# FERMAT: An Alternative to Accuracy for Numerical Reasoning

arXiv: https://arxiv.org/abs/2305.17491 · HTML: https://mlsanity.com/paper/2305.17491/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 27 May 2023.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Answering Complex Open-Domain Questions with Multi-Hop Dense Retrieval](https://mlsanity.com/paper/2009.12756/) (2020)
- [Injecting Numerical Reasoning Skills into Language Models](https://mlsanity.com/paper/2004.04487/) (2020)
- ["Going on a vacation" takes longer than "Going for a walk": A Study of Temporal Commonsense Understanding](https://mlsanity.com/paper/1909.03065/) (2019)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [Teaching Algorithmic Reasoning via In-context Learning](https://mlsanity.com/paper/2211.09066/) (2022)
- [Quoref: A Reading Comprehension Dataset with Questions Requiring Coreferential Reasoning](https://mlsanity.com/paper/1908.05803/) (2019)
- [Transforming Question Answering Datasets Into Natural Language Inference Datasets](https://mlsanity.com/paper/1809.02922/) (2018)
- [INFOTABS: Inference on Tables as Semi-structured Data](https://mlsanity.com/paper/2005.06117/) (2020)
- [Giving BERT a Calculator: Finding Operations and Arguments with Reading Comprehension](https://mlsanity.com/paper/1909.00109/) (2019)
- [QuaRel: A Dataset and Models for Answering Questions about Qualitative Relationships](https://mlsanity.com/paper/1811.08048/) (2018)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [Adversarial Examples for Evaluating Math Word Problem Solvers](https://mlsanity.com/paper/2109.05925/) (2021)

## Built on by (most cited first, 3 of 3)

- [How to Leverage Digit Embeddings to Represent Numbers?](https://mlsanity.com/paper/2407.00894/) (2024)
- [Enhancing Quantitative Reasoning Skills of Large Language Models through Dimension Perception](https://mlsanity.com/paper/2312.17532/) (2023)
- [Revealing the Numeracy Gap: An Empirical Investigation of Text Embedding Models](https://mlsanity.com/paper/2509.05691/) (2025)

## Abstract (arXiv)

While pre-trained language models achieve impressive performance on various NLP benchmarks, they still struggle with tasks that require numerical reasoning. Recent advances in improving numerical reasoning are mostly achieved using very large language models that contain billions of parameters and are not accessible to everyone. In addition, numerical reasoning is measured using a single score on existing datasets. As a result, we do not have a clear understanding of the strengths and shortcomings of existing models on different numerical reasoning aspects and therefore, potential ways to improve them apart from scaling them up. Inspired by CheckList (Ribeiro et al., 2020), we introduce a multi-view evaluation set for numerical reasoning in English, called FERMAT. Instead of reporting a single score on a whole dataset, FERMAT evaluates models on various key numerical reasoning aspects such as number understanding, mathematical operations, and training dependency. Apart from providing a comprehensive evaluation of models on different numerical reasoning aspects, FERMAT enables a systematic and automated generation of an arbitrarily large training or evaluation set for each aspect.The datasets and codes are publicly available to generate further multi-view data for ulterior tasks and languages.