Machine systems inherently generate signals in which fault conditions and various physical variables are physically coupled. Although many existing fault classification studies rely solely on direct fault labels, the aforementioned signals naturally embed additional information shaped by other physically coupled information. Herein, we leverage this coupling through a multi-task learning (MTL) framework that jointly learns fault conditions and the related physical variables. Among MTL architectures, crosstalk structures have distinct advantages because they allow for controlled information exchange between tasks through the cross-talk layer while preventing negative transfer, in contrast to shared trunk architectures that often mix incompatible features. We build on our previously introduced residual neural dimension reductor model, and extend its application to two benchmarks where physical coupling is prominent. The first benchmark is a drone fault dataset, in which machine type and maneuvering direction significantly alter the frequency components of measured signals even under the same nominal condition. By learning fault classification together with these physical attributes, the cross-talk architecture can better classify faults. The second benchmark dataset is the motor compound fault dataset. In this system, each fault component, inner race fault, outer race fault, misalignment, and unbalance is coupled to the other. For motor compound fault, we also test classification performance when we use single-channel data or multi-channel data as input to the classifier. Across both benchmarks, our residual neural dimension reductor, consistently outperformed single-task models, multi-class models that merge all label combinations, and shared trunk multi-task models.