Numerical Reasoning in Language Models

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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.

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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.

Riazi-8B: An Urdu Large Language Model for Mathematical Reasoning
Jun 24, 2026Azher Ali, Ibtsam Haider, Raja Khurram Shahzad +2Numerical Reasoning in Language Models LLM Fine-Tuning
School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan · Department of Communication, Quality Management and Information Systems, Mid Sweden University, Ostersund, Sweden
Cliff Tokens: Analyzing Failure Trigger Tokens in LLM Mathematical Reasoning
Jun 24, 2026Jaeyong Ko, Jinu Lee, Pilsung Kang +1Numerical Reasoning in Language Models LLM Reliability
Seoul National University · Boston University
Nothing from Something: Can a Language Model Discover 0?
Jun 15, 2026Phoebe Zeng, Thomas L. Griffiths, Brenden M. LakeNumerical Reasoning in Language Models Language Model Pretraining
Department of Computer Science, Princeton University
Localizing Anchoring Pathways in Language Models
Jun 11, 2026Hillary N. Owusu, Sarah Wiegreffe, Naomi H. FeldmanNumerical Reasoning in Language Models LLM Interpretability
University of Maryland, College Park
Arithmetic Pedagogy for Language Models
Jun 3, 2026Andhika Bernard Lumbantobing, Hokky SitungkirNumerical Reasoning in Language Models Language Model Pretraining
Bandung Fe Institute & Adjunct Science Fellow in InaAI · Adjunct Science Fellow in InaAI · AI Research Center IT Del +1
Language Models Compare Quantities Using Number-specific and Unit-specific Heuristics
Jun 2, 2026Mutsumi Sasaki, Go kamoda, Ryosuke Takahashi +4Numerical Reasoning in Language Models LLM Evaluation
Tohoku University · SOKENDAI · NINJAL +2
PyraMathBench: Evaluating and Improving Mathematical Capability in Large Language Models
Jun 2, 2026Zetian Ouyang, Linlin Wang, Gerard de Melo +1Numerical Reasoning in Language Models Mathematical Reasoning Benchmarks
East China Normal University · Hasso Plattner Institute, University of Potsdam
Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
Jun 2, 2026Malia Barker, Bishal Lakha, Edoardo Serra +1Numerical Reasoning in Language Models Mathematical Reasoning Benchmarks
Department of Computer Science, Boise State University, Boise, ID, USA · University of L'Aquila, L'Aquila, Italy
Off-the-Shelf LLMs as Process Scorers: Training-Free Alternative to PRMs for Mathematical Reasoning
Jun 1, 2026Atoosa Chegini, Soheil FeiziNumerical Reasoning in Language Models Inference-Time Search
Department of Computer Science, University of Maryland
Represented Is Not Computed: A Causal Test of Candidate Algorithmic Intermediates in a Transformer
May 21, 2026Ishita Darade, Sushrut ThoratNumerical Reasoning in Language Models Transformer Interpretability
MKSSS’s Cummins College of Engineering for Women, Pune 411052, India · Institute of Cognitive Science, Osnabrück University, Osnabrück 49069, Germany
Does Slightly Mean Somewhat? Measuring Vague Intensity Words in LLM Numeric Actions
May 20, 2026Daniel TabachNumerical Reasoning in Language Models LLM Evaluation
Georgia Institute of Technology
Text Analytics Evaluation Framework: A Case Study on LLMs and Social Media
May 20, 2026Yuefeng Shi, Nedjma Ousidhoum, Jose Camacho-ColladosNumerical Reasoning in Language Models Social Media Analysis
School of Computer Science and Informatics, Cardiff University
The Readout Shortcut: Positional Number Copying Dominates Arithmetic CoT Readout in Small Language Models
May 20, 2026Ming LiuNumerical Reasoning in Language Models CoT Faithfulness
Amazon
DEL: Digit Entropy Loss for Numerical Learning of Large Language Models
May 19, 2026Zhaohui Zheng, Chenhang He, Shihao Wang +3Numerical Reasoning in Language Models Neural Network Optimization
The Hong Kong Polytechnic University · VCIP, College of Computer Science, Nankai University
Teaching Language Models to Think in Code
May 8, 2026Hyeon Hwang, Jiwoo Lee, Jaewoo KangNumerical Reasoning in Language Models LLM Mathematical Reasoning
Korea University · Korea University, AIGEN Sciences
The Right Answer, the Wrong Direction: Why Transformers Fail at Counting and How to Fix It
May 5, 2026Gabriel GarciaNumerical Reasoning in Language Models Transformer Interpretability
Independent Researcher
Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts
May 1, 2026Sheridan Feucht, Tal Haklay, Usha Bhalla +9Numerical Reasoning in Language Models LLM Interpretability
aNortheastern University · bTechnion IIT · cHarvard University +1
A Triadic Suffix Tokenization Scheme for Numerical Reasoning
Apr 13, 2026Olga ChetverinaTokenization Subword Tokenization
Lecturer at MIPT, Moscow, Russia.
How Robust Are Large Language Models for Clinical Numeracy? An Empirical Study on Numerical Reasoning Abilities in Clinical Contexts
Apr 13, 2026Minh-Vuong Nguyen, Fatemeh Shiri, Zhuang Li +1Numerical Reasoning in Language Models Clinical Language Model Evaluation
School of Computing Technologies, RMIT University, Australia
TEMPER: Testing Emotional Perturbation in Quantitative Reasoning
Apr 9, 2026Atahan Dokme, Benjamin Reichman, Larry HeckFraming Effects in Language Models LLM Evaluation
Georgia Institute of Technology
Limits of Difficulty Scaling: Hard Samples Yield Diminishing Returns in GRPO-Tuned SLMs
Apr 7, 2026Suraj Yadav, Siddharth Yadav, Parth GoyalRL for Language Model Reasoning Small Language Models
IIIT Delhi
Document-Level Numerical Reasoning across Single and Multiple Tables in Financial Reports
Apr 4, 2026Yi-Cheng Wang, Wei-An Wang, Chu-Song ChenNumerical Reasoning in Language Models Financial QA
Department of Computer Science and Information Engineering, National Taiwan University · FinTech Center, National Taiwan University
CharTool: Tool-Integrated Visual Reasoning for Chart Understanding
Apr 3, 2026Situo Zhang, Yifan Zhang, Zichen Zhu +6Chart Understanding Chart QA
X-LANCE Lab, Shanghai Jiao Tong University, Shanghai, China · East China Normal University, Shanghai, China · Shanghai Innovation Institution, Shanghai, China +1
Reinforcement Learning-based Semi-supervised Knowledge Distillation with LLM-as-a-Judge
Apr 3, 2026Yiyang Shen, Lifu Tu, Weiran WangRL for Language Model Reasoning Knowledge Distillation
University of Iowa · Oracle AI
SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation
Apr 2, 2026Haomin Zhuang, Xiangqi Wang, Yili Shen +2Mathematical Problem Generation Numerical Reasoning in Language Models
University of Notre Dame
Math Takes Two: A test for emergent mathematical reasoning in communication
Mar 30, 2026Michael Cooper, Samuel CooperMathematical Reasoning Benchmarks LLM Mathematical Reasoning
Cooper Cognitive
Avoiding Overthinking and Underthinking: Curriculum-Aware Budget Scheduling for LLMs
Mar 29, 2026Amirul Rahman, Aisha Karim, Kenji Nakamura +1Efficient Language Model Reasoning Inference-Time Compute Allocation
University of Malaya
Arithmetic OOD Failure Unfolds in Stages in Minimal GPTs
Mar 27, 2026Seine A. ShintaniNumerical Reasoning in Language Models OOD Generalization
Department of Biomedical Sciences, College of Life and Health Sciences, Chubu University, Kasugai, Aichi 487-8501, Japan · Center for Mathematical Science and Artificial Intelligence, Chubu University, Kasugai, Aichi 487-8501, Japan · Institute for Advanced Research, Nagoya University, Nagoya, Aichi 464-8601, Japan
Robust Reasoning Benchmark
Mar 26, 2026Pavel Golikov, Evgenii Opryshko, Gennady Pekhimenko +1Language Model Robustness LLM Evaluation
University of Toronto · Vector Institute
TAPO: Translation Augmented Policy Optimization for Multilingual Mathematical Reasoning
Mar 26, 2026Xu Huang, Zhejian Lai, Zixian Huang +2Cross-Lingual Reasoning in Language Models RL for Language Model Reasoning
National Key Laboratory for Novel Software Technology, Nanjing University · Shanghai Artificial Intelligence Laboratory

