# Controlling Equational Reasoning in Large Language Models with Prompt Interventions

arXiv: https://arxiv.org/abs/2307.09998 · HTML: https://mlsanity.com/paper/2307.09998/

## 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 29 of its 56 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [Retrieval Augmentation Reduces Hallucination in Conversation](https://mlsanity.com/paper/2104.07567/) (2021)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [Harnessing the Power of LLMs in Practice: A Survey on ChatGPT and Beyond](https://mlsanity.com/paper/2304.13712/) (2023)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [OpenAGI: When LLM Meets Domain Experts](https://mlsanity.com/paper/2304.04370/) (2023)
- [Will we run out of data? Limits of LLM scaling based on human-generated data](https://mlsanity.com/paper/2211.04325/) (2022)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [NaturalProofs: Mathematical Theorem Proving in Natural Language](https://mlsanity.com/paper/2104.01112/) (2021)
- [NaturalProver: Grounded Mathematical Proof Generation with Language Models](https://mlsanity.com/paper/2205.12910/) (2022)
- [A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models](https://mlsanity.com/paper/2210.12023/) (2022)
- [A Symbolic Framework for Evaluating Mathematical Reasoning and Generalisation with Transformers](https://mlsanity.com/paper/2305.12563/) (2023)
- [Evaluating Token-Level and Passage-Level Dense Retrieval Models for Math Information Retrieval](https://mlsanity.com/paper/2203.11163/) (2022)
- [An automatically discovered chain-of-thought prompt generalizes to novel models and datasets](https://mlsanity.com/paper/2305.02897/) (2023)
- [Large Language Models, scientific knowledge and factuality: A framework to streamline human expert evaluation](https://mlsanity.com/paper/2305.17819/) (2023)

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

- [Scalable and Accurate Graph Reasoning with LLM-based Multi-Agents](https://mlsanity.com/paper/2410.05130/) (2024)

## Abstract (arXiv)

This paper investigates how hallucination rates in Large Language Models (LLMs) may be controlled via a symbolic data generation framework, exploring a fundamental relationship between the rate of certain mathematical errors and types of input intervention. Specifically, we systematically generate data for a derivation generation task using a symbolic engine, applying targeted interventions to prompts to perturb features of mathematical derivations such as the surface forms of symbols, equational tree structures, and mathematical context. We then evaluate the effect of prompt interventions across a range of LLMs including fine-tuned T5 models, GPT, and LLaMa-based models. Our experiments suggest that T5-Large can outperform the few-shot performance of GPT-4 on various evaluation sets generated via the framework. However, an extensive evaluation based on human analysis, template-based error detection, and text generation metrics reveals model weaknesses beyond what the reference-based metrics singularly describe. We use these results to tie characteristic distributional footprints of interventions to the human evaluation of LLM derivation quality, potentially leading to significant control over fine-grained mathematical capabilities of language models with respect to specific types of errors.