| --- |
| license: apache-2.0 |
| task_categories: |
| - text-generation |
| language: |
| - en |
| tags: |
| - arithmetic |
| - interpretability |
| - sorl |
| - mechanistic-interpretability |
| - addition |
| - subtraction |
| size_categories: |
| - 1M<n<10M |
| --- |
| |
| # Arithmetic SoRL Data |
|
|
| Training and evaluation data for the **SoRL Arithmetic Interpretability Study**. |
|
|
| We train small transformers on integer addition and subtraction, then use |
| [Self-Organizing Reinforcement Learning (SoRL)](https://github.com/fangyuan-ksgk/mod_gpt) |
| to externalize the model's carry/borrow circuits as explicit abstraction tokens. |
|
|
| Reference: Quirke et al., "Understanding Addition and Subtraction in Transformers" (2024) |
|
|
| ## Dataset Structure |
|
|
| Each subfolder contains `train.parquet`, `val.parquet`, and `config.json`. |
|
|
| | Subfolder | Digits | Operations | Train | Val | Sequence Length | |
| |---|---|---|---|---|---| |
| | `add_6digit` | 6 | addition | 500K | 10K | 21 tokens | |
| | `add_sub_6digit` | 6 | add + sub | 500K | 10K | 21 tokens | |
| | `add_4digit` | 4 | addition | 500K | 10K | 15 tokens | |
| | `add_sub_4digit` | 4 | add + sub | 500K | 10K | 15 tokens | |
|
|
| ## Format |
|
|
| Each row has: |
| - **tokens**: list of ints — the full input sequence (operands + operator + answer) |
| - **labels**: list of str — per-answer-digit sub-task label |
| - **op**: `"add"` or `"sub"` |
| - **x_digits**, **y_digits**, **z_digits**: the raw digit lists (MSB first) |
| |
| ### Token format |
| |
| Addition: `XXXXXX+YYYYYY=ZZZZZZZ` (n_digits + operator + n_digits + equals + n_digits+1) |
| |
| Subtraction: `XXXXXX-YYYYYY=ZZZZZZZ` (x >= y guaranteed, answer zero-padded) |
| |
| Token IDs: 0-9 = digits, 10 = `+`, 11 = `=`, 12 = `-` |
| |
| ### Sub-task labels |
| |
| Each answer digit is labeled with the arithmetic sub-task it requires: |
| |
| **Addition:** |
| | Label | Name | Description | |
| |---|---|---| |
| | BA | Base Add | Simple addition, no carry | |
| | MC1 | Make Carry | digit_sum >= 10, generates carry | |
| | MS9 | Make Sum 9 | digit_sum == 9, propagates carry if present | |
| | UC1 | Use Carry | carry_in=1, digit_sum != 9 | |
| | US9 | Use Sum 9 | carry_in=1, digit_sum == 9 (cascade, hardest) | |
|
|
| **Subtraction:** |
| | Label | Name | Description | |
| |---|---|---| |
| | BS | Base Sub | Simple subtraction, no borrow | |
| | MB1 | Make Borrow | x_i < y_i, needs borrow | |
| | MD9 | Make Diff 9 | x_i == y_i, propagates borrow if present | |
| | UB1 | Use Borrow | borrow_in=1, x_i != y_i | |
| | UD9 | Use Diff 9 | borrow_in=1, x_i == y_i (cascade, hardest) | |
|
|
| ## Data Enrichment |
|
|
| Following Quirke et al.: 60% of batches have 40% of digit positions forced to sum-to-9, |
| increasing the frequency of US9 (carry cascade) examples from ~6% to ~8%. |
|
|
| ## Usage |
|
|
| ```python |
| from datasets import load_dataset |
| |
| ds = load_dataset("thoughtworks/arithmetic-sorl-data", data_dir="add_6digit") |
| print(ds["train"][0]) |
| # {'tokens': [1, 2, 3, 4, 5, 6, 10, 6, 5, 4, 3, 2, 1, 11, 0, 7, 7, 7, 7, 7, 7], |
| # 'labels': ['BA', 'UC1', 'MS9', ...], 'op': 'add', ...} |
| ``` |
|
|
| ## Related |
|
|
| - Model checkpoints: [thoughtworks/arithmetic-sorl](https://huggingface.co/thoughtworks/arithmetic-sorl) |
| - Code: [mod_gpt/arithmetic/](https://github.com/fangyuan-ksgk/mod_gpt/tree/amir/arithmetic/arithmetic) |
| - SoRL paper: Yu & Abdullah, "Intention-Level Alignment with Weak Supervision" (2025) |
|
|
