Datasets:

chengshuaizhao
/

DataAlchemy

input stringlengths 21 21	output stringlengths 7 7	element stringlengths 7 7	transformation stringclasses 1 value	instruction stringclasses 1 value	answer stringlengths 7 7
A A A A [F1] <answer>	N N N N	A A A A	[F1]	<answer>	N N N N
A A A B [F1] <answer>	N N N O	A A A B	[F1]	<answer>	N N N O
A A A C [F1] <answer>	N N N P	A A A C	[F1]	<answer>	N N N P
A A A D [F1] <answer>	N N N Q	A A A D	[F1]	<answer>	N N N Q
A A A E [F1] <answer>	N N N R	A A A E	[F1]	<answer>	N N N R
A A A F [F1] <answer>	N N N S	A A A F	[F1]	<answer>	N N N S
A A A G [F1] <answer>	N N N T	A A A G	[F1]	<answer>	N N N T
A A A H [F1] <answer>	N N N U	A A A H	[F1]	<answer>	N N N U
A A A I [F1] <answer>	N N N V	A A A I	[F1]	<answer>	N N N V
A A A J [F1] <answer>	N N N W	A A A J	[F1]	<answer>	N N N W
A A A K [F1] <answer>	N N N X	A A A K	[F1]	<answer>	N N N X
A A A L [F1] <answer>	N N N Y	A A A L	[F1]	<answer>	N N N Y
A A A M [F1] <answer>	N N N Z	A A A M	[F1]	<answer>	N N N Z
A A A N [F1] <answer>	N N N A	A A A N	[F1]	<answer>	N N N A
A A A O [F1] <answer>	N N N B	A A A O	[F1]	<answer>	N N N B
A A A P [F1] <answer>	N N N C	A A A P	[F1]	<answer>	N N N C
A A A Q [F1] <answer>	N N N D	A A A Q	[F1]	<answer>	N N N D
A A A R [F1] <answer>	N N N E	A A A R	[F1]	<answer>	N N N E
A A A S [F1] <answer>	N N N F	A A A S	[F1]	<answer>	N N N F
A A A T [F1] <answer>	N N N G	A A A T	[F1]	<answer>	N N N G
A A A U [F1] <answer>	N N N H	A A A U	[F1]	<answer>	N N N H
A A A V [F1] <answer>	N N N I	A A A V	[F1]	<answer>	N N N I
A A A W [F1] <answer>	N N N J	A A A W	[F1]	<answer>	N N N J
A A A X [F1] <answer>	N N N K	A A A X	[F1]	<answer>	N N N K
A A A Y [F1] <answer>	N N N L	A A A Y	[F1]	<answer>	N N N L
A A A Z [F1] <answer>	N N N M	A A A Z	[F1]	<answer>	N N N M
A A B A [F1] <answer>	N N O N	A A B A	[F1]	<answer>	N N O N
A A B B [F1] <answer>	N N O O	A A B B	[F1]	<answer>	N N O O
A A B C [F1] <answer>	N N O P	A A B C	[F1]	<answer>	N N O P
A A B D [F1] <answer>	N N O Q	A A B D	[F1]	<answer>	N N O Q
A A B E [F1] <answer>	N N O R	A A B E	[F1]	<answer>	N N O R
A A B F [F1] <answer>	N N O S	A A B F	[F1]	<answer>	N N O S
A A B G [F1] <answer>	N N O T	A A B G	[F1]	<answer>	N N O T
A A B H [F1] <answer>	N N O U	A A B H	[F1]	<answer>	N N O U
A A B I [F1] <answer>	N N O V	A A B I	[F1]	<answer>	N N O V
A A B J [F1] <answer>	N N O W	A A B J	[F1]	<answer>	N N O W
A A B K [F1] <answer>	N N O X	A A B K	[F1]	<answer>	N N O X
A A B L [F1] <answer>	N N O Y	A A B L	[F1]	<answer>	N N O Y
A A B M [F1] <answer>	N N O Z	A A B M	[F1]	<answer>	N N O Z
A A B N [F1] <answer>	N N O A	A A B N	[F1]	<answer>	N N O A
A A B O [F1] <answer>	N N O B	A A B O	[F1]	<answer>	N N O B
A A B P [F1] <answer>	N N O C	A A B P	[F1]	<answer>	N N O C
A A B Q [F1] <answer>	N N O D	A A B Q	[F1]	<answer>	N N O D
A A B R [F1] <answer>	N N O E	A A B R	[F1]	<answer>	N N O E
A A B S [F1] <answer>	N N O F	A A B S	[F1]	<answer>	N N O F
A A B T [F1] <answer>	N N O G	A A B T	[F1]	<answer>	N N O G
A A B U [F1] <answer>	N N O H	A A B U	[F1]	<answer>	N N O H
A A B V [F1] <answer>	N N O I	A A B V	[F1]	<answer>	N N O I
