Machine systems inherently generate signals in which fault conditions and various variables influence signals measured from machine system. Although many existing fault classification studies rely solely on direct fault labels, the aforementioned signals naturally embed additional information shaped by other variables. Herein, we leverage this through a multi-task learning (MTL) framework that jointly learns fault conditions and other variables influencing measured signals. Among MTL architectures, cross-talk 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 system influenced by multiple variables. 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 drone status. The second benchmark dataset is motor compound fault dataset. In this system, severity of each fault component, inner race fault, outer race fault, misalignment, and unbalance influences measured signal. 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.