arXiv subjects

Minghai Lu

Publications and source records attributed to Minghai Lu.

3 recordsLinked to original sources

arXiv2025

Adaptive Proof Refinement with LLM-Guided Strategy Selection

Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models (LLMs) show potential in proof generation, they frequently produce incorrect proofs on the first attempt and require additional strategies for iterative refinement. However, existing approaches employ fixed refinement strategies and cannot dynamically choose an effective strategy based on the particular issues in a generated proof, which limits their performance. To overcome this limitation, we introduce Adapt, a novel proof refinement framework that leverages an LLM-guided decision-maker to dynamically select a suitable refinement strategy according to the state of the proof assistant and available context of an incorrect proof. We evaluate Adapt on two benchmarks against four existing methods and find that it significantly outperforms the best baseline on both by proving 16.63% and 18.58% more theorems, respectively. Furthermore, we demonstrate Adapt's generalizability by evaluating it across five different LLMs. We also conduct ablation studies to measure the contribution of each component and compare the trade-offs of alternative decision-maker designs.

cs.SE↗

arXiv2024

Proof Automation with Large Language Models

Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise in automatically generating informal proofs in natural language, they are less effective at generating formal proofs in interactive theorem provers. In this paper, we conduct a formative study to identify common mistakes made by LLMs when asked to generate formal proofs. By analyzing 520 proof generation errors made by GPT-3.5, we found that GPT-3.5 often identified the correct high-level structure of a proof, but struggled to get the lower-level details correct. Based on this insight, we propose PALM, a novel generate-then-repair approach that first prompts an LLM to generate an initial proof and then leverages targeted symbolic methods to iteratively repair low-level problems. We evaluate PALM on a large dataset that includes more than 10K theorems. Our results show that PALM significantly outperforms other state-of-the-art approaches, successfully proving 76.6% to 180.4% more theorems. Moreover, PALM proves 1270 theorems beyond the reach of existing approaches. We also demonstrate the generalizability of PALM across different LLMs.

cs.SE↗

arXiv2024

Automated Deep Learning Optimization via DSL-Based Source Code Transformation

As deep learning models become increasingly bigger and more complex, it is critical to improve model training and inference efficiency. Though a variety of highly optimized libraries and packages (known as DL kernels) have been developed, it is tedious and time-consuming to figure out which kernel to use, where to use, and how to use them correctly. To address this challenge, we propose an Automated Deep learning OPTimization approach called Adopter. We design a Domain-Specific Language (DSL) to represent DL model architectures and leverage this DSL to specify model transformation rules required to integrate a DL kernel into a model. Given the source code of a DL model and the transformation rules for a set of kernels, Adopter first performs inter-procedural analysis to identify and express the model architecture in our DSL. Then, Adopter performs scope analysis and sub-sequence matching to identify locations in the model architecture where the transformation rules can be applied. Finally, Adopter proposes a synthesis-based code transformation method to apply the transformation rule. We curated a benchmark with 199 models from Hugging Face and a diverse set of DL kernels. We found that, compared to a state-of-the-art automated code transformation technique, Adopter helps improve the precision and recall by 3% and 56%, respectively. An in-depth analysis of 9 models revealed that on average, Adopter improved the training speed by 22.7% while decreasing the GPU memory usage by 10.5%.

cs.SE↗