Multimodal learning robust to missing modality has attracted increasing attention due to its practicality. Existing methods tend to address it by learning a common subspace representation for different modality combinations. However, we reveal that they are sub-optimal due to their implicit constraint on intra-class representation. Specifically, the sample with different modalities within the same class will be forced to learn representations in the same direction. This hinders the model from capturing modality-specific information, resulting in insufficient learning. To this end, we propose a novel Decoupled Multimodal Representation Network (DMRNet) to assist robust multimodal learning. Specifically, DMRNet models the input from different modality combinations as a probabilistic distribution instead of a fixed point in the latent space, and samples embeddings from the distribution for the prediction module to calculate the task loss. As a result, the direction constraint from the loss minimization is blocked by the sampled representation. This relaxes the constraint on the inference representation and enables the model to capture the specific information for different modality combinations. Furthermore, we introduce a hard combination regularizer to prevent DMRNet from unbalanced training by guiding it to pay more attention to hard modality combinations. Finally, extensive experiments on multimodal classification and segmentation tasks demonstrate that the proposed DMRNet outperforms the state-of-the-art significantly.

In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a single hidden layer. The transformations of both deep rectifier nets and deep residual nets are conducted to demonstrate the advantages of the residual nets over the conventional neural nets and the advantages of the deep neural nets over the shallow neural nets. In summary, for two rectifier nets with different depths but with same total number of hidden units, the corresponding single hidden layer representation of the deeper net is much more complex than the corresponding single hidden representation of the shallower net. Similarly, for a residual net and a conventional rectifier net with the same structure except for the skip connections in the residual net, the corresponding single hidden layer representation of the residual net is much more complex than the corresponding single hidden layer representation of the conventional net.