用费舍尔信息矩阵实现参数级聚合，提升异构数据下的联邦学习效果。
Fisher-Informed Parameterwise Aggregation for Federated Learning with Heterogeneous Data
- 基于费舍尔信息矩阵为每个参数分配独立权重，实现精准参数级聚合。
- 在非独立同分布数据下，相比平均法显著减少客户端漂移，提升模型精度。
- 低秩近似保持高效性，适合实际联邦学习场景，尤其适用于图像分类任务。
联邦学习在分布式客户端间聚合模型更新，但标准的一阶方法（如FedAvg）对所有参数使用相同的标量权重。在非独立同分布（non-IID）数据下，这种统一加权方式会导致客户端间更新严重错位，引发客户端漂移并降低全局模型性能。本文提出费舍尔信息引导的参数级聚合（FIPA），将客户端级别的标量权重替换为参数特定的费舍尔信息矩阵（FIM）权重，实现真正意义上的参数级缩放，捕捉不同客户端数据对各参数的独特影响。通过低秩近似，FIPA保持通信与计算效率。在非线性函数回归、偏微分方程学习和图像分类任务中，FIPA均持续优于基于平均的聚合方法，并可与当前先进的客户端优化算法结合，进一步提升图像分类准确率。结果表明，FIPA在异构数据分布下具有显著优势。
原文摘要 · Abstract (English)
Federated learning aggregates model updates from distributed clients, but standard first order methods such as FedAvg apply the same scalar weight to all parameters from each client. Under non-IID data, these uniformly weighted updates can be strongly misaligned across clients, causing client drift and degrading the global model. Here we propose Fisher-Informed Parameterwise Aggregation (FIPA), a second-order aggregation method that replaces client-level scalar weights with parameter-specific Fisher Information Matrix (FIM) weights, enabling true parameter-level scaling that captures how each client's data uniquely influences different parameters. With low-rank approximation, FIPA remains communication- and computation-efficient. Across nonlinear function regression, PDE learning, and image classification, FIPA consistently improves over averaging-based aggregation, and can be effectively combined with state-of-the-art client-side optimization algorithms to further improve image classification accuracy. These results highlight the benefits of FIPA for federated learning under heterogeneous data distributions.
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