Related papers: Block Format Error Bounds and Optimal Block Size S…

Prior work has observed that fetch-directed prefetching (FDIP) is highly effective at covering instruction cache misses. The key to FDIP's effectiveness is having a sufficiently large BTB to accommodate the application's branch working set.…

While critical for alignment, Supervised Fine-Tuning (SFT) incurs the risk of catastrophic forgetting, yet the layer-wise emergence of instruction-following capabilities remains elusive. We investigate this mechanism via a comprehensive…

Symmetric nonnegative matrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix…

Backpropagation (BP) has been a successful optimization technique for deep learning models. However, its limitations, such as backward- and update-locking, and its biological implausibility, hinder the concurrent updating of layers and do…

As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…

In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation,…

In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a…

The IEEE 754 floating-point standard is the bedrock of modern computing, but its structural requirements -- a hidden leading bit, Base-2 bit-level normalization, and Sign-Magnitude encoding -- impose significant silicon area and power…

For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…

Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…

With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…

As the demand for deep learning grows, cost reduction through quantization has become essential for both training and inference. In 2022, the Open Compute Project (OCP) consortium standardized narrow precision formats for deep learning,…

We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…

In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a…

Microscaling is a critical technique for preserving the quality of Large Language Models (LLMs) quantized to ultra-low precision formats. Intuitively, finer block sizes should yield lower quantization error; however, a paradox recently…

We propose a new complex block floating-point format to reduce implementation complexity. The new format achieves wordlength reduction by sharing an exponent across the block of samples, and uses box encoding for the shared exponent to…

State-of-the-art generic low-precision training algorithms use a mix of 16-bit and 32-bit precision, creating the folklore that 16-bit hardware compute units alone are not enough to maximize model accuracy. As a result, deep learning…

In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…

As large language models (LLMs) grow in parameter size and context length, computation precision has been reduced from 16-bit to 4-bit to improve inference efficiency. However, this reduction causes accuracy degradation due to activation…

In the Two-Bar Charts Packing Problem (2-BCPP), it is required to pack the bar charts (BCs) consisting of two bars into the horizontal unit-height strip of minimal length. The bars may move vertically within the strip, but it is forbidden…