Many loss functions in representation learning are invariant under a continuous symmetry transformation. For example, the loss function of word embeddings (Mikolov et al., 2013) remains unchanged if we simultaneously rotate all word and context embedding vectors. We show that representation learning models for time series possess an approximate continuous symmetry that leads to slow convergence of gradient descent. We propose a new optimization algorithm that speeds up convergence using ideas from gauge theory in physics. Our algorithm leads to orders of magnitude faster convergence and to more interpretable representations, as we show for dynamic extensions of matrix factorization and word embedding models. We further present an example application of our proposed algorithm that translates modern words into their historic equivalents.

A simple framework Probabilistic Multi-view Graph Embedding (PMvGE) is proposed for multi-view feature learning with many-to-many associations so that it generalizes various existing multi-view methods. PMvGE is a probabilistic model for predicting new associations via graph embedding of the nodes of data vectors with links of their associations. Multi-view data vectors with many-to-many associations are transformed by neural networks to feature vectors in a shared space, and the probability of new association between two data vectors is modeled by the inner product of their feature vectors. While existing multi-view feature learning techniques can treat only either of many-to-many association or non-linear transformation, PMvGE can treat both simultaneously. By combining Mercer's theorem and the universal approximation theorem, we prove that PMvGE learns a wide class of similarity measures across views. Our likelihood-based estimator enables efficient computation of non-linear transformations of data vectors in large-scale datasets by minibatch SGD, and numerical experiments illustrate that PMvGE outperforms existing multi-view methods.

Many graph analytics problems can be solved via iterative algorithms where the solutions are often characterized by a set of steady-state conditions. Different algorithms respect to different set of fixed point constraints, so instead of using these traditional algorithms, can we learn an algorithm which can obtain the same steady-state solutions automatically from examples, in an effective and scalable way? How to represent the meta learner for such algorithm and how to carry out the learning? In this paper, we propose an embedding representation for iterative algorithms over graphs, and design a learning method which alternates between updating the embeddings and projecting them onto the steady-state constraints. We demonstrate the effectiveness of our framework using a few commonly used graph algorithms, and show that in some cases, the learned algorithm can handle graphs with more than 100,000,000 nodes in a single machine.

The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original problem of network representation in task-agnostic manner. Here, we coherently propose an approach for embedding entire graphs and show that our feature representations with SVM classifier increase classification accuracy of CNN algorithms and traditional graph kernels. For this we describe a recently discovered graph object, \textit{anonymous walk}, on which we design task-independent algorithms for learning graph representations in explicit and distributed way. Overall, our work represents a new scalable unsupervised learning of state-of-the-art representations of entire graphs.