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We present a fast and simple technique to convert images into a radiance surface-based scene representation. Building on existing radiance volume reconstruction algorithms, we introduce a subtle yet impactful modification of the loss…
In this paper, we present a work in progress about a deep learning based approach for automatic code optimization in polyhedral compilers. The proposed technique explores combinations of affine and non-affine loop transformations to find…
Decoding and repair schemes are proposed for shift-exclusive-or (shift-XOR) product-matrix (PM) regenerating codes, which outperform the existing schemes in terms of both communication and computation costs. In particular, for the shift-XOR…
Achieving efficient execution of machine learning models has attracted significant attention recently. To generate tensor programs efficiently, a key component of DNN compilers is the cost model that can predict the performance of each…
We prove the equivalence between the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems for the maximal totally real subfield of the $2^r 3^s$-th cyclotomic field for $r \geq 3$ and $s \geq 1$.…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
We study the computational complexity of decomposing finite discrete dynamical systems (FDDSs) in terms of the semiring operations of alternative and synchronous execution, which is useful for the analysis of discrete phenomena in science…
Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Neural radiance-density field methods have become increasingly popular for the task of novel-view rendering. Their recent extension to hash-based positional encoding ensures fast training and inference with visually pleasing results.…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
We show a new algorithm and its implementation for multiplying bit-polynomials of large degrees. The algorithm is based on evaluating polynomials at a specific set comprising a natural set for evaluation with additive FFT and a high order…
We examine in detail the accuracy, efficiency and implementation issues that arise when a simplified code structure is employed to evaluate the partition function of the two-dimensional square Ising model on periodic lattices though…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
Decimal-to-binary conversion is important to modern binary computers. The classical method to solve this problem is based on division operation. In this paper, we investigate a decimal-to-binary conversion method based on addition…
The computation of triangular decompositions are based on two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations relying on modular…