Related papers: Upgrading Subgroup Triple Product Property Triples
Generative models typically sample outputs independently, and recent inference-time guidance and scaling algorithms focus on improving the quality of individual samples. However, in real-world applications, users are often presented with a…
Sparse data structures are commonly used in neural networks to reduce the memory footprint. These data structures are compact but cause irregularities such as random memory accesses, which prevent efficient use of the memory hierarchy. GPUs…
We present new algorithms for computing the low $n$ bits or the high $n$ bits of the product of two $n$-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full $2n$-bit product,…
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…
Data augmentation methods in combination with deep neural networks have been used extensively in computer vision on classification tasks, achieving great success; however, their use in time series classification is still at an early stage.…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical…
We wish to renew the discussion over recent combinatorial structures that are 3-uniform hypergraph expanders, viewing them in a more general perspective, shedding light on a previously unknown relation to the zig-zag product. We do so by…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix…
In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
It is well known that the generalized (or quotient) singular values of a matrix pair $(A, C)$ can be obtained from the generalized eigenvalues of a matrix pencil consisting of two augmented matrices. The downside of this reformulation is…
We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing subproblems in order to accelerate the convergence of the CG…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
Many state-of-the-art results obtained with deep networks are achieved with the largest models that could be trained, and if more computation power was available, we might be able to exploit much larger datasets in order to improve…
In this paper, we give strong lower bounds on the size of the sets of products of matrices in some certain groups. More precisely, we prove an analogue of a result due to Chapman and Iosevich for matrices in $SL_2(\mathbb{F}_p)$ with…
A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…
Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…