Related papers: A Domain-Specific Compiler for Linear Algebra Oper…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
Despite significant investment in software infrastructure, machine learning systems, runtimes and compilers do not compose properly. We propose a new design aiming at providing unprecedented degrees of modularity, composability and…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
We introduce DISTAL, a compiler for dense tensor algebra that targets modern distributed and heterogeneous systems. DISTAL lets users independently describe how tensors and computation map onto target machines through separate format and…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
We develop a first line of attack for solving programming competition-style problems from input-output examples using deep learning. The approach is to train a neural network to predict properties of the program that generated the outputs…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…
Optimizing compilers are mainly equipped to optimize control flow. The optimization of data structures is left to the programmer and it is the programmer's responsibility to design the data structures to suit the target hardware. Very…
New low-precision accelerators, vector instruction sets, and library functions make maximizing accuracy and performance of numerical code increasingly challenging. Two lines of work$\unicode{x2013}$traditional compilers and numerical…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
A compiler processes the code written in a high level language and produces machine executable code. The compiler writers often face the challenge of keeping the compilation times reasonable. That is because aggressive optimization passes…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
Specialized hardware accelerators are becoming important for more and more applications. Thanks to specialization, they can achieve high performance and energy efficiency but their design is complex and time consuming. This problem is…
As the usage of deep learning becomes increasingly popular in mobile and embedded solutions, it is necessary to convert the framework-specific network representations into executable code for these embedded platforms. This paper consists of…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…