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In multi-dimensional classification (MDC), the semantics of objects are characterized by multiple class variables from different dimensions. Existing MDC approaches focus on designing effective class dependency modeling strategies to enhance classification performance. However, the intercoupling of multiple class variables poses a significant challenge to the precise modeling of class dependencies. In this paper, we make the first attempt towards escaping from class dependency modeling for addressing MDC problems. Accordingly, a novel MDC approach named DCOM is proposed by decoupling the interactions of different dimensions in MDC. Specifically, DCOM endeavors to identify a latent factor that encapsulates the most salient and critical feature information. This factor will facilitate partial conditional independence among class variables conditioned on both the original feature vector and the learned latent embedding. Once the conditional independence is established, classification models can be readily induced by employing simple neural networks on each dimension. Extensive experiments conducted on benchmark data sets demonstrate that DCOM outperforms other state-of-the-art MDC approaches.