Multi-directional Geodesic Neural Networks via Equivariant Convolution

We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the surface, which extend the classic real-valued signals and which can be naturally convolved with with real-valued template functions. As a result, rather than trying to fix a canonical orientation or only keeping the maximal response across all alignments of a 2D template at every point of the surface, as done in previous works, we show how information across all rotations can be kept across different layers of the neural network. Our construction, which we call multi-directional geodesic convolution, or directional convolution for short, allows, in particular, to propagate and relate directional information across layers and thus different regions on the shape. We first define directional convolution in the continuous setting, prove its key properties and then show how it can be implemented in practice, for shapes represented as triangle meshes. We evaluate directional convolution in a wide variety of learning scenarios ranging from classification of signals on surfaces, to shape segmentation and shape matching, where we show a significant improvement over several baselines

Learning SO(3) Equivariant Representations with Spherical CNNs

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio

Explicit Interaction Model towards Text Classification

Text classification is one of the fundamental tasks in natural language processing. Recently, deep neural networks have achieved promising performance in the text classification task compared to shallow models. Despite of the significance of deep models, they ignore the fine-grained (matching signals between words and classes) classification clues since their classifications mainly rely on the text-level representations. To address this problem, we introduce the interaction mechanism to incorporate word-level matching signals into the text classification task. In particular, we design a novel framework, EXplicit interAction Model (dubbed as EXAM), equipped with the interaction mechanism. We justified the proposed approach on several benchmark datasets including both multi-label and multi-class text classification tasks. Extensive experimental results demonstrate the superiority of the proposed method. As a byproduct, we have released the codes and parameter settings to facilitate other researches.Comment: 8 page