Related papers: Wanted: Floating-Point Add Round-off Error instruc…

Many recent computational accelerators provide non-standard (e.g., reduced precision) arithmetic operations to enhance performance for floating-point matrix multiplication. Unfortunately, the properties of these accelerators are not widely…

Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…

The unprecedented demand for computing resources to train DNN models has led to a search for minimal numerical encoding. Recent state-of-the-art (SOTA) proposals advocate for multi-level scaled narrow bitwidth numerical formats. In this…

This paper introduces a checksum algorithm that provides a new point in the performance/complexity/effectiveness checksum tradeoff space. It has better fault detection properties than single-sum and dual-sum modular addition checksums. It…

Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only…

There is a growing interest in the use of reduced-precision arithmetic, exacerbated by the recent interest in artificial intelligence, especially with deep learning. Most architectures already provide reduced-precision capabilities (e.g.,…

Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…

Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD…

As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to…

Electronic devices primarily aim to offer low power consumption, high speed, and a compact area. The performance of very large-scale integration (VLSI) devices is influenced by arithmetic operations, where multiplication is a crucial…

Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and…

This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…

Latency and energy consumption are key metrics in the performance of deep neural network (DNN) accelerators. A significant factor contributing to latency and energy is data transfers. One method to reduce transfers or data is reusing data…

The torrential influx of floating-point data from domains like IoT and HPC necessitates high-performance lossless compression to mitigate storage costs while preserving absolute data fidelity. Leveraging GPU parallelism for this task…

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…

Fault tolerance overhead of high performance computing (HPC) applications is becoming critical to the efficient utilization of HPC systems at large scale. HPC applications typically tolerate fail-stop failures by checkpointing. Another…

This paper provides a rounding-error analysis for two-grid methods that use one relaxation step both before and after coarsening. The analysis is based on floating point arithmetic and focuses on a two-grid scheme that is perturbed on the…

Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or…

We consider the prospect of a processor that can perform interval arithmetic at the same speed as conventional floating-point arithmetic. This makes it possible for all arithmetic to be performed with the superior security of interval…

Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…