Dual encoders perform retrieval by encoding documents and queries into dense low-
dimensional vectors, scoring each document by its inner product with the query. We …

Dimensionality reduction is standard practice for filtering noise and identifying relevant
features in large-scale data analyses. In biology, single-cell genomics studies typically begin …

Given a matrix $ A\in\mathbb {R}^{n\times d} $ and a vector $ b\in\mathbb {R}^ n $, we
consider the regression problem with $\ell_\infty $ guarantees: finding a vector …

Given a metric space, the (k, z)-clustering problem consists of finding k centers such that the
sum of the of distances raised to the power z of every point to its closest center is minimized …

Consider an instance of Euclidean k-means or k-medians clustering. We show that the cost
of the optimal solution is preserved up to a factor of (1+ ε) under a projection onto a random …

The (k, z)-clustering problem consists of finding a set of k points called centers, such that the
sum of distances raised to the power of z of every data point to its closest center is …

We analyze neural ordinary differential equations (NODEs) from a control theoretical
perspective to address some of the main properties and paradigms of deep learning (DL), in …

Modern datasets and models are notoriously difficult to explore and analyze due to their
inherent high dimensionality and massive numbers of samples. Existing visualization …

The slow convergence rate and pathological curvature issues of first-order gradient methods
for training deep neural networks, initiated an ongoing effort for developing faster $\mathit …

Modern datasets and models are notoriously difficult to explore and analyze due to their
inherent high dimensionality and massive numbers of samples. Existing visualization …