nl-assignment-midtraining

The midtraining corpus of the number-assignment puzzle experiments: 39,760 step-by-step solution traces for 9,940 puzzles with 5-8 people (Levels 1-4), 17.9M GPT-2 tokens. Every trace is written by a deterministic solver program, not by a language model. The same corpus is also given as the tokenized shard that was mixed into pretraining.

The puzzles

Each puzzle names n people who each picked a different number from a shown set of n numbers. Clues relate the numbers: sums ("Liam's and Nora's numbers add up to 12"), differences ("Felix's number is 18 more than Jasper's"), comparisons ("larger than"), parity, multiples ("exactly twice", "exactly three times") and extremes ("has the largest number"). A puzzle is generated from a random solution: true clues are added until checking every permutation leaves exactly one assignment, then a few redundant clues are added and the clue order is shuffled. The answer is the full assignment Name=number, ... inside \boxed{...}.

Level	People	Numbers drawn from	Redundant clues	In this corpus
1	5	1-30	0	2,476 questions, 9,904 traces
2	6	1-30	0	2,473 questions, 9,892 traces
3	7	1-30	2	2,492 questions, 9,968 traces
4	8	1-36	3	2,499 questions, 9,996 traces
5	9	1-40	4	none (RL prompts and tests only)
6	10	1-44	5	none (RL prompts and tests only)

How the traces are written

• The questions use only sum, difference, comparison and parity clues: for each level, questions with "twice", "three times", "largest" or "smallest" clues were removed, then 2,500 questions were sampled (seed 7). RL prompts and test questions use every clue type.
• A solver narrates candidate elimination. For each clue it lists the value pairs that remain ("From Felix - Jasper = 18, the only options are (Felix,Jasper) in {(23,5)}."), fixes a person once one value is left, and removes that value from everyone else. The trace ends with \boxed{answer}.
• Each question gets 4 distinct traces from up to 8 solver variants (clue order, unary-first or binary-first processing, wording). A variant is kept only if it reaches the gold answer. The solver never guesses; questions it could not finish were dropped, so 2,473-2,499 of the 2,500 questions per level remain, each with exactly 4 traces.
• No GPU and no language model are involved.

Separation from RL prompts and tests

qid is the first 16 hex characters of the SHA-256 of the question text. None of the 9,940 questions appears, by qid or by exact text, in the 1,024-question test sets of Levels 4, 5 and 6 or in the RL prompt pools (20,000 prompts each for Levels 4 and 5, 5,000 for Level 6). The 4 traces of a question are alternative derivations of the same puzzle, not independent questions.

Files

File	Rows	Content
midtraining_traces.jsonl	39,760	all traces, Levels 1-4, shuffled; this is also the document order of the tokenized shard
rl_demonstrations.jsonl	9,996	the Level 4 rows of midtraining_traces.jsonl, in the same order (2,499 questions)
tokenized/shard_000000.bin, .idx	39,760 documents	midtraining_traces.jsonl tokenized for pretraining (below)
tokenized/shard_000000.metadata.json		tokenization contract, counts and sha256 of the source file, .bin and .idx

Field	Meaning
qid	question id (16 hex characters); the 4 traces of a question share it
prompt	the puzzle text followed by "\n\nAnswer: " (the exact model input)
target	the solver's trace, ending with \boxed{...}
answer	the gold assignment, Name=number, ...

from datasets import load_dataset
traces = load_dataset("sfanm/nl-assignment-midtraining", "midtraining_traces", split="train")
demos = load_dataset("sfanm/nl-assignment-midtraining", "rl_demonstrations", split="train")

Tokenized shard

• Megatron indexed dataset (MMIDIDX, version 1), uint16 GPT-2 BPE token ids: 39,760 documents, 17,879,758 tokens (mean 449.7 per document).
• Each document is the GPT-2 tokens of prompt, then of target, then EOS id 50256, with no BOS (contract separate_prompt_response_gpt2_eos_v1). Local file paths in the original metadata were replaced by repository-relative names; nothing else was changed.
• sha256 of .bin: 801bd07ee1e6c0edc38552df0b88b8e82699893d472341d5d904401ff04523c8; of .idx: 90d3ec17dfe8f699c21b28502912df448050cacb5996a619218e7b3ff0557340; of midtraining_traces.jsonl: 98df21c7a14437d9e8ba0ba8f390a186acd0d60412b5bcaa57131f0cf8851d1d.
• Download it with huggingface_hub.snapshot_download(..., allow_patterns="tokenized/*") and read it with Megatron-Core's IndexedDataset (prefix shard_000000).

How the data was used

• Mixed into pretraining. A 124M-parameter model (sfanm/d12-pretrain-climbmix15B-dolmino5B is its final checkpoint without traces) was pretrained for 38,147 updates of 256 sequences of 2,048 tokens. In the last 8,147 updates (from update 30,000), each update added k packed 2,048-token sequences from the tokenized shard to the 256 pretraining sequences, for k = 4, 8, 16, 24, 32 or 64: 67M to 1.07B trace tokens, or 3.7 to 59.7 passes over the shard.
• Supervised fine-tuning baseline. The final pretrained model was fine-tuned on midtraining_traces.jsonl for 8 epochs, with loss on the target tokens only.
• RL demonstrations. RL on Level 4, 5 and 6 prompts appended rows of rl_demonstrations.jsonl to each update as demonstrations.

Limitations

• Synthetic puzzles in a narrow template language; the traces follow a fixed narration style.
• The traces cover only 5-8 people and four of the six clue types, by design.

Code

Code: to be added.

License

Apache-2.0. All content is generated by the authors' own code (puzzle generator and solver); no third-party text is included.

Authors and citation

Authors and citation: to be added.