| --- |
| pretty_name: CFRL reasoning tasks (Countdown, Game24, Sudoku, Knights-and-Knaves) |
| license: other |
| license_name: mit-with-upstream-terms |
| license_link: LICENSE |
| language: |
| - en |
| task_categories: |
| - text-generation |
| size_categories: |
| - 1M<n<10M |
| tags: |
| - reasoning |
| - program-verified |
| - countdown |
| - game24 |
| - sudoku |
| - knights-and-knaves |
| - flow-matching |
| --- |
| |
| # CFRL reasoning tasks |
|
|
| The four program-verified reasoning datasets of the paper **CFRL** (reinforcement learning for continuous flow |
| language models), in the exact form used to fine-tune and evaluate the ELF-B checkpoints at |
| [tufts-ml/CFRL](https://huggingface.co/tufts-ml/CFRL). Every prompt has a program verifier that decides whether a |
| model output is correct without reference to the stored answer, so rewards are exact and label-free. |
|
|
| | task | `train` | `valid` (held out) | prompt | response | |
| |---|---|---|---|---| |
| | `countdown` | 500,000 | 2,000 | four or five integers and a target, e.g. `12 5 4 3 -> 25` | a chain of equations, e.g. `12-5=7 , 4*7=28 , 28-3=25` | |
| | `game24` | 13,150 | 1,601 | four numbers in 1..13, target 24 | a chain of equations reaching 24 | |
| | `sudoku` | 400,000 | 2,000 | the 81 cells of the puzzle, `*` for blanks | all 81 cells of the solution | |
| | `kk` | 300,000 | 2,000 | one statement per character, 4 to 6 characters | the knight/knave assignment | |
|
|
| The `valid` split holds the held-out prompts of the paper. They are split by index into a validation half (even |
| indices, used to select checkpoints) and a test half (odd indices, on which every reported accuracy is measured). |
| Game24 is split by number set: no held-out number set appears in training in any order. |
|
|
| ## Format |
|
|
| Each split is a Hugging Face `datasets` folder written with `Dataset.save_to_disk` (Arrow). Download the |
| repository and load a split with `datasets.load_from_disk` (`load_dataset` does not read this format): |
|
|
| ```python |
| from huggingface_hub import snapshot_download |
| from datasets import load_from_disk |
| |
| root = snapshot_download("tufts-ml/CFRL-data", repo_type="dataset") # all four tasks, 850 MB |
| ds = load_from_disk(f"{root}/countdown/train") |
| print(ds[0]["input"], "||", ds[0]["target"]) |
| ``` |
|
|
| To fetch a single task, pass `allow_patterns="countdown/*"` to `snapshot_download`. |
|
|
| Columns shared by all tasks: `input` and `target` (the raw strings), `condition_input_ids` and `input_ids` |
| (the T5-small token ids of prompt and response, each followed by EOS, as the ELF models consume them). Countdown |
| and Game24 add `nums`, `tgt` and `n_nums`; Knights-and-Knaves adds `n_nums` (the number of characters); Sudoku adds |
| `rating`, `clues` and `source` carried over from the upstream collection; the `valid` splits carry `index`. |
|
|
| To use the files with the CFRL code release, download them into its `data/` folder: |
|
|
| ```bash |
| hf download tufts-ml/CFRL-data --repo-type dataset --local-dir data |
| ``` |
|
|
| ## Where the data comes from |
|
|
| **Countdown, Game24 and Knights-and-Knaves are generated by the CFRL code** (`cfrl/tasks/build_*.py` in the |
| release) with seeded Python generators and no external input. The task formulations follow earlier work: |
|
|
| - **Countdown** follows the formulation of Stream of Search (Gandhi et al., 2024): random integers in 1..99, a |
| target in 10..100, and a derivation as a sequence of binary operations. One random valid derivation per problem |
| is stored as the supervised target; the verifier accepts any valid derivation. |
| - **Game24** follows the Game of 24 of Tree of Thoughts (Yao et al., 2023): reach 24 from four numbers in 1..13, |
| each used once. All 1,345 solvable unordered number sets were enumerated and split by set. |
| - **Knights-and-Knaves** follows Xie et al. (2024): each of 4 to 6 characters makes one statement ("A: C knave", |