A A B W [F1] <answer>	N N O J	A A B W	[F1]	<answer>	N N O J
A A B X [F1] <answer>	N N O K	A A B X	[F1]	<answer>	N N O K
A A B Y [F1] <answer>	N N O L	A A B Y	[F1]	<answer>	N N O L
A A B Z [F1] <answer>	N N O M	A A B Z	[F1]	<answer>	N N O M
A A C A [F1] <answer>	N N P N	A A C A	[F1]	<answer>	N N P N
A A C B [F1] <answer>	N N P O	A A C B	[F1]	<answer>	N N P O
A A C C [F1] <answer>	N N P P	A A C C	[F1]	<answer>	N N P P
A A C D [F1] <answer>	N N P Q	A A C D	[F1]	<answer>	N N P Q
A A C E [F1] <answer>	N N P R	A A C E	[F1]	<answer>	N N P R
A A C F [F1] <answer>	N N P S	A A C F	[F1]	<answer>	N N P S
A A C G [F1] <answer>	N N P T	A A C G	[F1]	<answer>	N N P T
A A C H [F1] <answer>	N N P U	A A C H	[F1]	<answer>	N N P U
A A C I [F1] <answer>	N N P V	A A C I	[F1]	<answer>	N N P V
A A C J [F1] <answer>	N N P W	A A C J	[F1]	<answer>	N N P W
A A C K [F1] <answer>	N N P X	A A C K	[F1]	<answer>	N N P X
A A C L [F1] <answer>	N N P Y	A A C L	[F1]	<answer>	N N P Y
A A C M [F1] <answer>	N N P Z	A A C M	[F1]	<answer>	N N P Z
A A C N [F1] <answer>	N N P A	A A C N	[F1]	<answer>	N N P A
A A C O [F1] <answer>	N N P B	A A C O	[F1]	<answer>	N N P B
A A C P [F1] <answer>	N N P C	A A C P	[F1]	<answer>	N N P C
A A C Q [F1] <answer>	N N P D	A A C Q	[F1]	<answer>	N N P D
A A C R [F1] <answer>	N N P E	A A C R	[F1]	<answer>	N N P E
A A C S [F1] <answer>	N N P F	A A C S	[F1]	<answer>	N N P F
A A C T [F1] <answer>	N N P G	A A C T	[F1]	<answer>	N N P G
A A C U [F1] <answer>	N N P H	A A C U	[F1]	<answer>	N N P H
A A C V [F1] <answer>	N N P I	A A C V	[F1]	<answer>	N N P I
A A C W [F1] <answer>	N N P J	A A C W	[F1]	<answer>	N N P J
A A C X [F1] <answer>	N N P K	A A C X	[F1]	<answer>	N N P K
A A C Y [F1] <answer>	N N P L	A A C Y	[F1]	<answer>	N N P L
A A C Z [F1] <answer>	N N P M	A A C Z	[F1]	<answer>	N N P M
A A D A [F1] <answer>	N N Q N	A A D A	[F1]	<answer>	N N Q N
A A D B [F1] <answer>	N N Q O	A A D B	[F1]	<answer>	N N Q O
A A D C [F1] <answer>	N N Q P	A A D C	[F1]	<answer>	N N Q P
A A D D [F1] <answer>	N N Q Q	A A D D	[F1]	<answer>	N N Q Q
A A D E [F1] <answer>	N N Q R	A A D E	[F1]	<answer>	N N Q R
A A D F [F1] <answer>	N N Q S	A A D F	[F1]	<answer>	N N Q S
A A D G [F1] <answer>	N N Q T	A A D G	[F1]	<answer>	N N Q T
A A D H [F1] <answer>	N N Q U	A A D H	[F1]	<answer>	N N Q U
A A D I [F1] <answer>	N N Q V	A A D I	[F1]	<answer>	N N Q V
A A D J [F1] <answer>	N N Q W	A A D J	[F1]	<answer>	N N Q W
A A D K [F1] <answer>	N N Q X	A A D K	[F1]	<answer>	N N Q X
A A D L [F1] <answer>	N N Q Y	A A D L	[F1]	<answer>	N N Q Y
A A D M [F1] <answer>	N N Q Z	A A D M	[F1]	<answer>	N N Q Z
A A D N [F1] <answer>	N N Q A	A A D N	[F1]	<answer>	N N Q A
A A D O [F1] <answer>	N N Q B	A A D O	[F1]	<answer>	N N Q B
A A D P [F1] <answer>	N N Q C	A A D P	[F1]	<answer>	N N Q C
A A D Q [F1] <answer>	N N Q D	A A D Q	[F1]	<answer>	N N Q D
A A D R [F1] <answer>	N N Q E	A A D R	[F1]	<answer>	N N Q E
A A D S [F1] <answer>	N N Q F	A A D S	[F1]	<answer>	N N Q F
A A D T [F1] <answer>	N N Q G	A A D T	[F1]	<answer>	N N Q G
A A D U [F1] <answer>	N N Q H	A A D U	[F1]	<answer>	N N Q H
A A D V [F1] <answer>	N N Q I	A A D V	[F1]	<answer>	N N Q I

