Numerical Reasoning in Language Models

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Overview

Numerical reasoning asks whether language models can read quantities, perform arithmetic, compare values, and use numerical evidence in mathematical and practical settings. Researchers test these abilities with math benchmarks such as GSM8K and MATH, as well as table, spreadsheet, financial, scientific, clinical, and multilingual tasks. Approaches include digit-aware representations, chain-of-thought and code execution, calculator and retrieval tools, symbolic solvers, and supervised or reinforcement-learning training with verifiable rewards. Mechanistic analyses examine whether numbers are merely represented or actually used, while tests of formatting, distractors, long contexts, units, and distribution shifts reveal reliability gaps; a central tension is fluent explanations versus consistently correct, auditable computation.

Latest papers

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156 papers30 papers in the last four weeks, up 30% on the four weeks before. 0.2% of all new papers.

  1. ThermoQA: A Three-Tier Benchmark for Evaluating Thermodynamic Reasoning in Large Language Models

    Mar 25, 2026Kemal DüzkarLLM EvaluationScientific Reasoning in Language Models

    Olivenet Kyrenia, Cyprus

  2. The Geometric Price of Discrete Logic: Context-driven Manifold Dynamics of Number Representations

    Mar 24, 2026Long Zhang, Dai-jun Lin, Wei-neng ChenRepresentation Geometry in Language ModelsLLM Interpretability

    School of Computer Science and Engineering, South China University of Technology, Guangzhou City, Guangdong Province, China

  3. Can Large Language Models Reason and Optimize Under Constraints?

    Mar 24, 2026Fabien Bernier, Salah Ghamizi, Pantelis Dogoulis +1Constraint-Guided Reasoning in Language ModelsLLM Evaluation

    SnT – University of Luxembourg, Luxembourg · Luxembourg Institute of Health (LIH), Luxembourg

  4. Revisiting Tree Search for LLMs: Gumbel and Sequential Halving for Budget-Scalable Reasoning

    Mar 22, 2026Leonid Ugadiarov, Yuri Kuratov, Aleksandr Panov +1Monte Carlo Tree SearchSequential Decision Making

    AXXX, Moscow, Russia · MIRAI, Moscow, Russia

  5. Weber's Law in Transformer Magnitude Representations: Efficient Coding, Representational Geometry, and Psychophysical Laws in Language Models

    Mar 21, 2026Jon-Paul CacioliRepresentation Geometry in Language ModelsNumerical Reasoning in Language Models

    Independent Researcher, Melbourne Australia

  6. Reasoning Gets Harder for LLMs Inside A Dialogue

    Mar 20, 2026Ivan Kartáč, Mateusz Lango, Ondřej DušekSpatial Reasoning in Language ModelsMulti-Turn Dialogue Evaluation

    Charles University, Faculty of Mathematics and Physics Institute of Formal and Applied Linguistics Prague, Czechia

  7. FinTradeBench: A Financial Reasoning Benchmark for LLMs

    Mar 19, 2026Yogesh Agrawal, Aniruddha Dutta, Md Mahadi Hasan +2Financial Reasoning in Language ModelsFinancial Reasoning Benchmarks

    University of Central Florida

  8. Multi-Step Semantic Reasoning in Generative Retrieval

    Mar 12, 2026Steven Dong, Yubao Tang, Maarten de RijkeGenerative RetrievalNumerical Reasoning in Language Models

    University of Amsterdam, Amsterdam, The Netherlands

  9. DeReason: A Difficulty-Aware Curriculum Improves Decoupled SFT-then-RL Training for General Reasoning

    Mar 11, 2026Hanxu Hu, Yuxuan Wang, Maggie Huan +4RL for Language Model ReasoningRL Fine-Tuning

    University of Zurich · University of Pennsylvania · ETH Zurich +2

  10. Think Twice Before You Write -- an Entropy-based Decoding Strategy to Enhance LLM Reasoning

    Mar 10, 2026Jiashu He, Meizhu Liu, Olaitan P Olaleye +9Language Model DecodingEfficient Language Model Reasoning

    Oracle AI Science · University of Pennsylvania

  11. SciTaRC: A Plan-Annotated Scientific Tabular QA Benchmark for Language Reasoning and Complex Computation

    Mar 9, 2026Hexuan Wang, Yaxuan Ren, Srikar Bommireddypalli +5Table QAScientific Reasoning in Language Models

    Center for Language and Speech Processing, Johns Hopkins University

  12. Adaptive Loops and Memory in Transformers: Think Harder or Know More?

    Mar 9, 2026Markus Frey, Behzad Shomali, Ali Hamza Bashir +3TransformerMemory-Augmented Language Models

    Lamarr Institute · Fraunhofer IAIS · University of Bonn

  13. FinSheet-Bench: From Simple Lookups to Complex Reasoning, Where LLMs Break on Financial Spreadsheets

    Mar 7, 2026Jan Ravnik, Matjaž Ličen, Felix Bührmann +3Table QALLM Evaluation

    Qubera AG, Gartenstrasse 33, 8002 Zürich · University of Zurich, Department of Informatics, Binzmühlestrasse 14, 8050 Zürich

  14. CONE: Embeddings for Complex Numerical Data Preserving Unit and Variable Semantics

    Mar 5, 2026Gyanendra Shrestha, Anna Pyayt, Michael GubanovNumerical Reasoning in Language ModelsRepresentation Learning

    Florida State University · University of South Florida

  15. Neuro-Symbolic Financial Reasoning via Deterministic Fact Ledgers and Adversarial Low-Latency Hallucination Detector

    Mar 4, 2026Pedram AgandFinancial Reasoning in Language ModelsNeuro-Symbolic Reasoning

    FactAI Lab, Vancouver, BC, Canada.

