Related papers: A 3D Parallel Algorithm for QR Decomposition

Despite significant advances in Large Language Models (LLMs), planning tasks still present challenges for LLM-based agents. Existing planning methods face two key limitations: heavy constraints and cascading errors. To address these…

Despite recent advances in architectures for mobile devices, deep learning computational requirements remains prohibitive for most embedded devices. To address that issue, we envision sharing the computational costs of inference between…

In this paper, we present the QR Algorithm with Permutations that shows an improved convergence rate compared to the classical QR algorithm. We determine a bound for performance based on best instantaneous convergence, and develop low…

Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…

Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…

Recently, large language models (LLMs) have shown surprising performance in task-specific workloads as well as general tasks with the given prompts. However, to achieve unprecedented performance, recent LLMs use billions to trillions of…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…

Quantum computing is expected to become a foundational technology for solving problems that exceed the capabilities of classical systems. As quantum algorithms and hardware technologies continue to advance, the need for scalable…

Distributed quantum computing (DQC) is a promising approach to extending the computational power of near-term quantum devices. However, the non-local quantum communication between quantum devices is much more expensive and error-prone than…

We present a linear optics quantum computation scheme with a greatly reduced cost in resources compared to KLM. The scheme makes use of elements from cluster state computation and achieves comparable resource usage to those schemes while…

This paper presents "Predictive Pipelined Decoding (PPD)," an approach that speeds up greedy decoding in Large Language Models (LLMs) while maintaining the exact same output as the original decoding. Unlike conventional strategies, PPD…

Hiding or minimizing the communication cost is key in order to obtain good performance on large-scale systems. While communication overlapping attempts to hide communications cost, 2.5D communication avoiding algorithms improve performance…

Variational quantum algorithms (VQAs) have emerged as a promising near-term technique to explore practical quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, the inefficient parameter training process due to the…

Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…

Arrival of multicore systems has enforced a new scenario in computing, the parallel and distributed algorithms are fast replacing the older sequential algorithms, with many challenges of these techniques. The distributed algorithms provide…

We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…

MapReduce is a widely used framework for distributed computing. Data shuffling between the Map phase and Reduce phase of a job involves a large amount of data transfer across servers, which in turn accounts for increase in job completion…

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…

Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…

The presented work provides a procedure for optimizing the communication cost of a distributed quantum circuit (DQC) in terms of the number of qubit teleportations. Because of technology limitations which do not allow large quantum…