Related papers: AutoHOOT: Automatic High-Order Optimization for Te…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Auto-scheduling for tensor programs is a process where a search algorithm automatically explores candidate schedules (program transformations) for a given program on a target hardware platform to improve its performance. However this can be…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and…

In this work, we develop deterministic and random sketching-based algorithms for two types of tensor interpolative decompositions (ID): the core interpolative decomposition (CoreID, also known as the structure-preserving HOSVD) and the…

We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…

Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…

One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…

This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

Automated machine learning aims to automate the whole process of machine learning, including model configuration. In this paper, we focus on automated hyperparameter optimization (HPO) based on sequential model-based optimization (SMBO).…

Fully Homomorphic Encryption (FHE) is an encryption scheme that allows for computation to be performed directly on encrypted data, effectively closing the loop on secure and outsourced computing. Data is encrypted not only during rest and…

In this paper, we investigate a distributed aggregative optimization problem in a network, where each agent has its own local cost function which depends not only on the local state variable but also on an aggregated function of state…

We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…

Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…

This paper introduces a novel method for finding integer sets that satisfy the Pythagorean theorem by leveraging the Higher-Order Binary Optimization (HOBO) formulation. Unlike the Quadratic Unconstrained Binary Optimization (QUBO)…