# Concept Generalization in Humans and Large Language Models: Insights from the Number Game

arXiv: https://arxiv.org/abs/2512.20162 · HTML: https://mlsanity.com/paper/2512.20162/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Better & Faster Large Language Models via Multi-token Prediction](https://mlsanity.com/paper/2404.19737/) (2024)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Turning large language models into cognitive models](https://mlsanity.com/paper/2306.03917/) (2023)
- [Number Cookbook: Number Understanding of Language Models and How to Improve It](https://mlsanity.com/paper/2411.03766/) (2024)
- [MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Code](https://mlsanity.com/paper/2410.08196/) (2024)
- [Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Study](https://mlsanity.com/paper/2506.04810/) (2025)
- [Benchmarking Large Language Models for Math Reasoning Tasks](https://mlsanity.com/paper/2408.10839/) (2024)
- [Thinking Machines: Mathematical Reasoning in the Age of LLMs](https://mlsanity.com/paper/2508.00459/) (2025)

## Built on by (most cited first, 1 of 1)

- [Hypothesis generation and updating in large language models](https://mlsanity.com/paper/2605.05851/) (2026)

## Abstract (arXiv)

We compare human and large language model (LLM) generalization in the number game, a concept inference task. Using a Bayesian model as an analytical framework, we examined the inductive biases and inference strategies of humans and LLMs. The Bayesian model captured human behavior better than LLMs in that humans flexibly infer rule-based and similarity-based concepts, whereas LLMs rely more on mathematical rules. Humans also demonstrated a few-shot generalization, even from a single example, while LLMs required more samples to generalize. These contrasts highlight the fundamental differences in how humans and LLMs infer and generalize mathematical concepts.