning
- evaluation
- decomposition
configs:
- config_name: math5000
  data_files:
  - split: test
    path: data/math5000/*.parquet
- config_name: amc23
  data_files:
  - split: test
    path: data/amc23/*.parquet
- config_name: aime24
  data_files:
  - split: test
    path: data/aime24/*.parquet
- config_name: aime25
  data_files:
  - split: test
    path: data/aime25/*.parquet
---
# Math recursive evaluation traces

Full saved evaluation trajectories for GRPO-BINARY and GRPO-TW at fixed step-100 checkpoints. **158,400 rollouts**, including all successes and failures from the original evaluation and three additional repeats.

## Browse

Select a benchmark configuration (`math5000`, `amc23`, `aime24`, `aime25`). Every configuration has a `test` split and the same columns. One row is one complete rollout, not one child call and not an average.

| Benchmark | Questions | Samples per question per run/model/method | Rollout rows |
|---|---:|---:|---:|
| math5000 | 5000 | 1 | 120,000 |
| amc23 | 40 | 16 | 15,360 |
| aime24 | 30 | 16 | 11,520 |
| aime25 | 30 | 16 | 11,520 |

## Columns

- `question`, `reference_answer`: exact frozen evaluation inputs, including documented repairs.
- `model_output`: all complete call outputs in recorded order, with call identifiers and roles. No summaries or truncation in the stored data.
- `trajectory`: structured list containing every saved call field, including complete `input_text`, `output_text`, parent IDs, aggregation links, token counts, and parse status. Recorded order is not a claim that parallel calls executed sequentially.
- `decoding_method`: `free_choice`, `forced_direct`, or `forced_decomposition`; the intervention applies at the root. `root_action` records the actual root action. Recursive child behavior remains visible in the trajectory.
- `model` / `model_id`, `checkpoint_step`, `checkpoint_manifest_sha256`: model identity; this digest identifies the checkpoint manifest, not a direct hash of the weights.
- `run`: `original`, `repeat_1`, `repeat_2`, or `repeat_3`. `repeat=0` denotes the original. `sample_index` is zero based.
- `temperature`: 0 for MATH5000 (one greedy answer); 0.5 for AMC/AIME (16 samples per question). All use top-p 1 and top-k 0.
- `base_seed`, `cell_seed`, `shard_id`: recorded run and execution-cell seeds. These are not independently assigned per-rollout seeds.
- `answer_correct`: audited final-answer equivalence; `format_valid`: saved protocol validity; `strict_correct`: both. The reported evaluation table uses strict correctness.
- `original_grading_json`, `audited_grading_json`, `adjudication_json`, `grading_method`, `reviewer`: preserve parser results and applied exact prediction/reference-pair review decisions. Codex review is AI review, not human annotation.
- `source_file`, `source_line`, hashes, and dataset revision fields: immutable source provenance. Source paths are repository-relative.

## Reproduce the three-repeat evaluation

Filter to `repeat` in `[1, 2, 3]`; the original is retained for provenance and is excluded from the reported three-repeat mean and sample SD. For each run/model/method, mean@k is the mean of `strict_correct`; pass@16 is the fraction of questions with at least one strictly correct answer among that run’s 16 samples. Compute per-run metrics first and then average the three runs. Pooling 48 samples would be a different metric.

```python
from datasets import load_dataset
ds = load_dataset("parksoojae/math-recursive-eval-traces", "math5000", split="test", token=True)
repeats = ds.filter(lambda row: row["repeat"] in (1, 2, 3))
```

## Provenance and limitations

The export was read back from Parquet and checked against all 96 audited run/model/method/benchmark cells, including answer-only and strict mean/pass metrics (384 comparisons). Every trajectory was round-trip checked. No new inference, regrading, checkpoint upload, or modification of frozen artifacts occurred.

These are repeats of inference with fixed trained checkpoints, not independent training seeds. Correct final answers do not certify correct reasoning. Frozen grading is retained, including known limitations; later qualitative failure-audit flags do not silently override benchmark grades. This release does not include the subjective failure-category labels as benchmark truth.

See `provenance/` for input repairs, source hashes, exact-pair adjudications, per-run score tables, and validation results.

## Upstream benchmark sources

- **math5000**: [DigitalLearningGmbH/MATH-lighteval](https://huggingface.co/datasets/DigitalLearningGmbH/MATH-lighteval/tree/0530c78699ea5e8eb5530600900e1f328b48acad), test split, revision `0530c78699ea5e8eb5530600900e1f328b48acad`.
- **amc23**: [math-ai/amc23](https://huggingface.co/datasets/math-ai/amc23/tree/80815d37005feb82cd7f8fbc6901d5d3eff43057), test split, revision `80815d37005feb82cd7f8fbc6901d5d3eff43057`.
- **aime24**: [math-ai/aime24](https://huggingface.co/datasets/math-ai/aime24/tree/83a7f387baaa524a8bda0022eac0541582297103), test split, revision `83a7f387baaa524a8bda0022eac0541582297103`.
- **aime25**: [math-ai/aime25](https://huggingface.co/datasets/math-ai/aime25/tree/563bb8404243c5f09de6ec262f2db674fe5bce9b), test split, revision `563bb8404243c5f09de6ec262f2db674fe5bce9b`.

Questions and reference answers retain their upstream rights and terms; this private export does not grant a new blanket license to the combined material. Upstream provenance is recorded rather than assigning an unsupported aggregate license.