Conflicting objectives present a considerable challenge in interleaving multi-task learning, necessitating the need for meticulous design and balance to ensure effective learning of a representative latent data space across all tasks without mutual negative impact. Drawing inspiration from the concept of marginal and conditional probability distributions in probability theory, we design a principled and well-founded approach to disentangle the original input into marginal and conditional probability distributions in the latent space of a variational autoencoder. Our proposed model, Deep Disentangled Interleaving Variational Encoding (DeepDIVE) learns disentangled features from the original input to form clusters in the embedding space and unifies these features via the cross-attention mechanism in the fusion stage. We theoretically prove that combining the objectives for reconstruction and forecasting fully captures the lower bound and mathematically derive a loss function for disentanglement using Na\"ive Bayes. Under the assumption that the prior is a mixture of log-concave distributions, we also establish that the Kullback-Leibler divergence between the prior and the posterior is upper bounded by a function minimized by the minimizer of the cross entropy loss, informing our adoption of radial basis functions (RBF) and cross entropy with interleaving training for DeepDIVE to provide a justified basis for convergence. Experiments on two public datasets show that DeepDIVE disentangles the original input and yields forecast accuracies better than the original VAE and comparable to existing state-of-the-art baselines.

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