Related papers: A Parallel Computing Method for the Higher Order T…
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…
We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To…
Training-free high-resolution (HR) image generation has garnered significant attention due to the high costs of training large diffusion models. Most existing methods begin by reconstructing the overall structure and then proceed to refine…
Transformer-based models are becoming deeper and larger recently. For better scalability, an underlying training solution in industry is to split billions of parameters (tensors) into many tasks and then run them across homogeneous…
We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \ge 2$), where $D$ is…
Interprocessor communication often dominates the runtime of large matrix computations. We present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing…
Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes…
We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context, to compute dynamical correlation functions of correlated systems. We…
This work explores a distributed computing setting where $K$ nodes are assigned fractions (subtasks) of a computational task in order to perform the computation in parallel. In this setting, a well-known main bottleneck has been the…
A distributed-memory parallelization strategy for the density matrix renormalization group is proposed for cases where correlation functions are required. This new strategy has substantial improvements with respect to previous works. A…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a…
We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
Accurate and fast treatment of electron-electron interactions remains a central challenge in electronic structure theory because post-Hartree-Fock methods often suffered from the computational cost for 4-index electron repulsion integrals…
This paper presents \pandora, a novel parallel algorithm for efficiently constructing dendrograms for single-linkage hierarchical clustering, including \hdbscan. Traditional dendrogram construction methods from a minimum spanning tree…
A parallel algorithm for the implementation of the recursive Green's function technique, which is extensively applied in the coherent scattering formalism, is developed. The algorithm performs a domain decomposition of the scattering region…