Jun 24, 2026J/K move · Enter open · S save

Riazi-8B: An Urdu Large Language Model for Mathematical Reasoning

Azher Ali, Ibtsam Haider, Raja Khurram Shahzad, Seemab Latif+1

School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan · Department of Communication, Quality Management and Information Systems, Mid Sweden University, Ostersund, Sweden

Numerical Reasoning in Language Models LLM Fine-Tuning Language Modeling Low-Resource Language Processing LLM Mathematical Reasoning

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Recent LLMs demonstrate strong mathematical reasoning capabilities, but existing gains rely heavily on English-centric training resources and benchmarks. As a result, reasoning performance degrades substantially in low-resource languages such as Urdu, where reasoning-oriented datasets and adapted models remain scarce. Urdu lacks both reasoning-oriented resources and models adapted for multi-step mathematical problem solving, limiting the applicability of recent progress to Urdu-speaking users. We address this gap through Riazi-8B, an Urdu mathematical reasoning model developed through a two-step adaptation process comprising continued pre-training on Urdu Wikipedia and supervised fine-tuning on Urdu Chain-of-Thought data derived from GSM8K. We evaluate Riazi-8B on MGSM-Urdu against existing Urdu instruction-tuned models. Our results show consistent improvements in answer correctness, reasoning quality, response completeness, and Urdu generation. Our findings demonstrate that combining Urdu language adaptation with reasoning-focused fine-tuning is an effective strategy for extending mathematical reasoning capabilities to low-resource languages.