Numerical Reasoning in Language Models

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.