Client contribution estimation in Federated Learning is necessary for identifying clients' importance and for providing fair rewards. Current methods often rely on server-side validation data or self-reported client information, which can compromise privacy or be susceptible to manipulation. We introduce a data-free signal based on the matrix von Neumann (spectral) entropy of the final-layer updates, which measures the diversity of the information contributed. We instantiate two practical schemes: (i) SpectralFed, which uses normalized entropy as aggregation weights, and (ii) SpectralFuse, which fuses entropy with class-specific alignment via a rank-adaptive Kalman filter for per-round stability. Across CIFAR-10/100 and the naturally partitioned FEMNIST and FedISIC benchmarks, entropy-derived scores show a consistently high correlation with standalone client accuracy under diverse non-IID regimes - without validation data or client metadata. We compare our results with data-free contribution estimation baselines and show that spectral entropy serves as a useful indicator of client contribution.

翻译：联邦学习中的客户端贡献估计对于识别客户端重要性和提供公平奖励至关重要。现有方法通常依赖服务器端验证数据或客户端自报信息，这可能会损害隐私或易受操纵。我们提出了一种基于矩阵冯·诺依曼（谱）熵的无数据信号，该熵测量最终层更新中信息贡献的多样性。我们实例化了两种实用方案：（i）SpectralFed，使用归一化熵作为聚合权重；（ii）SpectralFuse，通过秩自适应卡尔曼滤波器将熵与类别特定对齐融合，以实现每轮稳定性。在CIFAR-10/100以及自然分区的FEMNIST和FedISIC基准测试中，熵导出的分数在不同非独立同分布环境下与独立客户端准确率始终呈现高度相关性，无需验证数据或客户端元数据。我们将结果与无数据贡献估计基线进行比较，表明谱熵可作为客户端贡献的有效指标。