# Models Can and Should Embrace the Communicative Nature of Human-Generated Math

arXiv: https://arxiv.org/abs/2409.17005 · HTML: https://mlsanity.com/paper/2409.17005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 25 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Assessing BERT's Syntactic Abilities](https://mlsanity.com/paper/1901.05287/) (2019)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [Building Machines that Learn and Think with People](https://mlsanity.com/paper/2408.03943/) (2024)
- [Premise Order Matters in Reasoning with Large Language Models](https://mlsanity.com/paper/2402.08939/) (2024)
- [A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models](https://mlsanity.com/paper/2210.12023/) (2022)
- [minicons: Enabling Flexible Behavioral and Representational Analyses of Transformer Language Models](https://mlsanity.com/paper/2203.13112/) (2022)
- [The Larger They Are, the Harder They Fail: Language Models do not Recognize Identifier Swaps in Python](https://mlsanity.com/paper/2305.15507/) (2023)
- [Do Language Models Exhibit the Same Cognitive Biases in Problem Solving as Human Learners?](https://mlsanity.com/paper/2401.18070/) (2024)
- [Reliable Reasoning Beyond Natural Language](https://mlsanity.com/paper/2407.11373/) (2024)
- [AI for Mathematics: A Cognitive Science Perspective](https://mlsanity.com/paper/2310.13021/) (2023)
- [Exploring the Reversal Curse and Other Deductive Logical Reasoning in BERT and GPT-Based Large Language Models](https://mlsanity.com/paper/2312.03633/) (2023)

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

- [MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs](https://mlsanity.com/paper/2410.13502/) (2024)

## Abstract (arXiv)

Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical entities but rich communicative intentions. While there are important advantages to treating math in a purely symbolic manner, we here hypothesize that there are benefits to treating math as situated linguistic communication and that language models are well suited for this goal, in ways that are not fully appreciated. We illustrate these points with two case studies. First, we ran an experiment in which we found that language models interpret the equals sign in a humanlike way -- generating systematically different word problems for the same underlying equation arranged in different ways. Second, we found that language models prefer proofs to be ordered in naturalistic ways, even though other orders would be logically equivalent. We advocate for AI systems that learn from and represent the communicative intentions latent in human-generated math.