Training Large Language Models (LLMs) with synthetic data is a prevalent practice in code generation. A key approach is self-training, where LLMs are iteratively trained on self-generated correct code snippets. In this case, the self-generated codes are drawn from a conditional distribution, conditioned on a specific seed description. However, the seed description is not the only valid representation that aligns with its intended meaning. With all valid descriptions and codes forming a joint space, codes drawn from the conditional distribution would lead to an underrepresentation of the full description-code space. As such, we propose Gibbs Fine-Tuning (GiFT), a novel self-training method inspired by Gibbs sampling. GiFT allows self-generated data to be drawn from the marginal distribution of the joint space, thereby mitigating the biases inherent in conditional sampling. We provide a theoretical analysis demonstrating the potential benefits of fine-tuning LLMs with code derived from the marginal distribution. Furthermore, we propose a perplexity-based code selection method to mitigate the imbalanced long-tail distribution of the self-generated codes. Empirical evaluation of two LLMs across four datasets demonstrates that GiFT achieves superior performance, particularly on more challenging benchmarks. Source code is available at https://github.com/Alex-HaochenLi/GiFT.

We introduce ESGenius, a comprehensive benchmark for evaluating and enhancing the proficiency of Large Language Models (LLMs) in Environmental, Social, and Governance (ESG) and sustainability-focused question answering. ESGenius comprises two key components: (i) ESGenius-QA, a collection of 1,136 Multiple-Choice Questions (MCQs) generated by LLMs and rigorously validated by domain experts, covering a broad range of ESG pillars and sustainability topics. Each question is systematically linked to its corresponding source text, enabling transparent evaluation and supporting Retrieval-Augmented Generation (RAG) methods; and (ii) ESGenius-Corpus, a meticulously curated repository of 231 foundational frameworks, standards, reports, and recommendation documents from 7 authoritative sources. Moreover, to fully assess the capabilities and adaptation potential of LLMs, we implement a rigorous two-stage evaluation protocol—Zero-Shot and RAG. Extensive experiments across 50 LLMs (0.5B to 671B) demonstrate that state-of-the-art models achieve only moderate performance in zero-shot settings, with accuracies around 55–70%, highlighting a significant knowledge gap for LLMs in this specialized, interdisciplinary domain. However, models employing RAG demonstrate significant performance improvements, particularly for smaller models. For example, DeepSeek-R1-Distill-Qwen-14B improves from 63.82% (zero-shot) to 80.46% with RAG. These results demonstrate the necessity of grounding responses in authoritative sources for enhanced ESG understanding. To the best of our knowledge, ESGenius is the first comprehensive QA benchmark designed to rigorously evaluate LLMs on ESG and sustainability knowledge, providing a critical tool to advance trustworthy AI in this vital domain.