Enhancing Cross-Lingual and Cross-Domain Adaptability in Large Language Models for Software Engineering
Keywords: Code Generation, Transfer learning
TL;DR: We introduce the Enhanced Dynamic Code Modeling (UDA-EDCM) system, which leverages advanced concepts from measure theory, differential geometry, and information geometry.
Abstract: This paper presents a groundbreaking mathematical framework for unsupervised domain adaptation (UDA) in the context of cross-lingual and cross-domain code modeling. We introduce the Enhanced Dynamic Code Modeling (UDA-EDCM) system, which leverages advanced concepts from measure theory, differential geometry, and information geometry to address the challenges posed by the diversity of natural and programming languages. At the core of UDA-EDCM is a novel measure-theoretic formulation of domain adaptation, utilizing optimal transport theory to minimize the discrepancy between source and target domains. We develop a Riemannian manifold approach to feature space alignment, introducing a Geodesic Flow Kernel that captures the intrinsic geometry of the code representation space. The UDA-EDCM operator is analyzed through the lens of functional analysis, revealing its spectral properties and their implications for generalization. Our information-theoretic bound on domain adaptation provides insights into the fundamental limits of knowledge transfer in code modeling. We present a unified theorem that synthesizes these diverse mathematical perspectives, offering a comprehensive characterization of UDA-EDCM's performance in terms of Wasserstein distance, empirical Rademacher complexity, and Fisher information. This theoretical foundation is complemented by an innovative optimization framework based on the Fisher Information Metric, ensuring efficient convergence in the probabilistic manifold of model parameters. Extensive experiments demonstrate that UDA-EDCM significantly outperforms existing approaches in zero-shot and few-shot learning scenarios across a wide range of programming languages and coding tasks. Our work not only advances the baselines in domain adaptation for code intelligence but also establishes a rigorous mathematical basis for future research in adaptive AI systems for software engineering.
Primary Area: transfer learning, meta learning, and lifelong learning
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Submission Number: 13017
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