Federated learning (FL) over heterogeneous IoT edge devices faces coupled system-modality-data heterogeneity: the lower-cost device carries both fewer sensors and less computational power, so the slowest device (straggler) produces the most incomplete gradient signals. Naively averaging their updates dilutes rare-modality information and wastes computation on absent-sensor parameters, whereas existing methods handle the triple heterogeneity (system, modality, data) in isolation and none addresses their coupling. To resolve this issue, we propose RELIEF, a framework that partitions the fusion-layer Low-Rank Adaptation (LoRA) projection matrix into modality-aligned column blocks and uses this partition as a unified interface for aggregation, elastic training, and communication. Each block is aggregated only within the cohort of devices possessing that modality, which eliminates cross-modal gradient interference; the server then allocates personalized training budgets by prioritizing blocks with the highest cohort-internal divergence, so that resource-constrained devices train fewer but more impactful parameters. We prove that cohort-wise aggregation removes interference from the convergence bound and that the divergence-guided allocation achieves sublinear regret. Experiments on two IoT sensor datasets (PAMAP2, MHEALTH) under both full-parameter (CNN) and parameter-efficient (LoRA) training show that RELIEF achieves up to 9.41x speedup and 37% energy reduction over FedAvg with up to 15.3 pp rare-modality F1 gains, and real-device validation on a two-Jetson AGX Orin testbed confirms these results.

翻译：联邦学习在异质物联网边缘设备上面临着系统-模态-数据的耦合异质性：低成本设备同时配备更少的传感器和更低的计算能力，因此最慢设备（掉队者）产生的梯度信号最不完整。简单平均其更新会稀释稀有模态信息，并在缺失传感器参数上浪费计算资源，而现有方法孤立地处理三重异质性（系统、模态、数据），且没有一种方法能解决其耦合问题。为解决该问题，我们提出RELIEF框架，该框架将融合层低秩自适应（LoRA）投影矩阵划分为模态对齐的列块，并将此划分作为聚合、弹性训练与通信的统一接口。每个列块仅在拥有该模态的设备群组内进行聚合，从而消除跨模态梯度干扰；随后服务器通过优先分配具有最高群组内差异度的列块的个性化训练预算，使资源受限设备训练更少但更具影响力的参数。我们证明了群组级聚合可消除收敛界中的干扰，且差异度引导的预算分配可实现次线性遗憾。在两个物联网传感器数据集（PAMAP2、MHEALTH）上进行的全参数（CNN）与参数高效（LoRA）训练实验表明：与FedAvg相比，RELIEF实现了最高9.41倍的加速比和37%的能耗降低，稀有模态F1分数提升高达15.3个百分点，且在双Jetson AGX Orin测试平台上的真实设备验证证实了这些结果。