| "B: A same C", "C: D diff B"); only puzzles with a unique solution are kept. The generator and the compact |
| statement format are the release's own. |
|
|
| **Sudoku is derived from a third-party collection.** The puzzles and solutions are taken from |
| [sapientinc/sudoku-extreme](https://huggingface.co/datasets/sapientinc/sudoku-extreme), the "Hardest Sudoku |
| Puzzle Dataset V2" released by Sapient Intelligence with the Hierarchical Reasoning Model (Wang et al., 2025). |
| That collection combines puzzles from the [tdoku benchmark sets](https://github.com/t-dillon/tdoku/blob/master/benchmarks/README.md#benchmarked-data-sets) |
| and the [enjoysudoku forum](http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-600.html#p277835), |
| exact-deduplicated and randomly permuted, with a difficulty rating from the tdoku solver. Our `train` split is |
| 400,000 puzzles sampled from its `train.csv` and our `valid` split 2,000 puzzles sampled from its `test.csv`, |
| so the two remain mathematically inequivalent as in the upstream collection. The `rating`, `clues` and `source` |
| columns are the upstream fields. The upstream dataset card states no license; the Sudoku splits here are |
| redistributed under the upstream collection's terms, whatever they are, and the MIT license of this repository |
| covers only the generated tasks and the packaging. |
|
|
| Token ids were produced with the T5-small tokenizer (Raffel et al., 2020), the encoder of ELF (Hu et al., 2026). |
|
|
| ## Reproducing the splits |
|
|
| `scripts/prepare_data.sh` in the code release regenerates the Countdown splits and the Sudoku `train` split |
| byte-for-byte. The remaining splits were produced by the same builders with different seeds or ordering than the |
| script states (Sudoku `valid`: seed 1; Knights-and-Knaves `valid`: seed 11, and `train`: seed 0 excluding the |
| `valid` prompts), and the Game24 split keeps a subset of the orderings of each training set. The files in this |
| repository are therefore the canonical splits; treat the script as documentation of the generators. |
|
|
| ## Citation |
|
|
| If you use this data, please cite the CFRL paper and the sources of the tasks: |
|
|
| ```bibtex |
| @article{gandhi2024sos, |
| title={Stream of Search ({SoS}): Learning to Search in Language}, |
| author={Gandhi, Kanishk and Lee, Denise and Grand, Gabriel and Liu, Muxin and Cheng, Winson and Sharma, Archit and Goodman, Noah D.}, |
| journal={arXiv preprint arXiv:2404.03683}, year={2024}} |
| @article{yao2023tot, |
| title={Tree of Thoughts: Deliberate Problem Solving with Large Language Models}, |
| author={Yao, Shunyu and Yu, Dian and Zhao, Jeffrey and Shafran, Izhak and Griffiths, Thomas L. and Cao, Yuan and Narasimhan, Karthik}, |
| journal={arXiv preprint arXiv:2305.10601}, year={2023}} |
| @article{xie2024kk, |
| title={On Memorization of Large Language Models in Logical Reasoning}, |
| author={Xie, Chulin and Huang, Yangsibo and Zhang, Chiyuan and Yu, Da and Chen, Xinyun and Lin, Bill Yuchen and Li, Bo and Ghazi, Badih and Kumar, Ravi}, |
| journal={arXiv preprint arXiv:2410.23123}, year={2024}} |
| @article{wang2025hrm, |
| title={Hierarchical Reasoning Model}, |
| author={Wang, Guan and Li, Jin and Sun, Yuhao and Chen, Xing and Liu, Changling and Wu, Yue and Lu, Meng and Song, Sen and Abbasi Yadkori, Yasin}, |
| journal={arXiv preprint arXiv:2506.21734}, year={2025}} |
| @misc{sudokuextreme, |
| title={Hardest Sudoku Puzzle Dataset V2 (sudoku-extreme)}, author={Sapient Intelligence}, |
| howpublished={\url{https://huggingface.co/datasets/sapientinc/sudoku-extreme}}} |
| @article{hu2026elf, |
| title={{ELF}: Embedded Language Flows}, |
| author={Hu, Keya and Qiu, Linlu and Lu, Yiyang and Zhao, Hanhong and Li, Tianhong and Kim, Yoon and Andreas, Jacob and He, Kaiming}, |
| journal={arXiv preprint arXiv:2605.10938}, year={2026}} |
| @article{cfrl2026, |
| title={CFRL: Reinforcement Learning for Continuous Flow Language Models}, |
| year={2026}} |
| ``` |
|
|
