The architecture of Transformer is based entirely on self-attention, and has been shown to outperform models that employ recurrence on sequence transduction tasks such as machine translation. The superior performance of Transformer has been attributed to propagating signals over shorter distances, between positions in the input and the output, compared to the recurrent architectures. We establish connections between the dynamics in Transformer and recurrent networks to argue that several factors including gradient flow along an ensemble of multiple weakly dependent paths play a paramount role in the success of Transformer. We then leverage the dynamics to introduce {\em Multiresolution Transformer Networks} as the first architecture that exploits hierarchical structure in data via self-attention. Our models significantly outperform state-of-the-art recurrent and hierarchical recurrent models on two real-world datasets for query suggestion, namely, \aol and \amazon. In particular, on AOL data, our model registers at least 20\% improvement on each precision score, and over 25\% improvement on the BLEU score with respect to the best performing recurrent model. We thus provide strong evidence that recurrence is not essential for modeling hierarchical structure.
University of Chicago（芝加哥大学）；CSAIL, MIT（麻省理工学院计算机科学与人工智能实验室）；Flatiron Institute（弗莱提荣研究所）
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA), MMF teased out hierarchical structure in symmetric matrices by constructing a sequence of wavelet bases. While effective for such matrices, there is plenty of data that is more naturally represented as nonsymmetric matrices (e.g. directed graphs), but nevertheless has similar hierarchical structure. In this paper, we explore techniques for extending MMF to a…
In this paper, we propose Multiresolution Equivariant Graph Variational Autoencoders (MGVAE), the first hierarchical generative model to learn and generate graphs in a multiresolution and equivariant manner. At each resolution level, MGVAE employs higher order message passing to encode the graph while learning to partition it into mutually exclusive clusters and coarsening into a lower resolution that eventually creates a hierarchy of latent distributions. MGVAE then constructs a hierarchical generative model to variationally decode into a hierarchy of coarsened graphs. Importantly, our propos…
Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structures
FPT Software AI Center（FPT软件人工智能中心）；Halıcıoğlu Data Science Institute, University of California San Diego（加州大学圣地亚哥分校哈利哲奥卢数据科学研究所）；University of Chicago（芝加哥大学）
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex multiscale or hierarchical strucutre. While MMF promises to yields a useful wavelet basis, finding the factorization itself is hard, and existing greedy methods tend to be brittle. In this paper we propose a learnable version of MMF that carfully optimizes the factorization with a combination of reinforcement learning and Stiefel manifold optimization through back…
The University of Sydney（悉尼大学）；Zhejiang Normal University（浙江师范大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学与自然科学研究所）；University of New South Wales（新南威尔士大学）
Graph Neural Networks (GNNs) have recently caught great attention and achieved significant progress in graph-level applications. In this paper, we propose a framework for graph neural networks with multiresolution Haar-like wavelets, or MathNet, with interrelated convolution and pooling strategies. The underlying method takes graphs in different structures as input and assembles consistent graph representations for readout layers, which then accomplishes label prediction. To achieve this, the multiresolution graph representations are first constructed and fed into graph convolutional layers fo…
University of Washington（华盛顿大学）；Lawrence Livermore National Lab（劳伦斯利弗莫尔国家实验室）
We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a…
Graph Hierarchical Recurrence for Long-Range Generalization
Department of Computer Science, University of Trento（特伦托大学计算机科学系）；Fondazione Bruno Kessler（布鲁诺·克谢勒基金会）；Department of Computer Science, University of Pisa（帕尔马大学计算机科学系）
The American University in Cairo (AUC)（开罗美国大学）；Microsoft Egypt Development Center (EGDC)（微软埃及开发中心）
We propose a novel architecture for labelling character sequences that achieves state-of-the-art results on the Tashkeela Arabic diacritization benchmark. The core is a two-level recurrence hierarchy that operates on the word and character levels separately---enabling faster training and inference than comparable traditional models. A cross-level attention module further connects the two, and opens the door for network interpretability. The task module is a softmax classifier that enumerates valid combinations of diacritics. This architecture can be extended with a recurrent decoder that optio…
It is widely believed that deep neural networks contain layer specialization, wherein neural networks extract hierarchical features representing edges and patterns in shallow layers and complete objects in deeper layers. Unlike common feed-forward models that have distinct filters at each layer, recurrent networks reuse the same parameters at various depths. In this work, we observe that recurrent models exhibit the same hierarchical behaviors and the same performance benefits with depth as feed-forward networks despite reusing the same filters at every recurrence. By training models of variou…
University of British Columbia（不列颠哥伦比亚大学）；McGill University（麦吉尔大学）；Mila
While using invariant and equivariant maps, it is possible to apply deep learning to a range of primitive data structures, a formalism for dealing with hierarchy is lacking. This is a significant issue because many practical structures are hierarchies of simple building blocks; some examples include sequences of sets, graphs of graphs, or multiresolution images. Observing that the symmetry of a hierarchical structure is the "wreath product" of symmetries of the building blocks, we express the equivariant map for the hierarchy using an intuitive combination of the equivariant linear layers of t…
University of Maryland（马里兰大学）；Institute for Adv. Computer Studies（高级计算机研究所）
Deep Reservoir Computing has emerged as a new paradigm for deep learning, which is based around the reservoir computing principle of maintaining random pools of neurons combined with hierarchical deep learning. The reservoir paradigm reflects and respects the high degree of recurrence in biological brains, and the role that neuronal dynamics play in learning. However, one issue hampering deep reservoir network development is that one cannot backpropagate through the reservoir layers. Recent deep reservoir architectures do not learn hidden or hierarchical representations in the same manner as d…
This paper presents our pioneering effort for emotion recognition in conversation (ERC) with pre-trained language models. Unlike regular documents, conversational utterances appear alternately from different parties and are usually organized as hierarchical structures in previous work. Such structures are not conducive to the application of pre-trained language models such as XLNet. To address this issue, we propose an all-in-one XLNet model, namely DialogXL, with enhanced memory to store longer historical context and dialog-aware self-attention to deal with the multi-party structures. Specifi…
