Related papers: Customizable Precision of Floating-Point Arithmeti…
Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
eXmY is a novel data type for quantization of ML models. It supports both arbitrary bit widths and arbitrary integer and floating point formats. For example, it seamlessly supports 3, 5, 6, 7, 9 bit formats. For a specific bit width, say 7,…
Differentiable vector graphics (VGs) are widely used in image vectorization and vector synthesis, while existing representations are costly to optimize and struggle to achieve high-quality rendering results for high-resolution images. This…
It is well known that the computation of accurate trajectories of the Lorenz system is a difficult problem. Computed solutions are very sensitive to the discretization error determined by the time step size and polynomial order of the…
Context. High-resolution numerical methods have been developed for nonlinear, discontinuous problems as they appear in simulations of astrophysical objects. One of the strategies applied is the concept of artificial viscosity. Aims.…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
In this paper, we propose a novel variable rate deep compression architecture that operates on raw 3D point cloud data. The majority of learning-based point cloud compression methods work on a downsampled representation of the data.…
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of…
This paper proposes hardware converters for the microscaling format (MX-format), a reduced representation of floating-point numbers. We present an algorithm and a memory-free hardware model for converting 32 single-precision floating-point…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…
Point cloud is a promising 3D representation for volumetric streaming in emerging AR/VR applications. Despite recent advances in point cloud compression, decoding and rendering high-quality images from lossy compressed point clouds is still…
We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…
Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
The spheroidal wave functions, which are the solutions to the Helmholtz equation in spheroidal coordinates, are notoriously difficult to compute. Because of this, practically no programming language comes equipped with the means to compute…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
We present a novel learning-based method to build a differentiable computational model of a real fluorescence microscope. Our model can be used to calibrate a real optical setup directly from data samples and to engineer point spread…
Users frequently seek to fabricate objects whose outer surfaces consist of regions with different surface attributes, such as color or material. Manufacturing such objects in a single piece is often challenging or even impossible. The…