Yingbin Liang

Peizhong Ju, Haibo Yang, Jia Liu et al.

Federated Learning (FL) has gained significant popularity due to its effectiveness in training machine learning models across diverse sites without requiring direct data sharing. While various algorithms along with their optimization analyses have shown that FL with local updates is a communication-efficient distributed learning framework, the generalization performance of FL with local updates has received comparatively less attention. This lack of investigation can be attributed to the complex interplay between data heterogeneity and infrequent communication due to the local updates within the FL framework. This motivates us to investigate a fundamental question in FL: Can we quantify the impact of data heterogeneity and local updates on the generalization performance for FL as the learning process evolves? To this end, we conduct a comprehensive theoretical study of FL's generalization performance using a linear model as the first step, where the data heterogeneity is considered for both the stationary and online/non-stationary cases. By providing closed-form expressions of the model error, we rigorously quantify the impact of the number of the local updates (denoted as $K$) under three settings ($K=1$, $K<\infty$, and $K=\infty$) and show how the generalization performance evolves with the number of rounds $t$. Our investigation also provides a comprehensive understanding of how different configurations (including the number of model parameters $p$ and the number of training samples $n$) contribute to the overall generalization performance, thus shedding new insights (such as benign overfitting) for implementing FL over networks.

Daouda Sow, Herbert Woisetschläger, Saikiran Bulusu et al.

Pretraining large language models (LLMs) on vast and heterogeneous datasets is crucial for achieving state-of-the-art performance across diverse downstream tasks. However, current training paradigms treat all samples equally, overlooking the importance or relevance of individual samples throughout the training process. Existing reweighting strategies, which primarily focus on group-level data importance, fail to leverage fine-grained instance-level information and do not adapt dynamically to individual sample importance as training progresses. In this paper, we introduce novel algorithms for dynamic, instance-level data reweighting aimed at improving both the efficiency and effectiveness of LLM pretraining. Our methods adjust the weight of each training sample based on its loss value in an online fashion, allowing the model to dynamically focus on more informative or important samples at the current training stage. In particular, our framework allows us to systematically devise reweighting strategies deprioritizing redundant or uninformative data, which we find tend to work best. Furthermore, we develop a new theoretical framework for analyzing the impact of loss-based reweighting on the convergence of gradient-based optimization, providing the first formal characterization of how these strategies affect convergence bounds. We empirically validate our approach across a spectrum of tasks, from pretraining 7B and 1.4B parameter LLMs to smaller-scale language models and linear regression problems, demonstrating that our loss-based reweighting approach can lead to faster convergence and significantly improved performance.

Lucas Carrit Delgado Pinheiro, Ziru Chen, Bruno Caixeta Piazza et al.

While task-specific demonstrations show early success in applying large language models (LLMs) to automate some astronomical research tasks, they only provide incomplete views of all necessary capabilities in solving astronomy problems, calling for more thorough understanding of LLMs' strengths and limitations. So far, existing benchmarks and evaluations focus on simple question-answering that primarily tests astronomical knowledge and fails to evaluate the complex reasoning required for real-world research in the discipline. Here, we address this gap by systematically benchmarking five state-of-the-art LLMs on the International Olympiad on Astronomy and Astrophysics (IOAA) exams, which are designed to examine deep conceptual understanding, multi-step derivations, and multimodal analysis. With average scores of 85.6% and 84.2%, Gemini 2.5 Pro and GPT-5 (the two top-performing models) not only achieve gold medal level performance but also rank in the top two among ~200-300 participants in all four IOAA theory exams evaluated (2022-2025). In comparison, results on the data analysis exams show more divergence. GPT-5 still excels in the exams with an 88.5% average score, ranking top 10 among the participants in the four most recent IOAAs, while other models' performances drop to 48-76%. Furthermore, our in-depth error analysis underscores conceptual reasoning, geometric reasoning, and spatial visualization (52-79% accuracy) as consistent weaknesses among all LLMs. Hence, although LLMs approach peak human performance in theory exams, critical gaps must be addressed before they can serve as autonomous research agents in astronomy.