README.md

---
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}}
```