Arithmetic Reasoning with LLM: Prolog Generation & Permutation

• URL: http://arxiv.org/abs/2405.17893v1
• Date: Tue, 28 May 2024 07:13:25 GMT
• Title: Arithmetic Reasoning with LLM: Prolog Generation & Permutation
• Authors: Xiaocheng Yang, Bingsen Chen, Yik-Cheung Tam,
• Abstract summary: We show that Prolog-based arithmetic problem-solving outperforms CoT generation in the GSM8K benchmark. We propose to permute the ground truth predicates for more robust LLM training via data augmentation.
• Score: 2.1867261071129125
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Instructing large language models (LLMs) to solve elementary school math problems has shown great success using Chain of Thought (CoT). However, the CoT approach relies on an LLM to generate a sequence of arithmetic calculations which can be prone to cascaded calculation errors. We hypothesize that an LLM should focus on extracting predicates and generating symbolic formulas from the math problem description so that the underlying calculation can be done via an external code interpreter. We investigate using LLM to generate Prolog programs to solve mathematical questions. Experimental results show that our Prolog-based arithmetic problem-solving outperforms CoT generation in the GSM8K benchmark across three distinct LLMs. In addition, given the insensitive ordering of predicates and symbolic formulas in Prolog, we propose to permute the ground truth predicates for more robust LLM training via data augmentation.

Related papers

• Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures [3.181878085746691]
  Large language models (LLMs) have demonstrated remarkable mathematical capabilities, largely driven by chain-of-thought (CoT) prompting. We propose that LLMs learn arithmetic by capturing algebraic structures, such as emphCommutativity and emphIdentity properties. Our findings indicate that leveraging algebraic structures can enhance the LLMs' arithmetic capabilities, offering insights into improving their arithmetic performance.
  arXiv  Detail & Related papers  (2024-11-25T10:23:11Z)
• Language Models are Symbolic Learners in Arithmetic [8.34588487873447]
  Large Language Models (LLMs) are thought to struggle with arithmetic learning due to inherent differences between language modeling and numerical computation. We first investigate whether LLMs leverage partial products during arithmetic learning. We find that although LLMs can identify some partial products after learning, they fail to leverage them for arithmetic tasks, conversely.
  arXiv  Detail & Related papers  (2024-10-21T01:57:16Z)
• Graph-Structured Speculative Decoding [52.94367724136063]
  Speculative decoding has emerged as a promising technique to accelerate the inference of Large Language Models. We introduce an innovative approach utilizing a directed acyclic graph (DAG) to manage the drafted hypotheses. We observe a remarkable speedup of 1.73$times$ to 1.96$times$, significantly surpassing standard speculative decoding.
  arXiv  Detail & Related papers  (2024-07-23T06:21:24Z)
• On the Design and Analysis of LLM-Based Algorithms [74.7126776018275]
  Large language models (LLMs) are used as sub-routines in algorithms. LLMs have achieved remarkable empirical success. Our proposed framework holds promise for advancing LLM-based algorithms.
  arXiv  Detail & Related papers  (2024-07-20T07:39:07Z)
• Neuro-Symbolic Integration Brings Causal and Reliable Reasoning Proofs [95.07757789781213]
  Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. The other line of work adopt LLM-free declarative solvers to do the reasoning task, rendering higher reasoning accuracy but lacking interpretability due to the black-box nature of the solvers. We present a simple extension to the latter line of work. Specifically, we showcase that the intermediate search logs generated by Prolog interpreters can be accessed and interpreted into human-readable reasoning.
  arXiv  Detail & Related papers  (2023-11-16T11:26:21Z)
• LPML: LLM-Prompting Markup Language for Mathematical Reasoning [8.995617701116142]
  We propose a novel framework that integrates the Chain-of-Thought (CoT) method with an external tool (Python REPL) Our approach enables LLMs to write the markup language and perform advanced mathematical reasoning using only zero-shot prompting.
  arXiv  Detail & Related papers  (2023-09-21T02:46:20Z)
• Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning [101.26814728062065]
  Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving.
  arXiv  Detail & Related papers  (2023-05-20T22:25:38Z)
• 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)
• PAL: Program-aided Language Models [112.94785609781503]
  We present Program-Aided Language models (PaL) to understand natural language problems. PaL offloads the solution step to a programmatic runtime such as a Python interpreter. We set new state-of-the-art results in all 12 benchmarks.
  arXiv  Detail & Related papers  (2022-11-18T18:56:13Z)

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.