# Enhancing Quantitative Reasoning Skills of Large Language Models through Dimension Perception

arXiv: https://arxiv.org/abs/2312.17532 · HTML: https://mlsanity.com/paper/2312.17532/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 29 Dec 2023.

## Placed in

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

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

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [OpenChat: Advancing Open-source Language Models with Mixed-Quality Data](https://mlsanity.com/paper/2309.11235/) (2023)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [Birds have four legs?! NumerSense: Probing Numerical Commonsense Knowledge of Pre-trained Language Models](https://mlsanity.com/paper/2005.00683/) (2020)
- [Neural Module Networks for Reasoning over Text](https://mlsanity.com/paper/1912.04971/) (2019)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [EQUATE: A Benchmark Evaluation Framework for Quantitative Reasoning in Natural Language Inference](https://mlsanity.com/paper/1901.03735/) (2019)
- [How Large Are Lions? Inducing Distributions over Quantitative Attributes](https://mlsanity.com/paper/1906.01327/) (2019)
- [Learning by Analogy: Diverse Questions Generation in Math Word Problem](https://mlsanity.com/paper/2306.09064/) (2023)
- [Practice Makes a Solver Perfect: Data Augmentation for Math Word Problem Solvers](https://mlsanity.com/paper/2205.00177/) (2022)
- [FERMAT: An Alternative to Accuracy for Numerical Reasoning](https://mlsanity.com/paper/2305.17491/) (2023)

## Built on by (most cited first, 4 of 4)

- [Laying the Foundation First? Investigating the Generalization from Atomic Skills to Complex Reasoning Tasks](https://mlsanity.com/paper/2403.09479/) (2024)
- [LoopServe: An Adaptive Dual-phase LLM Inference Acceleration System for Multi-Turn Dialogues](https://mlsanity.com/paper/2507.13681/) (2025)
- [LLM-R: A Framework for Domain-Adaptive Maintenance Scheme Generation Combining Hierarchical Agents and RAG](https://mlsanity.com/paper/2411.04476/) (2024)
- [Language Models Compare Quantities Using Number-specific and Unit-specific Heuristics](https://mlsanity.com/paper/2606.03982/) (2026)

## Abstract (arXiv)

Quantities are distinct and critical components of texts that characterize the magnitude properties of entities, providing a precise perspective for the understanding of natural language, especially for reasoning tasks. In recent years, there has been a flurry of research on reasoning tasks based on large language models (LLMs), most of which solely focus on numerical values, neglecting the dimensional concept of quantities with units despite its importance. We argue that the concept of dimension is essential for precisely understanding quantities and of great significance for LLMs to perform quantitative reasoning. However, the lack of dimension knowledge and quantity-related benchmarks has resulted in low performance of LLMs. Hence, we present a framework to enhance the quantitative reasoning ability of language models based on dimension perception. We first construct a dimensional unit knowledge base (DimUnitKB) to address the knowledge gap in this area. We propose a benchmark DimEval consisting of seven tasks of three categories to probe and enhance the dimension perception skills of LLMs. To evaluate the effectiveness of our methods, we propose a quantitative reasoning task and conduct experiments. The experimental results show that our dimension perception method dramatically improves accuracy (43.55%->50.67%) on quantitative reasoning tasks compared to GPT-4.