README.md

---
license: apache-2.0
language:
  - en
pretty_name: OLMo iGSM-Easy Arithmetic
task_categories:
  - question-answering
tags:
  - synthetic
  - reasoning
  - arithmetic
  - modular-arithmetic
  - multiple-choice
  - lm-evaluation-harness
size_categories:
  - n<1K
configs:
  - config_name: default
    data_files:
      - split: test
        path: data/test.jsonl
---

# OLMo iGSM-Easy Arithmetic

This repository contains a frozen, evaluation-only release of the synthetic
mod-7 arithmetic task called `iGSM-Easy Arithmetic` in the accompanying OLMo
evaluation code. It contains 750 examples: 250 examples at each target depth
2, 3, and 4.

This is an **i-GSM-style task variant**, not a claim to be an official release
of another dataset named iGSM. The `olmo-igsm-arith` name is used to make the
implementation provenance explicit.

## Dataset description

Each problem defines symbolic variables using conventional arithmetic
operators `+`, `-`, `*`, and `/`. All calculations are performed modulo 7 and
multi-operator expressions are evaluated strictly from left to right. Division
uses modular inverses and never has a zero divisor.

The evaluation prompt is built from `preamble`, `equations`, and `query`. A
model is scored by comparing the unnormalized continuation log-likelihood of
the seven choices ` 0` through ` 6`. The random baseline is `1/7`, or about
14.29%.

The recommended prompt is:

```text
{preamble}

{equations}
Question: {query}?
Answer:
```

The choices are:

```text
 0,  1,  2,  3,  4,  5,  6
```

## Dataset structure

The repository has one `default` configuration and one `test` split.

| Target depth | Examples |
|---:|---:|
| 2 | 250 |
| 3 | 250 |
| 4 | 250 |
| **Total** | **750** |

Load it with:

```python
from datasets import load_dataset

dataset = load_dataset("Mihara-bot/olmo-igsm-arith", split="test")
depth_2 = dataset.filter(lambda row: row["target_depth"] == 2)
```

### Fields

- `id`: Stable example identifier.
- `mod`: Arithmetic modulus; always 7.
- `ops_mode`: Operator mode; always `arith`.
- `question`: Combined question representation produced by the generator.
- `preamble`: Operator definitions and evaluation convention.
- `equations`: Shuffled variable definitions.
- `query`: Variable whose value must be predicted.
- `answer`: Integer gold answer in `[0, 6]`; also the choice index.
- `cot`: Generator-produced derivation. It is provided for auditing and is not
  part of the recommended evaluation prompt.
- `operator_table`: Structured operator definitions.
- `target_depth`: Requested dependency depth, one of 2, 3, or 4.
- `achieved_depth`: Verified dependency depth.
- `num_vars`: Number of variables in the problem.
- `num_necessary`: Variables required to answer the query.
- `num_distractors`: Number of generated distractor variables; always 0 in
  this release.
- `var_layer`: Mapping from variable name to dependency layer.

## Generation and reproducibility

The frozen data was generated with:

```bash
python generator/construct.py \
  --ops arith \
  --n 250 \
  --depths 2 3 4 \
  --distractors 0 \
  --seed 2 \
  --outdir generated
```

The authoritative data file is `data/test.jsonl`, with SHA-256:

```text
c8d77a9d3cc9cc6c5631b1b973231b674ea3d8845ec08fe5de406873e7efca9b
```

Run the included standard-library verifier before publishing or after
downloading:

```bash
python verify_dataset.py
```

The verifier checks the checksum, schema, unique IDs, answer range, per-depth
counts and answer histograms, and independently evaluates every symbolic
problem with the bundled generator.

See `manifest.json` for the complete generation parameters, expected
statistics, source commit, and file checksums. The frozen JSONL is the canonical
artifact; regenerating it is an audit mechanism rather than a runtime step.

## Intended use

This dataset is intended for zero-shot evaluation of language models on
synthetic multi-step modular arithmetic. It is suitable for a
multiple-choice/log-likelihood task in `lm-evaluation-harness` with raw
accuracy as the primary metric.

It is not intended as a training corpus. The included `cot` field must not be
inserted into the evaluation prompt unless a separate chain-of-thought setting
is explicitly being studied.

## Limitations

- The dataset is small and entirely synthetic.
- It tests modulo-7 symbolic arithmetic, not general mathematical ability.
- It contains only one fixed seed and no train or validation split.
- Public release makes future training contamination possible; record model
  training dates and decontamination policy when reporting results.
- Tokenization can affect raw continuation likelihoods. For OLMo-compatible
  evaluation, use the exact lowercase prompt and space-prefixed digit choices
  described above.

## Provenance

The data and generator were prepared from `olmo-eval-suite` commit
`72e5db1548589efc04dc3f8628b0daa7a342a173`. The generator is included in this
repository so that every record can be independently verified.

## License

The repository contents are released under the Apache License 2.0. See
`LICENSE`.