Recursive Arithmetic Transformer training frames

There was no static training file. The model sampled integers online every step. This dataset replays that sampler with the same Python RNGs used in train_recursive:

RNG	Seed	What it draws
mix_rng	seed + 91	task mix, operand lengths, integers
offset_rng	seed + 17	Position Coupling origin

seed = 42 for every run. Each train() call resets both RNGs, so later finetunes are not a continuation of earlier streams.

Code: Amartya-Roy/recursive-arithmetic-transformer

Regenerate locally:

python export_training_data.py --output data/hf

What a row is

One frame the transformer saw, not a full n-digit multiply.

Digits are least-significant first. Only completion is trained (label_mask).

task	Supervised target	Operands
base	scratchpad + 1×1 / 2×2 product	lengths 1–2
split	SPLIT, k, four copied half-pairs	lengths 3–12 (15% up to 32)
combine	digits of P_ll + (P_lh+P_hl)·10^k + P_hh·10^{2k}	templated COMBINE prompt

The unique multiply curriculum is only 1- and 2-digit pairs. Longer digit strings appear as copy (split) or add (combine).

Example (base)

<bos> 3 2 * 7 4 = 1 4 1 + 8 6 1 = 1 8 0 1 <eos>

23 × 47 = 1081. First supervised token is a digit, never SPLIT.

Example (split, learned router)

<bos> 4 3 2 1 * 8 7 6 5 = SPLIT 2 CALL 1 4 3 | 8 7 CALL 2 4 3 | 6 5 CALL 3 2 1 | 8 7 CALL 4 2 1 | 6 5 <eos>

1234 × 5678, k=2. The net copies halves; it does not emit the 8-digit product.

Example (combine)

<bos> COMBINE 2 | 2 5 6 2 | 4 0 9 1 | 6 3 9 | 2 7 6 = 2 5 6 6 0 0 7 <eos>

7006652 LSD-first. Place IDs (column position_ids) encode the 10^k / 10^{2k} shifts.

Configs (sequential trainings)

Config	Steps × batch	Mix base/split/combine	SPLIT in	Bit-identical to the run?
scratch_pretrain	15k × 64	0.40 / 0.30 / 0.30	prompt	no — current sampler replay
combine_finetune	10k × 64	0.10 / 0.10 / 0.80	prompt	no
combine_k2_finetune	10k × 64	0.10 / 0.10 / 0.80	prompt	no
allk_finetune	10k × 64	0.15 / 0.10 / 0.75	prompt	no — last length-gated ckpt
router_finetune	10k × 64	0.25 / 0.40 / 0.35	target	yes — recursive_block_router.pt

router_finetune is the dump that matches checkpoints/recursive_block_router.pt (8×8 exact 977/1000). split_train_max=12. First supervised token on split frames is SPLIT.

Earlier configs used a length-gated controller (SPLIT already in the prompt). Those dumps are replayed with the current sampler. Combine sampling evolved during development, so those rows show the recipe, not a guaranteed byte match to the original GPU stream.

Columns

Operands and products are strings so JSON does not round large integers.

Column	Meaning
run	which train() call
step, index_in_batch, global_index	where in the 10k/15k stream
task	base / split / combine
left, right, length	multiply operands (0 on combine)
k, r1–r4	combine parts (k also set on split)
target	product, combine sum, or SPLIT k a|b ...
text	full token string
prompt / completion	unsupervised prefix vs trained suffix
first_supervised_token	SPLIT or a digit
position_offset, position_ids	Place-value IDs
label_mask	1 = trained token
exact_replay	true only for router_finetune

License

MIT, same as the code repo.