  16. Probing Materials Knowledge in LLMs: From Latent Embeddings to Reliable Predictions

    Mar 2, 2026Vineeth Venugopal, Soroush Mahjoubi, Elsa OlivettiLLM ReliabilityLLM Evaluation

    Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA.

  17. MetaState: Persistent Working Memory Enhances Reasoning in Discrete Diffusion Language Models

    Mar 2, 2026Kejing Xia, Mingzhe Li, Lixuan Wei +5Diffusion Language ModelsPersistent Memory for Language Models

    Georgia Institute of Technology · University of Massachusetts Amherst · Harvard University

  18. One-Token Verification for Reasoning Correctness Estimation

    Mar 1, 2026Zhan Zhuang, Xiequn Wang, Zebin Chen +4Reasoning VerificationLLM Reasoning

    Southern University of Science and Technology, Shenzhen, China · City University of Hong Kong, Hong Kong SAR · Zhejiang University, Hangzhou, China

  19. DriveCode: Domain Specific Numerical Encoding for LLM-Based Autonomous Driving

    Mar 1, 2026Zhiye Wang, Yanbo Jiang, Rui Zhou +5Autonomous DrivingNumerical Reasoning in Language Models

    School of Information Science and Engineering, Lanzhou University, Lanzhou, China · State Key Laboratory of Intelligent Green Vehicle and Mobility, Tsinghua University, Beijing, China · The School of Vehicle and Mobility, Tsinghua University, Beijing, China +2

  20. Adaptive Problem Generation via Symbolic Representations

    Feb 22, 2026Teresa Yeo, Myeongho Jeon, Dulaj Weerakoon +4Mathematical Problem GenerationSynthetic Data Generation for Language Models

    Singapore-MIT Alliance for Research and Technology · Korea Advanced Institute of Science and Technology · Massachusetts Institute of Technology +1

  21. Post-Routing Arithmetic in Llama-3: Last-Token Result Writing and Rotation-Structured Digit Directions

    Feb 22, 2026Yao YanNumerical Reasoning in Language ModelsCircuits in Language Models

    Chongqing Normal University Chongqing Key Lab of Cognitive Intelligence and Intelligent Finance Chongqing, China

  22. ArabicNumBench: Evaluating Arabic Number Reading in Large Language Models

    Feb 21, 2026Anas Alhumud, Abdulaziz Alhammadi, Muhammad Badruddin KhanArabic NLPLLM Evaluation

    Saudi Data and Artificial Intelligence Authority, Saudi Arabia · Imam Mohammad Ibn Saud Islamic University, Saudi Arabia

  23. Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning

    Feb 20, 2026Lexiang Tang, Weihao Gao, Bingchen Zhao +4Efficient Language Model ReasoningLLM Reliability

    Peking University, Beijing, China · University of Edinburgh, Edinburgh, UK.

  24. Turbo Connection: Reasoning as Information Flow from Higher to Lower Layers

    Feb 20, 2026Mohan Tang, Sidi LuTransformerLarge Reasoning Models

    UCLA.

  25. BankMathBench: A Benchmark for Numerical Reasoning in Banking Scenarios

    Feb 19, 2026Yunseung Lee, Subin Kim, Youngjun Kwak +1Numerical Reasoning in Language ModelsMathematical Reasoning Benchmarks

    KakaoBank Corp., South Korea · Korea Advanced Institute of Science and Technology, South Korea

  26. GPSBench: Do Large Language Models Understand GPS Coordinates?

    Feb 18, 2026Thinh Hung Truong, Jey Han Lau, Jianzhong QiGeospatial ReasoningGeospatial Reasoning Benchmarks

    University of Melbourne.

  27. Large Language Models for Math Education in Low-Resource Languages: A Study in Sinhala and Tamil

    Feb 16, 2026Sukumar Kishanthan, Kumar Thushalika, Buddhi Jayasekara +1Numerical Reasoning in Language ModelsCross-Lingual Reasoning in Language Models

    Department of Computer Science and Engineering University of Moratuwa Moratuwa, Sri Lanka · Department of Electrical and Information Engineering University of Ruhuna Galle, Sri Lanka · Faculty of Information Technology and Communication Sciences Tampere University Tampere, Finland +1

  28. TTCS: Test-Time Curriculum Synthesis for Self-Evolving

    Jan 30, 2026Chengyi Yang, Zhishang Xiang, Yunbo Tang +5Test-Time TrainingLanguage Model Self-Improvement

    Xiamen University · Washington University in St. Louis · Renmin University of China

  29. MGSM-Pro: A Simple Strategy for Robust Multilingual Mathematical Reasoning Evaluation

    Jan 29, 2026Tianyi Xu, Kosei Uemura, Alfred Malengo Kondoro +6Numerical Reasoning in Language ModelsMathematical Reasoning Benchmarks

    McGill University · Mila-Quebec AI Institute · University of Toronto +7

  30. The Effect of Scripts and Formats on LLM Numeracy

    Jan 21, 2026Varshini Reddy, Craig W. Schmidt, Seth Ebner +3Numerical Reasoning in Language ModelsMultilingual Language Model Evaluation

    Kensho Technologies · Ben-Gurion University · MIT Cambridge, MA