Related papers: Towards Fixed-Point Formats Determination for Faus…
In this work, we propose an algorithm for a filter based on the Fast Fourier Transform (FFT), which, due to its characteristics, allows for an efficient computational implementation, ease of use, and minimizes amplitude variation in the…
The proliferation of low-precision units in modern high-performance architectures increasingly burdens domain scientists. Historically, the choice in HPC was easy: can we get away with 32 bit floating-point operations and lower bandwidth…
Digital mobile systems must function with low power, small size and weight, and low cost. High-performance desktop microprocessors, with built-in floating point hardware, are not suitable in these cases. For embedded systems, it can be…
Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using…
While recent progress in quantum hardware open the door for significant speedup in certain key areas (cryptography, biology, chemistry, optimization, machine learning, etc), quantum algorithms are still hard to implement right, and the…
The prevalence of online platforms and studies has generated the demand for automated grading tools, and as a result, there are plenty in the market. Such tools are developed to grade coding assignments quickly, accurately, and…
Fixed-point (FXP) inference has proven suitable for embedded devices with limited computational resources, and yet model training is continually performed in floating-point (FLP). FXP training has not been fully explored and the non-trivial…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…
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…
Fourier-domain Difference Map (FDM) for phase retrieval with two oversampled coded diffraction patterns are proposed. FDM is a 3-parameter family of fixed point algorithms including Fourier-domain Hybrid-Projection-Reflection (FHPR) and…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as 3 arctan 2 + ln…
A large number of different feature detectors has been proposed so far. Any existing approach presents strengths and weaknesses, which make a detector optimal only for a limited range of applications. A tool capable of selecting the optimal…
Understanding input substitution and output transformation possibilities is critical for efficient resource allocation and firm strategy. There are important examples of fixed proportion technologies where certain inputs are…
An intriguing phenomenon about JPEG compression has been observed since two decades ago- after repeating JPEG compression and decompression, it leads to a stable image that does not change anymore, which is a fixed point. In this work, we…
Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have…
Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication. We first study some past…