Add replayed recursive-arithmetic training frames (3.52M sequences)

README.md

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+---
+license: mit
+pretty_name: Recursive Arithmetic Transformer Training Frames
+task_categories:
+- text-generation
+language:
+- en
+tags:
+- arithmetic
+- multiplication
+- transformers
+- synthetic
+size_categories:
+- 1M<n<10M
+configs:
+  - config_name: router_finetune
+    default: true
+    data_files:
+      - split: train
+        path: router_finetune/train-*.jsonl.gz
+  - config_name: allk_finetune
+    data_files:
+      - split: train
+        path: allk_finetune/train-*.jsonl.gz
+  - config_name: combine_k2_finetune
+    data_files:
+      - split: train
+        path: combine_k2_finetune/train-*.jsonl.gz
+  - config_name: combine_finetune
+    data_files:
+      - split: train
+        path: combine_finetune/train-*.jsonl.gz
+  - config_name: scratch_pretrain
+    data_files:
+      - split: train
+        path: scratch_pretrain/train-*.jsonl.gz
+---
+
+# 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](https://github.com/Amartya-Roy/recursive-arithmetic-transformer)
+
+Regenerate locally:
+
+```bash
+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.

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sampling_recipe.json

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+{
+  "protocol": "recursive_block_multiply",
+  "seed_operands": "seed + 91",
+  "seed_offsets": "seed + 17",
+  "base_cutoff": 2,
+  "max_position_id": 512,
+  "digit_order": "least-significant first",
+  "runs": {
+    "scratch_pretrain": {
+      "updates": 15000,
+      "batch_size": 64,
+      "seed": 42,
+      "mix_weights": [
+        0.4,
+        0.3,
+        0.3
+      ],
+      "split_train_max": 8,
+      "split_copy_max": 32,
+      "combine_k_max": 16,
+      "combine_r_max": 12,
+      "learned_router": false,
+      "exact_replay": false,
+      "checkpoint": "checkpoints/recursive_block.pt (later overwritten by allk)",
+      "notes": "First 15k steps from random init. Replay uses the current sampler; early combine / split encoding lived in salt_cert_recursive.py and may not be bit-identical."
+    },
+    "combine_finetune": {
+      "updates": 10000,
+      "batch_size": 64,
+      "seed": 42,
+      "mix_weights": [
+        0.1,
+        0.1,
+        0.8
+      ],
+      "split_train_max": 8,
+      "split_copy_max": 32,
+      "combine_k_max": 16,
+      "combine_r_max": 12,
+      "learned_router": false,
+      "exact_replay": false,
+      "checkpoint": "runs/mult_transformer/recursive_block_combine.pt",
+      "notes": "Combine-heavy finetune. Replay uses the current sampler."
+    },
+    "combine_k2_finetune": {
+      "updates": 10000,
+      "batch_size": 64,
+      "seed": 42,
+      "mix_weights": [
+        0.1,
+        0.1,
+        0.8
+      ],
+      "split_train_max": 8,
+      "split_copy_max": 32,
+      "combine_k_max": 16,
+      "combine_r_max": 32,
+      "learned_router": false,
+      "exact_replay": false,
+      "checkpoint": "runs/mult_transformer/recursive_block_combine_k2.pt",
+      "notes": "Same mix as combine_finetune with longer combine operands (r_max=32)."
+    },
+    "allk_finetune": {
+      "updates": 10000,
+      "batch_size": 64,
+      "seed": 42,
+      "mix_weights": [
+        0.15,
+        0.1,
+        0.75
+      ],
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+      "split_copy_max": 32,
+      "combine_k_max": 16,
+      "combine_r_max": 32,
+      "learned_router": false,
+      "exact_replay": false,
+      "checkpoint": "checkpoints/recursive_block.pt",
+      "notes": "Last length-gated checkpoint (SPLIT already in the split prompt). Init for the router run. Replay uses the current sampler."
+    },
+    "router_finetune": {
+      "updates": 10000,
+      "batch_size": 64,
+      "seed": 42,
+      "mix_weights": [
+        0.25,
+        0.4,
+        0.35
+      ],
+      "split_train_max": 12,
+      "split_copy_max": 32,
+      "combine_k_max": 16,
+      "combine_r_max": 32,
+      "learned_router": true,
+      "exact_replay": true,
+      "checkpoint": "checkpoints/recursive_block_router.pt",
+      "notes": "10k finetune from recursive_block.pt. Same code path as train_recursive after the learned-router change. This is the dump that matches the public 8x8 97.7% checkpoint."
+    }
+  },
+  "regenerate": "python export_training_data.py --output data/hf"
+}

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