---
language: [en]
tags: [arithmetic, pretraining, sub-10M, ArithMark]
---
# Arithmetic-XL

## 12 Million Verified Arithmetic Examples for Language Model Pretraining

> *"Arithmetic is one of those things that humans learn in primary
> school but language models somehow manage to forget halfway through
> training."*

Arithmetic-XL is a **large-scale arithmetic pretraining dataset**
containing **over 12 million procedurally generated and verified
examples** designed to improve numerical reasoning in language models.

The dataset was created with one objective:

**Teach models how to think about arithmetic instead of simply
memorizing answers.**

Unlike many arithmetic datasets that focus only on direct
question-answer pairs, Arithmetic-XL follows a layered curriculum that
gradually introduces numerical concepts, multi-step computation,
operator precedence, compositional reasoning, adversarial examples, and
arithmetic embedded inside natural language.

Whether you're training a **5M parameter TinyLM** or a **multi-billion
parameter foundation model**, Arithmetic-XL provides a diverse
collection of arithmetic examples suitable for **pretraining**,
**continued pretraining**, and **specialized arithmetic fine-tuning**.

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# Why Another Arithmetic Dataset?

While training language models, I kept running into the same frustrating
problem.

The model could explain surprisingly complicated topics...

...and then confidently tell me that:

> **17 × 8 = 121**

That felt slightly concerning.

I searched for arithmetic datasets that were:

-   Large
-   Diverse
-   Procedurally verified
-   Suitable for pretraining
-   Rich enough to teach actual arithmetic patterns rather than simple
    memorization

I found some excellent datasets.

I also found datasets that contained the same question written five
hundred different ways.

After enough searching, I reached the conclusion every developer
eventually reaches:

> "Fine... I'll build it myself."

Several weeks, countless Python scripts, and far too many generated
equations later...

Arithmetic-XL was born.

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# What Makes Arithmetic-XL Different?

Arithmetic-XL is **not** simply a collection of equations.

It follows a structured curriculum inspired by how humans progressively
learn arithmetic.

Instead of immediately exposing the model to complicated expressions,
the dataset gradually increases difficulty through multiple specialized
layers.

The goal is to help models build numerical intuition before introducing
increasingly complex reasoning tasks.

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# Dataset Overview

  -----------------------------------------------------------------------
  Property                            Value
  ----------------------------------- -----------------------------------
  **Dataset Name**                    Arithmetic-XL

  **Total Examples**                  **12,000,000+**

  **Generation Method**               Hybrid Procedural + LLM Assisted

  **Verification**                    Computationally Verified

  **Primary Language**                English

  **Domain**                          Arithmetic Reasoning

  **Recommended Usage**               Pretraining / Continued Pretraining
                                      / Fine-tuning

  **License**                         MIT
  -----------------------------------------------------------------------