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We deal with the problem of learning the underlying disentangled latentfactors that are shared between the paired bi-modal data in cross-modalretrieval. Our assumption is that the data in both modalities are complex,structured, and high dimensional (e.g., image and text), for which theconventional deep auto-encoding latent variable models such as the VariationalAutoencoder (VAE) often suffer from difficulty of accurate decoder training orrealistic synthesis. A suboptimally trained decoder can potentially harm themodel's capability of identifying the true factors. In this paper we propose anovel idea of the implicit decoder, which completely removes the ambient datadecoding module from a latent variable model, via implicit encoder inversionthat is achieved by Jacobian regularization of the low-dimensional embeddingfunction. Motivated from the recent Identifiable VAE (IVAE) model, we modify itto incorporate the query modality data as conditioning auxiliary input, whichallows us to prove that the true parameters of the model can be identifiedunder some regularity conditions. Tested on various datasets where the truefactors are fully/partially available, our model is shown to identify thefactors accurately, significantly outperforming conventional encoder-decoderlatent variable models. We also test our model on the Recipe1M, the large-scalefood image/recipe dataset, where the learned factors by our approach highlycoincide with the most pronounced food factors that are widely agreed on,including savoriness, wateriness, and greenness.

Learning Disentangled Latent Factors from Paired Data in Cross-Modal Retrieval: An Implicit Identifiable VAE Approach