  Multimodal representation learning is gaining more and more interest within
the deep learning community. While bilinear models provide an interesting
framework to find subtle combination of modalities, their number of parameters
grows quadratically with the input dimensions, making their practical
implementation within classical deep learning pipelines challenging. In this
paper, we introduce BLOCK, a new multimodal fusion based on the
block-superdiagonal tensor decomposition. It leverages the notion of block-term
ranks, which generalizes both concepts of rank and mode ranks for tensors,
already used for multimodal fusion. It allows to define new ways for optimizing
the tradeoff between the expressiveness and complexity of the fusion model, and
is able to represent very fine interactions between modalities while
maintaining powerful mono-modal representations. We demonstrate the practical
interest of our fusion model by using BLOCK for two challenging tasks: Visual
Question Answering (VQA) and Visual Relationship Detection (VRD), where we
design end-to-end learnable architectures for representing relevant
interactions between modalities. Through extensive experiments, we show that
BLOCK compares favorably with respect to state-of-the-art multimodal fusion
models for both VQA and VRD tasks. Our code is available at
https://github.com/Cadene/block.bootstrap.pytorch.