End of preview. Expand in Data Studio

DataAlchemy: A Controllable Laboratory for the Science of Chain-of-Thought Reasoning

Supplementary data collection for the paper "Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens" (ACL 2026). Full generator, trainer, and evaluator live in the GitHub repo.

TL;DR

A symbolic data collection for controlled study of Chain-of-Thought (CoT) reasoning in LLMs. Each record pairs a prompt with a step-by-step reasoning trace and a final answer, produced under the DataAlchemy framework. The files span multiple compositions of base transformations at varying reasoning depths, enabling systematic probes of how CoT behavior shifts as the test distribution drifts from the training distribution.

File inventory

All 8 files share identical generation settings: every element is a 4-atom sequence drawn from {A…Z}, [F1] is ROT-13 (shift each atom by 13 positions), [F2] is a cyclic left shift by one position, reasoning traces are enabled, and no noise or subsampling is applied. Enumerating every possible 4-atom element gives 456,976 records per file (≈ 3.66 M records total).

File	Composition	`k`	# records	CoT	What the transformation does
`F1.jsonl`	`[F1]`	1	456,976	✓	ROT-13 on each atom
`F2.jsonl`	`[F2]`	1	456,976	✓	cyclic left shift by 1
`F1F1.jsonl`	`[F1] [F1]`	2	456,976	✓	ROT-13 twice (identity on atoms)
`F1F2.jsonl`	`[F1] [F2]`	2	456,976	✓	ROT-13, then cyclic shift
`F2F1.jsonl`	`[F2] [F1]`	2	456,976	✓	cyclic shift, then ROT-13
`F2F2.jsonl`	`[F2] [F2]`	2	456,976	✓	cyclic shift by 2 (equivalently)
`F1F1F1.jsonl`	`[F1] [F1] [F1]`	3	456,976	✓	ROT-13 three times
`F2F2F2.jsonl`	`[F2] [F2] [F2]`	3	456,976	✓	cyclic shift three times

