# Exposing Numeracy Gaps: A Benchmark to Evaluate Fundamental Numerical Abilities in Large Language Models

arXiv: https://arxiv.org/abs/2502.11075 · HTML: https://mlsanity.com/paper/2502.11075/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 55 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Builds on (most cited first, 30 of 41)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [FinanceBench: A New Benchmark for Financial Question Answering](https://mlsanity.com/paper/2311.11944/) (2023)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [Probing Pretrained Language Models for Lexical Semantics](https://mlsanity.com/paper/2010.05731/) (2020)
- [Impact of Pretraining Term Frequencies on Few-Shot Reasoning](https://mlsanity.com/paper/2202.07206/) (2022)
- [Domain Specialization as the Key to Make Large Language Models Disruptive: A Comprehensive Survey](https://mlsanity.com/paper/2305.18703/) (2023)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)

## Built on by (most cited first, 14 of 14)

- [Efficient numeracy in language models through single-token number embeddings](https://mlsanity.com/paper/2510.06824/) (2025)
- [Survey and Experiments on Mental Disorder Detection via Social Media: From Large Language Models and RAG to Agents](https://mlsanity.com/paper/2504.02800/) (2025)
- [Do LLMs Overthink Basic Math Reasoning? Benchmarking the Accuracy-Efficiency Tradeoff in Language Models](https://mlsanity.com/paper/2507.04023/) (2025)
- [White-Balance First, Adjust Later: Cross-Camera Color Constancy via Vision-Language Evaluation](https://mlsanity.com/paper/2605.19613/) (2026)
- [LoopServe: An Adaptive Dual-phase LLM Inference Acceleration System for Multi-Turn Dialogues](https://mlsanity.com/paper/2507.13681/) (2025)
- [TravelEval: A Comprehensive Benchmarking Framework for Evaluating LLM-Powered Travel Planning Agents](https://mlsanity.com/paper/2606.01046/) (2026)
- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)
- [SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation](https://mlsanity.com/paper/2604.01988/) (2026)
- [A Triadic Suffix Tokenization Scheme for Numerical Reasoning](https://mlsanity.com/paper/2604.11582/) (2026)
- [Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization](https://mlsanity.com/paper/2605.12106/) (2026)
- [Fighting Numerical Hallucinations via Data-centric Compilation for Online Financial QA](https://mlsanity.com/paper/2605.31064/) (2026)
- [The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models](https://mlsanity.com/paper/2606.03645/) (2026)
- [When Text and Numbers Disagree: Evidence Arbitration in Large Language Models](https://mlsanity.com/paper/2608.20116/) (2026)
- [PCFBench: A Diagnostic Benchmark for Product Carbon Footprint Estimation](https://mlsanity.com/paper/2608.27716/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated impressive capabilities in natural language processing tasks, such as text generation and semantic understanding. However, their performance on numerical reasoning tasks, such as basic arithmetic, numerical retrieval, and magnitude comparison, remains surprisingly poor. This gap arises from their reliance on surface-level statistical patterns rather than understanding numbers as continuous magnitudes. Existing benchmarks primarily focus on either linguistic competence or structured mathematical problem-solving, neglecting fundamental numerical reasoning required in real-world scenarios. To bridge this gap, we propose NumericBench, a comprehensive benchmark to evaluate six fundamental numerical capabilities: number recognition, arithmetic operations, contextual retrieval, comparison, summary, and logical reasoning. NumericBench includes datasets ranging from synthetic number lists to the crawled real-world data, addressing challenges like long contexts, noise, and multi-step reasoning. Extensive experiments on state-of-the-art LLMs, including GPT-4 and DeepSeek, reveal persistent weaknesses in numerical reasoning, highlighting the urgent need to improve numerically-aware language modeling. The benchmark is released in: https://github.com/TreeAI-Lab/NumericBench.