Datasets:

thoughtworks
/

arithmetic-sorl-data

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) 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

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', ...}

Model checkpoints: thoughtworks/arithmetic-sorl
Code: mod_gpt/arithmetic/
SoRL paper: Yu & Abdullah, "Intention-Level Alignment with Weak Supervision" (2025)