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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…

Performance optimization is the art of continuous seeking a harmonious mapping between the application domain and hardware. Recent years have witnessed a surge of deep learning (DL) applications in industry. Conventional wisdom for…

This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural…

Memory becomes a limiting factor in contemporary applications, such as analyses of the Webgraph and molecular sequences, when many objects need to be counted simultaneously. Robert Morris [Communications of the ACM, 21:840--842, 1978]…

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace…

This study explores the use of INT8-based emulation for accelerating traditional FP64-based HPC workloads on modern GPU architectures. Through SCILIB-Accel automatic BLAS offload tool for cache-coherent Unified Memory Architecture, we…

We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…

For successful deployment of deep neural networks on highly--resource-constrained devices (hearing aids, earbuds, wearables), we must simplify the types of operations and the memory/power resources used during inference. Completely avoiding…

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level…

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based…

We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of…

Three-dimensional integrated circuits promise power, performance, and footprint gains compared to their 2D counterparts, thanks to drastic reductions in the interconnects' length through their smaller form factor. We can leverage the…

In this paper, we propose a scalable approximate multiplier design, scaleTRIM, that approximates the multiplication operation using fitted linear functions, also referred to as linearization. We show that multiplication operations can be…

The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…

This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical…

The use of low numerical precision is a fundamental optimization included in modern accelerators for Deep Neural Networks (DNNs). The number of bits of the numerical representation is set to the minimum precision that is able to retain…

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…

The widely-used, weight-only quantized large language models (LLMs), which leverage low-bit integer (INT) weights and retain floating-point (FP) activations, reduce storage requirements while maintaining accuracy. However, this shifts the…

State-of-the-art sequential reasoning in Large Language Models (LLMs) has expanded the capabilities of Copilots beyond conversational tasks to complex function calling, managing thousands of API calls. However, the tendency of compositional…

Mixture of Experts (MoEs) have become a central component of many state-of-the-art open-source and proprietary large language models. Despite their widespread adoption, it remains unclear how close existing MoE architectures are to optimal…