Related papers: Efficient sparse polynomial factoring using the Fu…
Traditional segmentation methods for colonic polyps are mainly designed based on low-level features. They could not accurately extract the location of small colonic polyps. Although the existing deep learning methods can improve the…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…
The two currently fastest general-purpose integer factorization algorithms are the Quadratic Sieve and the Number Field Sieve. Both techniques are used to find so-called smooth values of certain polynomials, i.e., values that factor…
We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm…
We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
Semantic segmentation is a key prerequisite to robust image understanding for applications in \acrlong{ai} and Robotics. \acrlong{fss}, in particular, concerns the extension and optimization of traditional segmentation methods in…
SHAP (SHapley Additive exPlanations) has become a popular method to attribute the prediction of a machine learning model on an input to its features. One main challenge of SHAP is the computation time. An exact computation of Shapley values…
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…
We explore a new type of sparsity for the generalized moment problem (GMP) that we call ideal-sparsity. This sparsity exploits the presence of equality constraints requiring the measure to be supported on the variety of an ideal generated…
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…
We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage…
Deep Learning and factorization-based collaborative filtering recommendation models have undoubtedly dominated the scene of recommender systems in recent years. However, despite their outstanding performance, these methods require a…
We propose a new method to create compact convolutional neural networks (CNNs) by exploiting sparse convolutions. Different from previous works that learn sparsity in models, we directly employ hand-crafted kernels with regular sparse…
The recursive polynomial expansion for construction of a density matrix approximation with rigorous error control [J. Chem. Phys. 128, 074106 (2008)] is implemented in the quantum chemistry program Ergo [SoftwareX 7, 107 (2018)] using the…
Hash table is a fundamental data structure for quick search and retrieval of data. It is a key component in complex graph analytics and AI/ML applications. State-of-the-art parallel hash table implementations either make some simplifying…
Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM…