Related papers: Floating-floating point: a highly accurate number …
In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
This paper presents the analysis of the impact of a floating-point number precision reduction on the quality of text classification. The precision reduction of the vectors representing the data (e.g. TF-IDF representation in our case)…
High-throughput QR decomposition is a key operation in many advanced signal processing and communication applications. For some of these applications, using floating-point computation is becoming almost compulsory. However, there are scarce…
(Pseudo)random sampling, a costly yet widely used method in (probabilistic) machine learning and Markov Chain Monte Carlo algorithms, remains unfeasible on a truly large scale due to unmet computational requirements. We introduce an…
Floating point arithmetic is costly on FPGA platforms due to wide datapaths, normalization, and carry propagation, motivating alternative numerical representations that improve throughput and efficiency. This paper presents the Hybrid…
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.…
Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the…
Many modern search domains comprise high-dimensional vectors of floating point numbers derived from neural networks, in the form of embeddings. Typical embeddings range in size from hundreds to thousands of dimensions, making the size of…
The Graphic Processing Unit (GPU) has evolved into a powerful and flexible processor. The latest graphic processors provide fully programmable vertex and pixel processing units that support vector operations up to single floating-point…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
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…
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…
Neural network quantization is widely used to reduce model inference complexity in real-world deployments. However, traditional integer quantization suffers from accuracy degradation when adapting to various dynamic ranges. Recent research…
FP8 is a natural progression for accelerating deep learning training inference beyond the 16-bit formats common in modern processors. In this paper we propose an 8-bit floating point (FP8) binary interchange format consisting of two…
Post-training quantization (PTQ) is a powerful technique for model compression, reducing the numerical precision in neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point…
Errors in floating-point programs can lead to severe consequences, particularly in critical domains such as military, aerospace, and financial systems, making their repair a crucial research problem. In practice, some errors can be fixed…
Performing the inference step of deep learning in resource constrained environments, such as embedded devices, is challenging. Success requires optimization at both software and hardware levels. Low precision arithmetic and specifically low…
Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…