Related papers: Low-dimensional Embeddings for Interpretable Ancho…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

Deep learning algorithms have recently gained significant attention due to their impressive performance. However, their high complexity and un-interpretable mode of operation hinders their confident deployment in real-world safety-critical…

We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the "local…

There are two main approaches to the distributed representation of words: low-dimensional deep learning embeddings and high-dimensional distributional models, in which each dimension corresponds to a context word. In this paper, we combine…

End-to-end acoustic-to-word speech recognition models have recently gained popularity because they are easy to train, scale well to large amounts of training data, and do not require a lexicon. In addition, word models may also be easier to…

Word embeddings are a popular way to improve downstream performances in contemporary language modeling. However, the underlying geometric structure of the embedding space is not well understood. We present a series of explorations using…

An incremental approach for computation of convex hull for data points in two-dimensions is presented. The algorithm is not output-sensitive and costs a time that is linear in the size of data points at input. Graham's scan is applied only…

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…

This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…

Previous researches have shown that learning multiple representations for polysemous words can improve the performance of word embeddings on many tasks. However, this leads to another problem. Several vectors of a word may actually point to…

The focus of past machine learning research for Reading Comprehension tasks has been primarily on the design of novel deep learning architectures. Here we show that seemingly minor choices made on (1) the use of pre-trained word embeddings,…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

One of the long-standing challenges in lexical semantics consists in learning representations of words which reflect their semantic properties. The remarkable success of word embeddings for this purpose suggests that high-quality…

We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the…

Network embeddings, which learn low-dimensional representations for each vertex in a large-scale network, have received considerable attention in recent years. For a wide range of applications, vertices in a network are typically…

Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…

Many words have evolved in meaning as a result of cultural and social change. Understanding such changes is crucial for modelling language and cultural evolution. Low-dimensional embedding methods have shown promise in detecting words'…

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…

Social network alignment aims at aligning person identities across social networks. Embedding based models have been shown effective for the alignment where the structural proximity preserving objective is typically adopted for the model…

The words of a language reflect the structure of the human mind, allowing us to transmit thoughts between individuals. However, language can represent only a subset of our rich and detailed cognitive architecture. Here, we ask what kinds of…