dapo-filtered

A small, difficulty-banded slice of competition math, cut so that a specific policy solves each problem rarely but not never. Built for rejection fine-tuning (RFT) and RL experiments, where a set the model never solves gives nothing to bootstrap from and a set it always solves gives nothing to learn.

Source: open-r1/DAPO-Math-17k-Processed (config en). Answers are bare integers; the reward is exact-match on a \boxed{} answer.

Files

file	rows	what
train.parquet	128	the training set: problems with 1 <= n_correct <= 4 out of 16
pool.parquet	28	remaining in-band problems, for regrowing or swapping the set
scored.parquet	1500	every scored candidate, with n_correct and mean_response_chars
candidates.parquet	1500	the unscored input slice (first 1500 rows of the source train split)
filter_summary.json	—	model, sampling settings, band, and the full distribution

scored.parquet is the reusable artefact: any other difficulty band can be cut from it on CPU, without re-running generation.

How the difficulty was measured

Every candidate was sampled 16 times with Qwen/Qwen3-4B-Instruct-2507 and graded with exact-match on the boxed answer:

setting	value
rollouts per problem	16
temperature / top_p	0.6 / 0.95
max_tokens	8192
thinking	off (this model has no <think> mode)

n_correct is how many of the 16 were right. Over all 1500 candidates, pass@16 = 0.898.

The distribution is strongly U-shaped — most problems are either always or never solved, which is exactly why a band is needed:

n_correct	problems		n_correct	problems
0/16	153		9–12/16	203
1–4/16	156		13–16/16	858
5–8/16	130

train.parquet takes 128 of the 156 problems in the 1–4 band. Its mean per-rollout accuracy for this model is 14.3%.

Columns

• prompt — chat messages: a system turn requesting a \boxed{} final answer, then the problem
• reward_model.ground_truth — the bare answer string (integers)
• data_source — math_dapo
• extra_info.index — unique integer id per problem
• n_correct (scored/train/pool) — correct rollouts out of 16
• mean_response_chars (scored/train/pool) — mean response length in characters

Note on the system prompt

The source dataset instructs the model to answer as Answer: $Answer. This set replaces that with a \boxed{} instruction, because the grader extracts the last \boxed{} and scores anything else wrong — a correct Answer: 34 would otherwise score as incorrect. If you re-grade with a different extractor, adjust the prompt to match.

Caveats

• Selection is stochastic. vLLM sampling was not seeded, so re-running the filter yields a somewhat different set. Use these files rather than rebuilding if you want to compare against results measured on them.
• Truncation. On the 128 selected problems, 34.8% of rollouts hit the 8192-token cap. Truncation is concentrated in failures — correct responses have p90 ≈ 7521 tokens — but measured accuracy is a floor, not the true number.
• Difficulty is model-specific. The band describes Qwen3-4B-Instruct-2507 under the settings above. Another model will find a different set easy or hard.