BEATS: Optimizing LLM Mathematical Capabilities with BackVerify and Adaptive Disambiguate based Efficient Tree Search
- URL: http://arxiv.org/abs/2409.17972v2
- Date: Sun, 29 Sep 2024 12:24:28 GMT
- Title: BEATS: Optimizing LLM Mathematical Capabilities with BackVerify and Adaptive Disambiguate based Efficient Tree Search
- Authors: Linzhuang Sun, Hao Liang, Jingxuan Wei, Bihui Yu, Conghui He, Zenan Zhou, Wentao Zhang,
- Abstract summary: Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains.
They still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics.
We propose a novel approach, BEATS, to enhance mathematical problem-solving abilities.
- Score: 22.672130194493793
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.
Related papers
- Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrieval [22.865124583257987]
We present how analogy from similarly structured questions can improve large language models' problem-solving capabilities.
Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt.
Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method.
arXiv Detail & Related papers (2024-11-25T15:01:25Z) - Autoformulation of Mathematical Optimization Models Using LLMs [50.030647274271516]
We develop an automated approach to creating optimization models from natural language descriptions for commercial solvers.
We identify the three core challenges of autoformulation: (1) defining the vast, problem-dependent hypothesis space, (2) efficiently searching this space under uncertainty, and (3) evaluating formulation correctness.
arXiv Detail & Related papers (2024-11-03T20:41:38Z) - HARDMath: A Benchmark Dataset for Challenging Problems in Applied Mathematics [1.5716764919736026]
We introduce HARDMath, a dataset featuring challenging applied mathematics problems that require analytical approximation techniques.
Our framework auto-generates a large number of problems with solutions validated against numerical ground truths.
We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts.
arXiv Detail & Related papers (2024-10-13T20:09:41Z) - Navigating the Labyrinth: Evaluating and Enhancing LLMs' Ability to Reason About Search Problems [59.72548591120689]
We introduce a new benchmark, SearchBench, containing 11 unique search problem types.
We show that even the most advanced LLMs fail to solve these problems end-to-end in text.
Instructing LLMs to generate code that solves the problem helps, but only slightly, e.g., GPT4's performance rises to 11.7%.
arXiv Detail & Related papers (2024-06-18T00:44:58Z) - MindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time [51.5039731721706]
MindStar is a purely inference-based searching method for large language models.
It formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths.
It significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1.
arXiv Detail & Related papers (2024-05-25T15:07:33Z) - GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers [68.77382332826167]
Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks.
One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly.
This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations.
arXiv Detail & Related papers (2024-02-29T15:26:14Z) - Evaluating and Improving Tool-Augmented Computation-Intensive Math
Reasoning [75.74103236299477]
Chain-of-thought prompting(CoT) and tool augmentation have been validated as effective practices for improving large language models.
We propose a new approach that can deliberate the reasoning steps with tool interfaces, namely textbfDELI.
Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines.
arXiv Detail & Related papers (2023-06-04T17:02:59Z) - SatLM: Satisfiability-Aided Language Models Using Declarative Prompting [68.40726892904286]
We propose a new satisfiability-aided language modeling (SatLM) approach for improving the reasoning capabilities of large language models (LLMs)
We use an LLM to generate a declarative task specification rather than an imperative program and leverage an off-the-shelf automated theorem prover to derive the final answer.
We evaluate SATLM on 8 different datasets and show that it consistently outperforms program-aided LMs in the imperative paradigm.
arXiv Detail & Related papers (2023-05-16T17:55:51Z) - MathPrompter: Mathematical Reasoning using Large Language Models [7.953723258038284]
Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks.
MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways.
arXiv Detail & Related papers (2023-03-04T04:43:49Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.