# StreetMath: Study of LLMs' Approximation Behaviors

arXiv: https://arxiv.org/abs/2510.25776 · HTML: https://mlsanity.com/paper/2510.25776/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 28 of 28)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text](https://mlsanity.com/paper/2310.06786/) (2023)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [A Primer on Neural Network Models for Natural Language Processing](https://mlsanity.com/paper/1510.00726/) (2015)
- [Falcon Mamba: The First Competitive Attention-free 7B Language Model](https://mlsanity.com/paper/2410.05355/) (2024)
- [Pre-trained Large Language Models Use Fourier Features to Compute Addition](https://mlsanity.com/paper/2406.03445/) (2024)
- [MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning](https://mlsanity.com/paper/2402.17231/) (2024)
- [Break the Chain: Large Language Models Can be Shortcut Reasoners](https://mlsanity.com/paper/2406.06580/) (2024)
- [Language Models Encode Numbers Using Digit Representations in Base 10](https://mlsanity.com/paper/2410.11781/) (2024)
- [Interpreting Arithmetic Mechanism in Large Language Models through Comparative Neuron Analysis](https://mlsanity.com/paper/2409.14144/) (2024)
- [Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks](https://mlsanity.com/paper/2406.02356/) (2024)
- [Language Model Probabilities are Not Calibrated in Numeric Contexts](https://mlsanity.com/paper/2410.16007/) (2024)
- [Probing for Arithmetic Errors in Language Models](https://mlsanity.com/paper/2507.12379/) (2025)
- [Math Neurosurgery: Isolating Language Models' Math Reasoning Abilities Using Only Forward Passes](https://mlsanity.com/paper/2410.16930/) (2024)
- [Exploring and Exploiting the Inherent Efficiency within Large Reasoning Models for Self-Guided Efficiency Enhancement](https://mlsanity.com/paper/2506.15647/) (2025)

## Built on by (most cited first, 2 of 2)

- [Adaptive Detector-Verifier Framework for Zero-Shot Polyp Detection in Open-World Settings](https://mlsanity.com/paper/2512.12492/) (2025)
- [Anchored, Not Graded: Vision-Language Models Fail at Slant-from-Texture Perception](https://mlsanity.com/paper/2606.06714/) (2026)

## Abstract (arXiv)

There is a substantial body of literature examining the mathematical reasoning capabilities of large language models (LLMs), particularly their performance on precise arithmetic operations in autoregressive architectures. However, their ability to perform approximate reasoning in informal, fast-paced mathematical operations has received far less attention, especially among non-autoregressive decoder models. Our work addresses this gap by introducing StreetMath, a benchmark designed to evaluate models' approximation abilities under real-world approximation scenarios. We conduct extensive evaluations across different LLM architectures: Qwen3-4B-Instruct-2507, Qwen3-4B-Thinking-2507, Dream-v0-Instruct-7B, Falcon-Mamba-7B-Instruct, and Mamba-GPT-3B. Furthermore, we apply mechanistic interpretability techniques to probe their internal computational states. Our analysis reveals that LLMs generally attempt to compute exact values or invoke external tools even in tasks that call for approximation. Moreover, while models sometimes reach the correct answer in early layers or steps, they still consume more tokens when solving approximation tasks. Additional experiments indicate that exact and approximate arithmetic operations rely on largely separate neural components. Drawing upon research on cognitive psychology, we argue that LLMs do not exhibit cognitive miserliness in the same way humans do in street math settings. We open source our work https://github.com/ctseng777/StreetMath