Related papers: Efficient long division via Montgomery multiply
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
An efficient decoder for the generalized first-order Reed-Muller code RM_q(1,m) is essential for the decoding of various block-coding schemes for orthogonal frequency-division multiplexing with reduced peak-to-mean power ratio. We present…
We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…
Computing-in-memory (CIM) has been demonstrated across various memory technologies, ranging from memristive crossbars performing analog dot-product computations to large-scale digital bitwise operations in commodity DRAM and other proposed…
Modular architectures are a promising approach to scale quantum devices to the point of fault tolerance and utility. Modularity is particularly appealing for superconducting qubits, as monolithically manufactured devices are limited in both…
In this paper, we develop and test a fast numerical algorithm, called MDI-LR, for efficient implementation of quasi-Monte Carlo lattice rules for computing $d$-dimensional integrals of a given function. It is based on the idea of converting…
Large Language Models (LLMs) consistently benefit from scaled Chain-of-Thought (CoT) reasoning, but also suffer from heavy computational overhead. To address this issue, efficient reasoning aims to incentivize short yet accurate thinking…
Large language models (LLMs) have demonstrated remarkable performance and tremendous potential across a wide range of tasks. However, deploying these models has been challenging due to the astronomical amount of model parameters, which…
Large Language Models (LLMs) face significant challenges in long-context processing, including quadratic computational costs, information forgetting, and the context fragmentation inherent in retrieval-augmented generation (RAG). We propose…
With the surge of the powerful quantum computer, lattice-based cryptography proliferated the latest cryptography hardware implementation due to its resistance against quantum computers. Among the computational blocks of lattice-based…
Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
Residue Number Systems (RNS) offer efficient modular arithmetic and natural parallelism, but direct integer division in RNS remains a difficult and comparatively underdeveloped operation. This paper builds on the type-II division algorithm…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…
Many popular machine learning models scale poorly when deployed on CPUs. In this paper we explore the reasons why and propose a simple, yet effective approach based on the well-known Divide-and-Conquer Principle to tackle this problem of…
Large language models (LLMs) have enabled the development of numerous specialized, task-specific variants. However, the maintenance and deployment of these individual models present substantial challenges in terms of resource utilization…
Recent breakthroughs in Large-scale language models (LLMs) have demonstrated impressive performance on various tasks. The immense sizes of LLMs have led to very high resource demand and cost for running the models. Though the models are…
Multimodal large language model (MLLM) inference splits into two phases with opposing hardware demands: vision encoding is compute-bound, while language generation is memory-bandwidth-bound. We show that under standard transformer KV…