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1. PAL: Program-aided Language Models

   Gao, Luyu; Madaan, Aman; Zhou, Shuyan; Alon, Uri; Liu, Pengfei; Yang, Yiming; Callan, Jamie; Neubig, Graham (July 2023, Proceedings of the 40th International Conference on Machine Learning)

   Large language models (LLMs) have demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed to prompting methods such as "chain-of-thought", which employ LLMs for both understanding the problem description by decomposing it into steps, as well as solving each step of the problem. While LLMs seem to be adept at this sort of step-by-step decomposition, LLMs often make logical and arithmetic mistakes in the solution part, even when the problem is decomposed correctly. In this paper, we present Program-Aided Language models (PAL): a novel approach that uses the LLM to read natural language problems and generate programs as the intermediate reasoning steps, but offloads the solution step to a runtime such as a Python interpreter. With PAL, decomposing the natural language problem into runnable steps remains the only learning task for the LLM, while solving is delegated to the interpreter. We demonstrate this synergy between a neural LLM and a symbolic interpreter across 13 mathematical, symbolic, and algorithmic reasoning tasks from BIG-Bench Hard and others. In all these natural language reasoning tasks, generating code using an LLM and reasoning using a Python interpreter leads to more accurate results than much larger models. For example, PAL using Codex achieves state-of-the-art few-shot accuracy on GSM8K, surpassing PaLM which uses chain-of-thought by absolute 15% top-1. 

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2. Leveraging Large Language Models to Generate Answer Set Programs

   https://doi.org/10.24963/kr.2023/37  

   Ishay, Adam; Yang, Zhun; Lee, Joohyung (September 2023, International Joint Conferences on Artificial Intelligence Organization)

   Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning capabilities are limited and relatively shallow, despite the application of various prompting techniques. In contrast, formal logic is adept at handling complex reasoning, but translating natural language descriptions into formal logic is a challenging task that non-experts struggle with. This paper proposes a neuro-symbolic method that combines the strengths of large language models and answer set programming. Specifically, we employ an LLM to transform natural language descriptions of logic puzzles into answer set programs. We carefully design prompts for an LLM to convert natural language descriptions into answer set programs in a step by step manner. Surprisingly, with just a few in-context learning examples, LLMs can generate reasonably complex answer set programs. The majority of errors made are relatively simple and can be easily corrected by humans, thus enabling LLMs to effectively assist in the creation of answer set programs. 

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3. Solving Math Word Problems Using Estimation Verification and Equation Generation

   Piehl, Mitchell; Wilson, Dillon; Kalita, Ananya; Kalita, Jugal (December 2025, International Conference on Machine Learning Applications (ICMLA))

   Large Language Models (LLMs) excel at various tasks, including problem-solving and question-answering. How- ever, LLMs often find Math Word Problems (MWPs) chal- lenging because solving them requires a range of reasoning and mathematical abilities with which LLMs seem to struggle. Recent efforts have helped LLMs solve more complex MWPs with improved prompts. This study proposes a novel method that initially prompts an LLM to create equations from a decomposition of the question, followed by using an external symbolic equation solver to produce an answer. To ensure the accuracy of the obtained answer, inspired by an established recommendation of math teachers, the LLM is instructed to solve the MWP a second time, but this time with the objective of estimating the correct answer instead of solving it exactly. The estimation is then compared to the generated answer to verify. If verification fails, an iterative rectification process is employed to ensure the correct answer is eventually found. This approach achieves new state-of-the-art results on datasets used by prior published research on numeric and algebraic MWPs, improving the previous best results by nearly two percent on average. In addition, the approach obtains satisfactory results on trigonometric MWPs, a task not previously attempted to the authors’ best knowledge. This study also introduces two new datasets, SVAMPClean and Trig300, to further advance the testing of LLMs’ reasoning abilities. 

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4. λ-Tune: Harnessing Large Language Models for Automated Database System Tuning

   https://doi.org/10.1145/3709652  

   Giannakouris, Victor; Trummer, Immanuel (February 2025, Proceedings of the ACM on Management of Data)

   We introduce λ-Tune, a framework that leverages Large Language Models (LLMs) for automated database system tuning. The design of λ-Tune is motivated by the capabilities of the latest generation of LLMs. Different from prior work, leveraging LLMs to extract tuning hints for single parameters, λ-Tune generates entire configuration scripts, based on a large input document, describing the tuning context. λ-Tune generates alternative configurations, using a principled approach to identify the best configuration, out of a small set of candidates. In doing so, it minimizes reconfiguration overheads and ensures that evaluation costs are bounded as a function of the optimal run time. By treating prompt generation as a cost-based optimization problem, λ-Tune conveys the most relevant context to the LLM while bounding the number of input tokens and, therefore, monetary fees for LLM invocations. We compare λ-Tune to various baselines, using multiple benchmarks and PostgreSQL and MySQL as target systems for tuning, showing that λ-Tune is significantly more robust than prior approaches. 

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5. SatLM: Satisfiability-Aided Language Models Using Declarative Prompting

   Ye, Xi; Chen, Qiaochu; Dillig, Isil; Durrett, Greg (December 2023, Advances in neural information processing systems)

   Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward reasoning (e.g., straightforward arithmetic), it is less effective for constraint solving problems that require more sophisticated planning and search. In this paper, we propose a new satisfiability-aided language modeling (SatLM) approach for improving the reasoning capabilities of 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. This approach has two key advantages. The declarative specification is closer to the problem description than the reasoning steps are, so the LLM can parse it out of the description more accurately. Furthermore, by offloading the actual reasoning task to an automated theorem prover, our approach can guarantee the correctness of the answer with respect to the parsed specification and avoid planning errors in the solving process. We evaluate SATLM on 8 different datasets and show that it consistently outperforms program-aided LMs in the imperative paradigm. In particular, SATLM outperforms program-aided LMs by 23% on a challenging subset of the GSM arithmetic reasoning dataset; SATLM also achieves a new SoTA on LSAT and BoardgameQA, surpassing previous models that are trained on the respective training sets. 

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