hi-todayis-jh/Polaris-Hard

Polaris-Hard

A random subset of Polaris-Dataset-53K, with 3,200 distinct math problems in a single train split.

Sampling

• —Source revision: `296f8e34132e63f4a1d70e0dcc8bddebb43f03e4`.
• —Seed: 42. Uniform random sampling without replacement within each group, followed by a deterministic shuffle of the combined selection.
• —Independent group RNGs: random.Random("polaris-hard-numeric-v1:{seed}:{difficulty}"), using sample on eligible zero-based source indices in source order. The dataset name provides a separate RNG namespace for each subset.
• —Final shuffle RNG: random.Random("polaris-hard-numeric-v1:{seed}:shuffle").
• —The original problem, answer, and difficulty fields are unchanged. Sampling is performed only after the numerical-answer and explicit-proof filters below; source fields are unchanged.
• —sampling_manifest.json records the source checksum, all selected source indices in output order, the Parquet checksum, and validation results.

Numerical-answer filtering

Policy: finite-real-no-explicit-proof-v1. This revision replaces the earlier unfiltered random sample; the earlier files remain accessible through Hub commit history.

1. 1.Wrap the original answer in \boxed{} and parse it with Math-Verify's default LatexExtractionConfig, with string fallback disabled.
2. 2.Retain exactly one finite real numeric expression with no free symbols. Integers, decimals, fractions, roots, and constants such as pi are supported. Symbolic expressions, equations, lists, sets, intervals, infinities, and unparsed strings are excluded.
3. 3.Require a score of 1 when the original boxed answer is passed through the same gold/prediction extraction configuration as the training Math-Verify metric and compared with itself. The parsing timeout and outer grading deadline are each one second.
4. 4.Conservatively exclude questions containing explicit proof-related wording: \b(?:prove|proof|proving|show|demonstrate|establish|justify)\b|证明|證明|证得|证出. This also excludes mixed tasks that request both a proof and a numerical result.

This checks numerical parseability and reward-format compatibility. It does not independently prove that every source answer is mathematically correct, nor is the wording filter a full semantic classifier. The full eligible source-index lists and rejection counts are recorded in the manifest, so the exact sampling pools can be reconstructed.

Difficulty labels

The source dataset defines difficulty as the pass rate estimated by Deepseek-R1-distill-Qwen-7B. Thus, 0/8 and 1/8 refer to that reference model's outcomes. They do not establish the success rate of another model, and a 0/8 label does not prove a problem is unsolvable. Original answer quality and any overlap with other datasets are inherited from the source.

Usage

from datasets import load_dataset

dataset = load_dataset("hi-todayis-jh/Polaris-Hard", split="train")

To reproduce the sampled rows, install datasets and huggingface_hub, math-verify==0.9.0, sympy==1.13.1, and latex2sympy2_extended==1.11.0, then run:

python reproduce.py --output-dir ./reproduced --seed 42 --name Polaris-Hard --group 0/8=2000 --group 1/8=1200 --repo-id hi-todayis-jh/Polaris-Hard --numeric-only

The dataset is a training subset; no held-out validation or test split is provided.

Attribution and license

The upstream dataset is provided by the POLARIS project, whose dataset card identifies DeepScaleR-Preview-Dataset and AReal-boba-Data as its sources. This subset retains the upstream Apache-2.0 license; see LICENSE. The changes made here are row selection and row ordering only.