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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. An empirical evaluation of pre-trained large language models for repairing declarative formal specifications

   https://doi.org/10.1007/s10664-025-10687-1  

   Alhanahnah, Mohannad; Rashedul_Hasan, Md; Xu, Lisong; Bagheri, Hamid (September 2025, Empirical Software Engineering)

   Abstract Automatic Program Repair (APR) has garnered significant attention as a practical research domain focused on automatically fixing bugs in programs. While existing APR techniques primarily target imperative programming languages like C and Java, there is a growing need for effective solutions applicable to declarative software specification languages. This paper systematically investigates the capacity of Large Language Models (LLMs) to repair declarative specifications in Alloy, a declarative formal language used for software specification. We designed six different repair settings, encompassing single-agent and dual-agent paradigms, utilizing various LLMs. These configurations also incorporate different levels of feedback, including an auto-prompting mechanism for generating prompts autonomously using LLMs. Our study reveals that dual-agent with auto-prompting setup outperforms the other settings, albeit with a marginal increase in the number of iterations and token usage. This dual-agent setup demonstrated superior effectiveness compared to state-of-the-art Alloy APR techniques when evaluated on a comprehensive set of benchmarks. This work is the first to empirically evaluate LLM capabilities to repair declarative specifications, while taking into account recent trending LLM concepts such as LLM-based agents, feedback, auto-prompting, and tools, thus paving the way for future agent-based techniques in software engineering. 

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3. LLM+AL: Bridging Large Language Models and Action Languages for Complex Reasoning about Actions

   Isay, Adam; Lee, Joohyung (February 2025, AAAI Press)

   Large Language Models (LLMs) have made significant strides in various intelligent tasks but still struggle with complex action reasoning tasks that require systematic search. To address this limitation, we introduce a method that bridges the natural language understanding capability of LLMs with the symbolic reasoning capability of action languages---formal languages for reasoning about actions. Our approach, termed {\sf LLM+AL}, leverages the LLM's strengths in semantic parsing and commonsense knowledge generation alongside the action language's expertise in automated reasoning based on encoded knowledge. We compare {\sf LLM+AL} against state-of-the-art LLMs, including {\sc ChatGPT-4}, {\sc Claude 3 Opus}, {\sc Gemini Ultra 1.0}, and {\sc o1-preview}, using benchmarks for complex reasoning about actions. Our findings indicate that while all methods exhibit various errors, {\sf LLM+AL}, with relatively simple human corrections, consistently leads to correct answers, whereas using LLMs alone does not yield improvements even after human intervention. {\sf LLM+AL} also contributes to automated generation of action languages. 

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4. 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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5. CLoQ: Enhancing Fine-Tuning of Quantized LLMs via Calibrated LoRA Initialization

   Deng, Yanxia; Zhang, Aozhong; Gurses, Selcuk; Wang, Naigang; Yang, Zi; Yin, Penghang (August 2025, Transactions on machine learning research)

   Fine-tuning large language models (LLMs) using low-rank adaptation (LoRA) has become a highly efficient approach for downstream tasks, particularly in scenarios with limited computational resources. However, applying LoRA techniques to quantized LLMs poses unique challenges due to the reduced representational precision of quantized weights. In this paper, we introduce CLoQ (Calibrated LoRA initialization for Quantized LLMs), a simplistic initialization strategy designed to overcome these challenges. Our approach focuses on minimizing the layer-wise discrepancy between the original LLM and its quantized counterpart with LoRA components during initialization. By leveraging a small calibration dataset, CLoQ quantizes a pre-trained LLM and determines the optimal LoRA components for each layer, ensuring a strong foundation for subsequent fine-tuning. A key contribution of this work is a novel theoretical result that enables the accurate and closed-form construction of these optimal LoRA components. We validate the efficacy of CLoQ across multiple tasks such as language generation, arithmetic reasoning, and commonsense reasoning, demonstrating that it consistently outperforms existing LoRA fine-tuning methods for quantized LLMs, especially at 2-bit. 

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