What Makes Multimodal Learning Better than Single (Provably)

The world provides us with data of multiple modalities. Intuitively, models fusingdata from different modalities outperform unimodal models, since more informationis aggregated. Recently, joining the success of deep learning, there is an influentialline of work on deep multimodal learning, which has remarkable empirical resultson various applications. However, theoretical justifications in this field are notablylacking.Can multimodal provably perform better than unimodal? In this paper, we answer this question under a most popular multimodal learningframework, which firstly encodes features from different modalities into a commonlatent space and seamlessly maps the latent representations into the task space. Weprove that learning with multiple modalities achieves a smaller population risk thanonly using its subset of modalities. The main intuition is that the former has moreaccurate estimate of the latent space representation. To the best of our knowledge,this is the first theoretical treatment to capture important qualitative phenomenaobserved in real multimodal applications. Combining with experiment results, weshow that multimodal learning does possess an appealing formal guarantee.