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In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We show that selecting a single data type (precision) for all values in Deep Neural Networks, even if that data type is different per layer, amounts to worst case design. Much shorter data types can be used if we target the common case by…
Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large…
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
The growing demands of distributed learning on resource constrained edge devices underscore the importance of efficient on device model compression. Tensor Train Decomposition (TTD) offers high compression ratios with minimal accuracy loss,…
We consider escaping saddle points of nonconvex problems where only the function evaluations can be accessed. Although a variety of works have been proposed, the majority of them require either second or first-order information, and only a…
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…
End-to-end image and video compression using auto-encoders (AE) offers new appealing perspectives in terms of rate-distortion gains and applications. While most complex models are on par with the latest compression standard like VVC/H.266…
The generation of voluminous scientific data poses significant challenges for efficient storage, transfer, and analysis. Recently, error-bounded lossy compression methods emerged due to their ability to achieve high compression ratios while…
Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…
Estimating the pose of a camera with respect to a 3D reconstruction or scene representation is a crucial step for many mixed reality and robotics applications. Given the vast amount of available data nowadays, many applications constrain…
Tries are popular data structures for storing a set of strings, where common prefixes are represented by common root-to-node paths. Over fifty years of usage have produced many variants and implementations to overcome some of their…
Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Toeplitz matrices are abundant in computational mathematics, and there is a rich literature on the development of fast and superfast algorithms for solving linear systems involving such matrices. Any Toeplitz matrix can be transformed into…
Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a…