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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…
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 acceleration of deep-learning kernels in hardware relies on matrix multiplications that are executed efficiently on Systolic Arrays (SA). To effectively trade off deep-learning training/inference quality with hardware cost, SA…
Recent renewed interest in optimizing and analyzing floating-point programs has lead to a diverse array of new tools for numerical programs. These tools are often complementary, each focusing on a distinct aspect of numerical programming.…
We review the current state of automatic differentiation (AD) for array programming in machine learning (ML), including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based…
In problems of mathematical physics, to study the structures of spaces using the Cayley-Klein models in theoretical calculations, the use of generalized complex numbers is required. In the case of computational experiments, such tasks…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
Mixed integer sets have a strong modeling capacity to describe practical systems. Nevertheless, incorporating a mixed integer set often renders an optimization formulation drastically more challenging to compute. In this paper, we study how…
A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material…
While Deep Neural Networks (DNNs) push the state-of-the-art in many machine learning applications, they often require millions of expensive floating-point operations for each input classification. This computation overhead limits the…
The Rust programming language is an attractive choice for robotics and related fields, offering highly efficient and memory-safe code. However, a key limitation preventing its broader adoption in these domains is the lack of high-quality,…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
Applications in the smart industry domain, such as interaction with collaborative robots using vocal commands or machine vision systems often requires the deployment of deep learning algorithms on heterogeneous low power computing…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
Data-flow analyses like points-to analysis can vastly improve the precision of other analyses, and help perform powerful code optimizations. However, whole-program points-to analysis of large programs tend to be expensive - both in terms of…
Artificial intelligence (AI) has rapidly evolved into a critical technology; however, electrical hardware struggles to keep pace with the exponential growth of AI models. Free space optical hardware provides alternative approaches for…
We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…
Voice Activity Detection (VAD) and Overlapped Speech Detection (OSD) are key pre-processing tasks for speaker diarization. In the meeting context, it is often easier to capture speech with a distant device. This consideration however leads…
This paper investigates the possibility of approximating multiple mathematical operations in latent space for expression derivation. To this end, we introduce different multi-operational representation paradigms, modelling mathematical…