DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.Comment: 10 pages, 11 Figure

Transfer and Multi-Task Learning for Noun-Noun Compound Interpretation

In this paper, we empirically evaluate the utility of transfer and multi-task learning on a challenging semantic classification task: semantic interpretation of noun--noun compounds. Through a comprehensive series of experiments and in-depth error analysis, we show that transfer learning via parameter initialization and multi-task learning via parameter sharing can help a neural classification model generalize over a highly skewed distribution of relations. Further, we demonstrate how dual annotation with two distinct sets of relations over the same set of compounds can be exploited to improve the overall accuracy of a neural classifier and its F1 scores on the less frequent, but more difficult relations.Comment: EMNLP 2018: Conference on Empirical Methods in Natural Language Processing (EMNLP

Developmental disorders

Introduction: Connectionist models have recently provided a concrete computational platform from which to explore how different initial constraints in the cognitive system can interact with an environment to generate the behaviors we find in normal development (Elman et al., 1996; Mareschal & Thomas, 2000). In this sense, networks embody several principles inherent to Piagetian theory, the major developmental theory of the twentieth century. By extension, these models provide the opportunity to explore how shifts in these initial constraints (or boundary conditions) can result in the emergence of the abnormal behaviors we find in atypical development. Although this field is very new, connectionist models have already been put forward to explain disordered language development in Specific Language Impairment (Hoeffner & McClelland, 1993), Williams Syndrome (Thomas & Karmiloff-Smith, 1999), and developmental dyslexia (Seidenberg and colleagues, see e.g. Harm & Seidenberg, in press); to explain unusual characteristics of perceptual discrimination in autism (Cohen, 1994; Gustafsson, 1997); and to explore the emergence of disordered cortical feature maps using a neurobiologically constrained model (Oliver, Johnson, Karmiloff-Smith, & Pennington, in press). In this entry, we will examine the types of initial constraints that connectionist modelers typically build in to their models, and how variations in these constraints have been proposed as possible accounts of the causes of particular developmental disorders. In particular, we will examine the claim that these constraints are candidates for what will constitute innate knowledge. First, however, we need to consider a current debate concerning whether developmental disorders are a useful tool to explore the (possibly innate) structure of the normal cognitive system. We will find that connectionist approaches are much more consistent with one side of this debate than the other

A dual framework for low-rank tensor completion

One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a variant of the latent trace norm that helps in learning a non-sparse combination of tensors. We develop a dual framework for solving the low-rank tensor completion problem. We first show a novel characterization of the dual solution space with an interesting factorization of the optimal solution. Overall, the optimal solution is shown to lie on a Cartesian product of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian optimization framework for proposing computationally efficient trust region algorithm. The experiments illustrate the efficacy of the proposed algorithm on several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on Synergies in Geometric Data Analysis 201