Datasets:
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configs:
- config_name: add_6digit
data_files:
- path: add_6digit/train.parquet
split: train
- path: add_6digit/val.parquet
split: validation
- path: add_6digit/eval_stratified.parquet
split: test
- config_name: add_sub_6digit
data_files:
- path: add_sub_6digit/train.parquet
split: train
- path: add_sub_6digit/val.parquet
split: validation
- path: add_sub_6digit/eval_stratified.parquet
split: test
language:
- en
license: apache-2.0
size_categories:
- 1M<n<10M
tags:
- arithmetic
- interpretability
- sorl
- mechanistic-interpretability
- addition
- subtraction
- quirke
task_categories:
- text-generation
---
# Arithmetic SoRL Data
Training and evaluation data for the **SoRL Arithmetic Interpretability Study**.
Small transformers trained on integer addition/subtraction, with
[SoRL](https://github.com/fangyuan-ksgk/mod_gpt) to externalize carry/borrow circuits
as explicit abstraction tokens.
Reference: Quirke et al., "Understanding Addition and Subtraction in Transformers" (2024)
## Dataset Structure
| Subfolder | Operations | Train | Val | Eval (stratified) |
|---|---|---|---|---|
| `add_6digit` | addition only | 500K | 10K | ~550 (50 per S0-S6 + 200 random) |
| `add_sub_6digit` | add + sub | 500K | 10K | ~1100 (50 per S0-S6 + M0-M6 + random) |
## Columns
| Column | Type | Description |
|---|---|---|
| `tokens` | list[int] | Full sequence (21 tokens for 6-digit) |
| `labels` | list[str] | Per-answer-digit sub-task label |
| `op` | str | `"add"` or `"sub"` |
| `complexity` | str | Quirke complexity: `S0`-`S6` (add) or `M0`-`M6` (sub) |
| `cascade_depth` | int | Max carry/borrow cascade length |
| `x_digits` | list[int] | First operand (MSB first) |
| `y_digits` | list[int] | Second operand (MSB first) |
| `z_digits` | list[int] | Answer (MSB first, n_digits+1) |
The `eval_stratified` split has an additional `eval_category` column.
## Sub-task Labels (Quirke et al.)
Each answer digit requires a specific arithmetic operation:
### Addition
| Label | Name | Condition | Role |
|---|---|---|---|
| SA | Base Add | `Dn + D'n < 9`, no carry | Simplest case |
| SC | Make Carry | `Dn + D'n >= 10` | Generates carry |
| SS | Sum is 9 | `Dn + D'n == 9` | Propagates carry if one arrives |
| UC | Use Carry | carry_in=1, sum != 9 | Consumes incoming carry |
| US | Use Sum-9 | carry_in=1, sum == 9 | Cascade: hardest case |
### Subtraction (x >= y)
| Label | Name | Condition | Role |
|---|---|---|---|
| MD | Base Diff | `Dn > D'n`, no borrow | Simplest case |
| MB | Make Borrow | `Dn < D'n` | Generates borrow |
| ME | Equal digits | `Dn == D'n` | Propagates borrow if one arrives |
| UB | Use Borrow | borrow_in=1, `Dn != D'n` | Consumes incoming borrow |
| UD | Use Equal | borrow_in=1, `Dn == D'n` | Cascade: hardest case |
## Complexity Classification (Quirke Table 8)
Complexity = length of longest carry/borrow cascade chain.
Example: `555555+444448=1000003` is **S6** — the carry from D0 cascades through
5 consecutive sum-9 positions.
```
S0: no carries ~10%
S1: isolated carries ~50%
S2: cascade of 2 ~26%
S3: cascade of 3 ~9%
S4: cascade of 4 ~3%
S5: cascade of 5 ~1%
S6: cascade of 6 <0.5%
```
## Data Enrichment
Following Quirke: 60% of batches have 40% of digit positions forced to sum-to-9,
increasing cascade frequency so the model sees enough S4-S6 cases.
## Usage
```python
from datasets import load_dataset
ds = load_dataset("thoughtworks/arithmetic-sorl-data", data_dir="add_6digit")
print(ds["train"][0])
# {'tokens': [...], 'labels': ['SA', 'UC', 'US', ...],
# 'complexity': 'S3', 'cascade_depth': 3, ...}
# Stratified eval
eval_ds = load_dataset("thoughtworks/arithmetic-sorl-data",
data_dir="add_6digit", data_files="eval_stratified.parquet")
```
## 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)
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