Related papers: Projection-based QLP Algorithm for Efficiently Com…
Quantization is wildly taken as a model compression technique, which obtains efficient models by converting floating-point weights and activations in the neural network into lower-bit integers. Quantization has been proven to work well on…
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
A new Lp-norm constraint least mean square (Lp-LMS) algorithm with new strategy of varying p is presented, which is applied to system identification in this letter. The parameter p is iteratively adjusted by the gradient method applied to…
Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme…
Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank…
Bayesian reasoning is a powerful mechanism for probabilistic inference in smart edge-devices. During such inferences, a low-precision arithmetic representation can enable improved energy efficiency. However, its impact on inference accuracy…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
Feasible path algorithms have been widely used for process optimisation due to its good convergence. The sequential quadratic programming (SQP) algorithm is usually used to drive the feasible path algorithms towards optimality. However,…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
Machine learning potentials (MLP) have revolutionized the field of atomistic simulations by describing the atomic interactions with the accuracy of electronic structure methods at a small fraction of the costs. Most current MLPs construct…
Quadratic assignment problems (QAPs) arise in a wide variety of domains, ranging from operations research to graph theory to computer vision to neuroscience. In the age of big data, graph valued data is becoming more prominent, and with it,…
Query Performance Prediction (QPP) estimates the retrieval quality of ranking models without the use of any human-assessed relevance judgements, and finds applications in query-specific selective decision making to improve overall retrieval…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
We present a new algorithm for convex separable quadratic programming (QP) called Nys-IP-PMM, a regularized interior-point solver that uses low-rank structure to accelerate solution of the Newton system. The algorithm combines the interior…
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…