Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization

• URL: http://arxiv.org/abs/2508.18091v1
• Date: Mon, 25 Aug 2025 14:52:56 GMT
• Title: Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization
• Authors: Mohammad J. Abdel-Rahman, Yasmeen Alslman, Dania Refai, Amro Saleh, Malik A. Abu Loha, Mohammad Yahya Hamed,
• Abstract summary: This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming.<n>We first conduct a systematic review and meta-analysis of recent literature to assess how well LLMs understand, structure, and solve optimization problems across domains.<n>Our systematic evidence is complemented by targeted experiments designed to evaluate the performance of state-of-the-art LLMs in automatically generating optimization models for problems in computer networks.
• Score: 1.246870021158888
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to assess how well LLMs understand, structure, and solve optimization problems across domains. The analysis is guided by critical review questions focusing on learning approaches, dataset designs, evaluation metrics, and prompting strategies. Our systematic evidence is complemented by targeted experiments designed to evaluate the performance of state-of-the-art LLMs in automatically generating optimization models for problems in computer networks. Using a newly constructed dataset, we apply three prompting strategies: Act-as-expert, chain-of-thought, and self-consistency, and evaluate the obtained outputs based on optimality gap, token-level F1 score, and compilation accuracy. Results show promising progress in LLMs' ability to parse natural language and represent symbolic formulations, but also reveal key limitations in accuracy, scalability, and interpretability. These empirical gaps motivate several future research directions, including structured datasets, domain-specific fine-tuning, hybrid neuro-symbolic approaches, modular multi-agent architectures, and dynamic retrieval via chain-of-RAGs. This paper contributes a structured roadmap for advancing LLM capabilities in mathematical programming.

Related papers

• Large Language Models: A Mathematical Formulation [9.837462698662947]
  Large language models (LLMs) process and predict sequences containing text to answer questions.<n>We provide a mathematical framework for LLMs by describing the encoding of text sequences into sequences of tokens.<n>We explain how these models are learned from data, and demonstrate how they are deployed to address a variety of tasks.
  arXiv  Detail & Related papers  (2026-01-21T21:22:49Z)
• Analytical Survey of Learning with Low-Resource Data: From Analysis to Investigation [192.53529928861818]
  Learning with high-resource data has demonstrated substantial success in artificial intelligence (AI)<n>However, the costs associated with data annotation and model training remain significant.<n>This survey employs active sampling theory to analyze the generalization error and label complexity associated with learning from low-resource data.
  arXiv  Detail & Related papers  (2025-10-10T03:15:42Z)
• Discrete Tokenization for Multimodal LLMs: A Comprehensive Survey [69.45421620616486]
  This work presents the first structured taxonomy and analysis of discrete tokenization methods designed for large language models (LLMs)<n>We categorize 8 representative VQ variants that span classical and modern paradigms and analyze their algorithmic principles, training dynamics, and integration challenges with LLM pipelines.<n>We identify key challenges including codebook collapse, unstable gradient estimation, and modality-specific encoding constraints.
  arXiv  Detail & Related papers  (2025-07-21T10:52:14Z)
• Enhancing Large Language Models through Structured Reasoning [15.472375478049823]
  We introduce a novel approach to enhance Large Language Models (LLMs) through explicit structured reasoning.<n>First, we convert unstructured data into structured formats by explicitly annotating reasoning steps.<n>We then employ this structured dataset to train LLMs through Supervised Fine-Tuning (SFT)
  arXiv  Detail & Related papers  (2025-06-25T08:36:12Z)
• A Survey on Mathematical Reasoning and Optimization with Large Language Models [0.5439020425819]
  Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem proving, and optimization techniques.<n>This survey explores the evolution of mathematical problem-solving in AI, from early statistical learning approaches to modern deep learning and transformer-based methodologies.
  arXiv  Detail & Related papers  (2025-03-22T10:49:32Z)
• Applications of Large Language Model Reasoning in Feature Generation [0.0]
  Large Language Models (LLMs) have revolutionized natural language processing through their state of art reasoning capabilities.<n>This paper explores the convergence of LLM reasoning techniques and feature generation for machine learning tasks.<n>The paper categorizes LLM-based feature generation methods across various domains including finance, healthcare, and text analytics.
  arXiv  Detail & Related papers  (2025-03-15T04:18:01Z)
• Systematic Analysis of LLM Contributions to Planning: Solver, Verifier, Heuristic [6.687149103409949]
  We provide a systematic analysis of how large language models (LLMs) contribute to solving planning problems.<n>Our analysis reveals that although it is difficult for LLMs to generate correct plans out-of-the-box, LLMs are much better at providing feedback signals to intermediate/incomplete solutions.
  arXiv  Detail & Related papers  (2024-12-12T18:16:46Z)
• EVOLvE: Evaluating and Optimizing LLMs For In-Context Exploration [76.66831821738927]
  Large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty.<n>We measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications.<n>Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs.
  arXiv  Detail & Related papers  (2024-10-08T17:54:03Z)
• 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)
• Exploring and Benchmarking the Planning Capabilities of Large Language Models [57.23454975238014]
  This work lays the foundations for improving planning capabilities of large language models (LLMs) We construct a comprehensive benchmark suite encompassing both classical planning benchmarks and natural language scenarios. We investigate the use of many-shot in-context learning to enhance LLM planning, exploring the relationship between increased context length and improved planning performance.
  arXiv  Detail & Related papers  (2024-06-18T22:57:06Z)
• LLM Inference Unveiled: Survey and Roofline Model Insights [62.92811060490876]
  Large Language Model (LLM) inference is rapidly evolving, presenting a unique blend of opportunities and challenges. Our survey stands out from traditional literature reviews by not only summarizing the current state of research but also by introducing a framework based on roofline model. This framework identifies the bottlenecks when deploying LLMs on hardware devices and provides a clear understanding of practical problems.
  arXiv  Detail & Related papers  (2024-02-26T07:33:05Z)
• Instruction Tuning for Large Language Models: A Survey [52.86322823501338]
  We make a systematic review of the literature, including the general methodology of supervised fine-tuning (SFT)<n>We also review the potential pitfalls of SFT along with criticism against it, along with efforts pointing out current deficiencies of existing strategies.
  arXiv  Detail & Related papers  (2023-08-21T15:35:16Z)

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.