# LLM for Complex Reasoning Task: An Exploratory Study in Fermi Problems

arXiv: https://arxiv.org/abs/2504.02671 · HTML: https://mlsanity.com/paper/2504.02671/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 41 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Making Retrieval-Augmented Language Models Robust to Irrelevant Context](https://mlsanity.com/paper/2310.01558/) (2023)
- [Personal LLM Agents: Insights and Survey about the Capability, Efficiency and Security](https://mlsanity.com/paper/2401.05459/) (2024)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Answering Questions by Meta-Reasoning over Multiple Chains of Thought](https://mlsanity.com/paper/2304.13007/) (2023)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs](https://mlsanity.com/paper/2402.16352/) (2024)
- [Can LLMs Learn from Previous Mistakes? Investigating LLMs' Errors to Boost for Reasoning](https://mlsanity.com/paper/2403.20046/) (2024)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [TELeR: A General Taxonomy of LLM Prompts for Benchmarking Complex Tasks](https://mlsanity.com/paper/2305.11430/) (2023)
- [Understanding the Performance and Estimating the Cost of LLM Fine-Tuning](https://mlsanity.com/paper/2408.04693/) (2024)
- [How Much Coffee Was Consumed During EMNLP 2019? Fermi Problems: A New Reasoning Challenge for AI](https://mlsanity.com/paper/2110.14207/) (2021)
- [LLMs as Meta-Reviewers' Assistants: A Case Study](https://mlsanity.com/paper/2402.15589/) (2024)
- [Benchmarking LLMs on the Semantic Overlap Summarization Task](https://mlsanity.com/paper/2402.17008/) (2024)

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

- [Multi-agent Scaling Across Disjunctive and Compensatory Tasks](https://mlsanity.com/paper/2609.31563/) (2026)

## Abstract (arXiv)

Fermi Problems (FPs) are mathematical reasoning tasks that require human-like logic and numerical reasoning. Unlike other reasoning questions, FPs often involve real-world impracticalities or ambiguous concepts, making them challenging even for humans to solve. Despite advancements in AI, particularly with large language models (LLMs) in various reasoning tasks, FPs remain relatively under-explored. This work conducted an exploratory study to examine the capabilities and limitations of LLMs in solving FPs. We first evaluated the overall performance of three advanced LLMs using a publicly available FP dataset. We designed prompts according to the recently proposed TELeR taxonomy, including a zero-shot scenario. Results indicated that all three LLMs achieved a fp_score (range between 0 - 1) below 0.5, underscoring the inherent difficulty of these reasoning tasks. To further investigate, we categorized FPs into standard and specific questions, hypothesizing that LLMs would perform better on standard questions, which are characterized by clarity and conciseness, than on specific ones. Comparative experiments confirmed this hypothesis, demonstrating that LLMs performed better on standard FPs in terms of both accuracy and efficiency.