Abstract:We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The Hermitian structure of the Kähler manifold is explicitly emergent if and only if the impulse response function of the highest degree in z is constant in model parameters. The Kählerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, α-generalization on the geometric tensors is linear in α. It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace-Beltrami operators on Kähler manifolds are in much simpler forms than those of the non-Kähler manifolds. Several time series models are studied in the Kählerian information geometry.

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The goal of multi-modal learning is to use complimentary information on the relevant task provided by the multiple modalities to achieve reliable and robust performance. Recently, deep learning has led significant improvement in multi-modal learning by allowing for fusing high level features obtained at intermediate layers of the deep neural network. This paper addresses a problem of designing robust deep multimodal learning architecture in the presence of the modalities degraded in quality. We introduce deep fusion architecture for object detection which processes each modality using the separate convolutional neural network (CNN) and constructs the joint feature maps by combining the intermediate features obtained by the CNNs. In order to facilitate the robustness to the degraded modalities, we employ the gated information fusion (GIF) network which weights the contribution from each modality according to the input feature maps to be fused. The combining weights are determined by applying the convolutional layers followed by the sigmoid function to the concatenated intermediate feature maps. The whole network including the CNN backbone and GIF is trained in an end-toend fashion. Our experiments show that the proposed GIF network offers the additional architectural flexibility to achieve the robust performance in handling some degraded modalities.