Data-Free Contribution Estimation in Federated Learning using Gradient von Neumann Entropy

arXiv cs.AI / 4/27/2026

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Key Points

The paper proposes a privacy-preserving, data-free way to estimate each client’s contribution in federated learning using the matrix (spectral) von Neumann entropy of final-layer update signals.
It introduces two practical aggregation/combination schemes, SpectralFed (entropy-based aggregation weights) and SpectralFuse (entropy plus class-specific alignment using a rank-adaptive Kalman filter) to improve per-round stability.
Experiments on CIFAR-10/100 and naturally partitioned FEMNIST and FedISIC under diverse non-IID settings show high correlation between the entropy-derived contribution scores and standalone client accuracy without using validation data or client metadata.
The method is benchmarked against existing data-free contribution estimation baselines, supporting spectral entropy as a useful indicator for fair client importance and reward assignment.
Overall, the approach aims to remove reliance on server-side validation datasets or potentially manipulable self-reported client information.

Abstract

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.