# Language Models Compare Quantities Using Number-specific and Unit-specific Heuristics

arXiv: https://arxiv.org/abs/2606.03982 · HTML: https://mlsanity.com/paper/2606.03982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)
- [Interpreting and Improving Large Language Models in Arithmetic Calculation](https://mlsanity.com/paper/2409.01659/) (2024)
- [Pre-trained Large Language Models Use Fourier Features to Compute Addition](https://mlsanity.com/paper/2406.03445/) (2024)
- [Language Models Encode Numbers Using Digit Representations in Base 10](https://mlsanity.com/paper/2410.11781/) (2024)
- [Language Models Encode the Value of Numbers Linearly](https://mlsanity.com/paper/2401.03735/) (2024)
- [The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces](https://mlsanity.com/paper/2410.13194/) (2024)
- [Understanding Addition and Subtraction in Transformers](https://mlsanity.com/paper/2402.02619/) (2024)
- [Survival of the Fittest Representation: A Case Study with Modular Addition](https://mlsanity.com/paper/2405.17420/) (2024)
- [LLMs Know More About Numbers than They Can Say](https://mlsanity.com/paper/2602.07812/) (2026)
- [Masked Measurement Prediction: Learning to Jointly Predict Quantities and Units from Textual Context](https://mlsanity.com/paper/2112.08616/) (2021)
- [On Generalization across Measurement Systems: LLMs Entail More Test-Time Compute for Underrepresented Cultures](https://mlsanity.com/paper/2506.02591/) (2025)
- [Enhancing Quantitative Reasoning Skills of Large Language Models through Dimension Perception](https://mlsanity.com/paper/2312.17532/) (2023)

## Abstract (arXiv)

Quantities with measurement units, such as 110 cm and 1.2 m, require language models (LMs) to combine a numeral with a symbolic unit scale. Here, we study how LMs compare such quantities in controlled settings spanning several unit systems. We find that accuracy degrades near the comparison boundary, where small changes in value determine the correct answer. The resulting errors are systematic: linear surrogate models predict LM preferences from numerical-difference and unit-scale-difference cues, and causal interventions on subspaces aligned with these variables shift model's output. The results suggest that LMs compare quantities through a bag of heuristics over numerals and units, rather than first converting both expressions to an exact shared-scale representation.