Related papers: Mixing Condition Numbers and Oracles for Accurate …
Optical flow estimation is one of the most studied problems in computer vision, yet recent benchmark datasets continue to reveal problem areas of today's approaches. Occlusions have remained one of the key challenges. In this paper, we…
This article is about twofold arithmetic. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function $y_0+y_1 \approx f(x_0+x_1)$ is nearly…
Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…
Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for…
Large language models (LLMs), with their billions of parameters, pose substantial challenges for deployment on edge devices, straining both memory capacity and computational resources. Block Floating Point (BFP) quantisation reduces memory…
Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing derivatives of arbitrary order is well understood,…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…
Proper representation of data in graphical visualizations becomes challenging when high accuracy in data types is required, especially in those situations where the difference between double-precision floating-point and single-precision…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
Real-world time series analysis faces significant challenges when dealing with irregular and incomplete data. While Neural Differential Equation (NDE) based methods have shown promise, they struggle with limited expressiveness, scalability…
Two optical flow estimation problems are addressed: i) occlusion estimation and handling, and ii) estimation from image sequences longer than two frames. The proposed ContinualFlow method estimates occlusions before flow, avoiding the use…
Data association in SLAM is fundamentally challenging, and handling ambiguity well is crucial to achieve robust operation in real-world environments. When ambiguous measurements arise, conservatism often mandates that the measurement is…
Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…
We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to…
As computer simulations continue to grow in size and complexity, they present a particularly challenging class of big data problems. Many application areas are moving toward exascale computing systems, systems that perform $10^{18}$ FLOPS…
The occlusion problem remains a crucial challenge in optical flow estimation (OFE). Despite the recent significant progress brought about by deep learning, most existing deep learning OFE methods still struggle to handle occlusions; in…
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…