Graph Out-of-Distribution (OOD) classification often suffers from sharp performance drops, particularly under category imbalance and structural noise. This work tackles two pressing challenges in this context: (1) the underperformance of minority classes due to skewed label distributions, and (2) their heightened sensitivity to structural noise in graph data. To address these problems, we propose two complementary solutions. First, Constrained Mean Optimization (CMO) improves minority class robustness by encouraging similarity-based instance aggregation under worst-case conditions. Second, the Neighbor-Aware Noise Reweighting (NNR) mechanism assigns dynamic weights to training samples based on local structural consistency, mitigating noise influence. We provide theoretical justification for our methods, and validate their effectiveness with extensive experiments on both synthetic and real-world datasets, showing significant improvements in Graph OOD generalization and classification accuracy. The code for our method is available at: https://anonymous.4open.science/r/CMO-NNR-2F30.

Federated learning (FL) is a promising paradigm to enable collaborative model training with decentralized data. However, the training process of Large Language Models (LLMs) generally incurs the update of significant parameters, which limits the applicability of FL techniques to tackle the LLMs in real scenarios. Prompt tuning can significantly reduce the number of parameters to update, but it either incurs performance degradation or low training efficiency. The straightforward utilization of prompt tuning in the FL often raises non-trivial communication costs and dramatically degrades performance. In addition, the decentralized data is generally non-Independent and Identically Distributed (non-IID), which brings client drift problems and thus poor performance. This paper proposes a Parameter-efficient prompt Tuning approach with Adaptive Optimization, i.e., FedPepTAO, to enable efficient and effective FL of LLMs. First, an efficient partial prompt tuning approach is proposed to improve performance and efficiency simultaneously. Second, a novel adaptive optimization method is developed to address the client drift problems on both the device and server sides to enhance performance further. Extensive experiments based on 10 datasets demonstrate the superb performance (up to 60.8\% in terms of accuracy) and efficiency (up to 97.59\% in terms of training time) of FedPepTAO compared with 9 baseline approaches. Our code is available at https://github.com/llm-eff/FedPepTAO.