提出细粒度信任机制，让联邦学习客户端按例判断是否信任他人预测。

Data heterogeneity poses a fundamental challenge in federated learning (FL), especially when clients differ not only in distribution but also in the reliability of their predictions across individual examples. While personalized FL (PFL) aims to address this, we observe that many PFL methods fail to outperform two necessary baselines, local training and centralized training. This suggests that meaningful personalization only emerges in a narrow regime, where global models are insufficient, but collaboration across clients still holds value. Our empirical findings point to two key ingredients for success in this regime: adaptivity in collaboration and fine-grained trust, at the level of individual examples. We show that these properties can be achieved within federated semi-supervised learning, where clients exchange predictions over a shared unlabeled dataset. This enables each client to align with public consensus when it is helpful, and disregard it when it is not, without sharing model parameters or raw data. As a concrete realization of this idea, we develop FEDMOSAIC, a personalized co-training method where clients reweight their loss and their contribution to pseudo-labels based on per-example agreement and confidence. FEDMOSAIC outperforms strong FL and PFL baselines across a range of non-IID settings, and we prove convergence under standard smoothness, bounded-variance, and drift assumptions. In contrast to many of these baselines, it also outperforms local and centralized training. These results clarify when federated personalization can be effective, and how fine-grained, trust-aware collaboration enables it.