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README.md

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+---
+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). Load with
+`datasets.load_from_disk`, not `load_dataset`:
+
+```python
+from datasets import load_from_disk
+ds = load_from_disk("data/countdown/train")
+print(ds[0]["input"], "||", ds[0]["target"])
+```
+
+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}}
+```