How to load

from datasets import load_dataset

ds = load_dataset("ChengshuaiZhao0/DataAlchemy", name="F1F2", split="train")
print(ds[0])
# {'input': 'A A A A [F1] [F2] <think>',
#  'output': 'N N N N [F2] <answer> N N N N',
#  'element': 'A A A A', 'transformation': '[F1] [F2]',
#  'instruction': '<think>', 'reasoning': 'N N N N [F2]',
#  'answer': 'N N N N'}

Or load any file directly as raw JSONL:

import json
with open("F1F2.jsonl") as f:
    records = [json.loads(line) for line in f]

Record schema

One JSON object per line. Invariant: input == element + " " + transformation + " " + instruction, and the full rendered line is input + " " + output.

Field	Type	Meaning
`input`	str	What the LM conditions on: `element + " " + transformation + " " + instruction`.
`output`	str	What the LM should produce: reasoning trace (if any) + `<answer>` + final element.
`element`	str	Input element atoms, space-joined.
`transformation`	str	Transformation tokens, e.g. `[F1] [F2]`.
`instruction`	str	Output-start marker: `<think>` for CoT, `<answer>` for no-CoT.
`reasoning`	str	Trace inside `output` before the final `<answer>`. Empty for `k=1`.
`answer`	str	Final element after `<answer>`.

Intended use

Two common usage examples:

Task generalization — pick subsets of the k=2 files (F1F1, F1F2, F2F1, F2F2) as training and test set. This probes how well CoT reasoning transfers to an unseen task of primitives.
Length / reasoning-depth generalization — use the single-primitive chains F1 → F1F1 → F1F1F1 (and analogously F2 → F2F2 → F2F2F2) to train at one depth k and evaluate at another. This probes whether CoT reasoning extrapolates to deeper reasoning chain than the model saw at training time.

Refer to experiments/ and the GitHub README for pre-wired launchers.

How the data was generated

Every file in this collection was produced with scripts/generate_data.py from the GitHub repo:

# k=1
python scripts/generate_data.py --transformations "[F1]" --element-length 4 --output data/F1.jsonl
python scripts/generate_data.py --transformations "[F2]" --element-length 4 --output data/F2.jsonl

# k=2
python scripts/generate_data.py --transformations "[F1]" "[F1]" --element-length 4 --output data/F1F1.jsonl
python scripts/generate_data.py --transformations "[F1]" "[F2]" --element-length 4 --output data/F1F2.jsonl
python scripts/generate_data.py --transformations "[F2]" "[F1]" --element-length 4 --output data/F2F1.jsonl
python scripts/generate_data.py --transformations "[F2]" "[F2]" --element-length 4 --output data/F2F2.jsonl

# k=3
python scripts/generate_data.py --transformations "[F1]" "[F1]" "[F1]" --element-length 4 --output data/F1F1F1.jsonl
python scripts/generate_data.py --transformations "[F2]" "[F2]" "[F2]" --element-length 4 --output data/F2F2F2.jsonl

Reproducibility & provenance

Every record is deterministic given --element-length, --rot-n, --pos-n, and the transformation list — no randomness is involved for these 8 base files. Re-running the commands above with the stated flags reproduces every file byte-for-byte.

License

Released under the MIT License.

Citation

If our data helped you out, we'd love it if you gave us a citation!

@article{zhao2025chain,
  title={Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens},
  author={Zhao, Chengshuai and Tan, Zhen and Ma, Pingchuan and Li, Dawei and Jiang, Bohan and Wang, Yancheng and Yang, Yingzhen and Liu, Huan},
  journal={arXiv preprint arXiv:2508.01191},
  year={2025}
}

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Paper for chengshuaizhao/DataAlchemy

Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens

Paper • 2508.01191 • Published Aug 2, 2025 • 240