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Understanding and accurately following instructions is critical for large language models (LLMs) to be effective across diverse tasks. In this work, we rigorously examine the key factors that enable models to generalize to unseen instructions, providing insights to guide the collection of data for instruction-tuning. Through controlled experiments, inspired by the Turing-complete Markov algorithm, we demonstrate that such generalization $\textbf{only emerges}$ when training data is diversified enough across semantic domains. Our findings also reveal that merely diversifying within limited domains fails to ensure robust generalization. In contrast, cross-domain data diversification, even under constrained data budgets, significantly enhances a model's adaptability. We further extend our analysis to real-world scenarios, including fine-tuning of $\textit{$\textbf{specialist}$}$ and $\textit{$\textbf{generalist}$}$ models. In both cases, we demonstrate that 1) better performance can be achieved by increasing the diversity of an established dataset while keeping the data size constant, and 2) when scaling up the data, diversifying the semantics of instructions is more effective than simply increasing the quantity of similar data. Our research provides important insights for dataset collation, particularly when optimizing model performance by expanding training data for both specialist and generalist scenarios. We show that careful consideration of data diversification is key: training specialist models with data extending beyond their core domain leads to significant performance improvements, while generalist models benefit from diverse data mixtures that enhance their overall instruction-following capabilities across a wide range of applications. Our results highlight the critical role of strategic diversification and offer clear guidelines for improving data quality., Comment: Fix formatting issues

Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a search through the proof space using a theorem prover. Unfortunately, the theorem prover provides only the crudest estimate of progress, resulting in effectively undirected search. To address this problem, we create QEDCartographer, an automated proof-synthesis tool that combines supervised and reinforcement learning to more effectively explore the proof space. QEDCartographer incorporates the proofs' branching structure, enabling reward-free search and overcoming the sparse reward problem inherent to formal verification. We evaluate QEDCartographer using the CoqGym benchmark of 68.5K theorems from 124 open-source Coq projects. QEDCartographer fully automatically proves 21.4% of the test-set theorems. Previous search-based proof-synthesis tools Tok, Tac, ASTactic, Passport, and Proverbot9001, which rely only on supervised learning, prove 9.6%, 9.8%, 10.9%, 12.5%, and 19.8%, respectively. Diva, which combines 62 tools, proves 19.2%. Comparing to the most effective prior tool, Proverbot9001, QEDCartographer produces 34% shorter proofs 29% faster, on average over the theorems both tools prove. Together, QEDCartographer and non-learning-based CoqHammer prove 30.3% of the theorems, while CoqHammer alone proves 26.6%. Our work demonstrates that reinforcement learning is a fruitful research direction for improving proof-synthesis tools' search mechanisms., Comment: Published in the International Conference on Software Engineering (ICSE) 2025: Alex Sanchez-Stern, Abhishek Varghese, Zhanna Kaufman, Dylan Zhang, Talia Ringer, and Yuriy Brun, QEDCartographer: Automating Formal Verification Using Reward-Free Reinforcement Learning, in Proceedings of the 47th International Conference on Software Engineering (ICSE), 2025

Preference learning provides a promising solution to address the limitations of supervised fine-tuning (SFT) for code language models, where the model is not explicitly trained to differentiate between correct and incorrect code. Recent findings demonstrate that on-policy data is the key to successful preference learning, where the preference data is collected using the same policy LM being trained. Inspired by this, we propose PLUM, an on-policy $\textbf{P}$reference $\textbf{L}$earning framework A$\textbf{u}$gmented with test cases for code L$\textbf{M}$ s. The framework operates in three key stages: (1) automatic generation of test cases from natural language instructions, (2) creation of a preference data by evaluating candidate code solutions sampled from the policy, which can then be used to (3) train the policy LM. PLUM levitates the need to train reward models, allowing for large scale on-policy and online preference data collation. PLUM is evaluated on both standard benchmarks (HumanEval, MBPP) and more challenging ones (LiveCodeBench), delivering substantial improvements over original SFT'ed models and other execution-feedback-driven approaches. We show PLUM's benefits are consistent across various widely-used code LMs even they have been well-trained with SFT. For example, PLUM increases pass rates by up to 4.8% on average on standard benchmarks and 11.8% on LiveCodeBench, demonstrating its effectiveness and generalizability. We also demonstrate the benefits of on-policy and online preference learning by comprehensive experimentation., Comment: Template

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.