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Quantization addresses the high resource demand for large language models (LLMs) by alleviating memory pressure and bandwidth congestion and providing significantly scaled compute power with a tolerable impact on accuracy. Four-bit floating…

Large language models (LLMs) demand extensive memory capacity during both fine-tuning and inference. To enable memory-efficient fine-tuning, existing methods apply block-wise quantization techniques, such as NF4 and AF4, to the network…

In modern low-power embedded platforms, floating-point (FP) operations emerge as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy…

With the increasing deployment of deep neural networks (DNNs) in terrestrial and aerospace safety-critical applications, system reliability has emerged as a co-equal design metric alongside computational efficiency. Algorithm-based fault…

We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…

In this work, we present a novel inner product design for stochastic computing. Stochastic computing is an emerging computing technique, that encodes a number in the probability of observing a one in a random bit stream. This leads to…

Conventional hardware-friendly quantization methods, such as fixed-point or integer, tend to perform poorly at very low word sizes as their shrinking dynamic ranges cannot adequately capture the wide data distributions commonly seen in…

Microscaling floating-point (MXFP) formats have emerged as a promising standard for deploying Multi-modal Large Language Models (MLLMs) and Large Language Models (LLMs) on modern accelerator architectures. However, existing Post-Training…

The state-of-the-art hardware platforms for training Deep Neural Networks (DNNs) are moving from traditional single precision (32-bit) computations towards 16 bits of precision -- in large part due to the high energy efficiency and smaller…

Modern AI hardware, such as Nvidia's Blackwell architecture, is increasingly embracing low-precision floating-point (FP) formats to handle the pervasive activation outliers in Large Language Models (LLMs). Despite this industry trend, a…

As cutting-edge large language models (LLMs) continue to transform various industries, their fast-growing model size and sequence length have led to memory traffic and capacity challenges. Recently, AMD, Arm, Intel, Meta, Microsoft, NVIDIA,…

Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the…

Precision scaling has emerged as a popular technique to optimize the compute and storage requirements of Deep Neural Networks (DNNs). Efforts toward creating ultra-low-precision (sub-8-bit) DNNs suggest that the minimum precision required…

A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite…

This article presents a powerful algorithmic framework for big data optimization, called the Block Successive Upper bound Minimization (BSUM). The BSUM includes as special cases many well-known methods for analyzing massive data sets, such…

Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both inter-node communications and even more-so in on-node data motion. A new approach to address this limitation is to…

Narrow bit-width data formats are key to reducing the computational and storage costs of modern deep learning applications. This paper evaluates Microscaling (MX) data formats that combine a per-block scaling factor with narrow…

Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…