  Despite the remarkable success of deep multi-modal learning in practice, it
has not been well-explained in theory. Recently, it has been observed that the
best uni-modal network outperforms the jointly trained multi-modal network,
which is counter-intuitive since multiple signals generally bring more
information. This work provides a theoretical explanation for the emergence of
such performance gap in neural networks for the prevalent joint training
framework. Based on a simplified data distribution that captures the realistic
property of multi-modal data, we prove that for the multi-modal late-fusion
network with (smoothed) ReLU activation trained jointly by gradient descent,
different modalities will compete with each other. The encoder networks will
learn only a subset of modalities. We refer to this phenomenon as modality
competition. The losing modalities, which fail to be discovered, are the
origins where the sub-optimality of joint training comes from. Experimentally,
we illustrate that modality competition matches the intrinsic behavior of
late-fusion joint training.
