Related papers: TSFC: a structure-preserving form compiler
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
Conventional works generally employ a two-phase model in which a generator selects the most important pieces, followed by a predictor that makes predictions based on the selected pieces. However, such a two-phase model may incur the…
Document structure extraction has been a widely researched area for decades with recent works performing it as a semantic segmentation task over document images using fully-convolution networks. Such methods are limited by image resolution…
This research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
Compilers convert between representations -- usually, from higher-level, human writable code to lower-level, machine-readable code. A compiler backend is the portion of the compiler containing optimizations and code generation routines for…
Continual learning (CL) has spurred the development of several methods aimed at consolidating previous knowledge across sequential learning. Yet, the evaluations of these methods have primarily focused on the final output, such as changes…
An optimizing compiler consists of a front end parsing a textual programming language into an intermediate representation (IR), a middle end performing optimizations on the IR, and a back end lowering the IR to a target representation (TR)…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation…
TPC (Three-Phase Consolidation) is here introduced as a simple but effective approach to continually learn new classes (and/or instances of known classes) while controlling forgetting of previous knowledge. Each experience (a.k.a. task) is…
There is an emerging interest in tensor factorization applications in big-data analytics and machine learning. To speed up the factorization of extra-large datasets, organized in multidimensional arrays (aka tensors), easy to compute…
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This…
Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of…
Current object detectors typically have a feature pyramid (FP) module for multi-level feature fusion (MFF) which aims to mitigate the gap between features from different levels and form a comprehensive object representation to achieve…
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…
How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…