Related papers: A Domain-Specific Compiler for Linear Algebra Oper…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
Frameworks for writing, compiling, and optimizing deep learning (DL) models have recently enabled progress in areas like computer vision and natural language processing. Extending these frameworks to accommodate the rapidly diversifying…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
We present SLinGen, a program generation system for linear algebra. The input to SLinGen is an application expressed mathematically in a linear-algebra-inspired language (LA) that we define. LA provides basic scalar/vector/matrix…
Selecting the right compiler optimisations has a severe impact on programs' performance. Still, the available optimisations keep increasing, and their effect depends on the specific program, making the task human intractable. Researchers…
We introduce Compositional Imitation Learning and Execution (CompILE): a framework for learning reusable, variable-length segments of hierarchically-structured behavior from demonstration data. CompILE uses a novel unsupervised,…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…
In this paper we propose a new non-linear classifier based on a combination of locally linear classifiers. A well known optimization formulation is given as we cast the problem in a $\ell_1$ Multiple Kernel Learning (MKL) problem using many…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
Current quantum programming is dominated by low-level, circuit-centric approaches that limit the potential for compiler optimization. This work presents how a high-level programming construct provides compilers with the semantic information…
Deep neural networks are a promising solution for applications that solve problems based on learning data sets. DNN accelerators solve the processing bottleneck as a domain-specific processor. Like other hardware solutions, there must be…
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…
Domain Large Language Models (LLMs) are developed for domain-specific tasks based on general LLMs. But it still requires professional knowledge to facilitate the expertise for some domain-specific tasks. In this paper, we investigate into…
Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper…
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
Reverse engineering of binary executables is a critical problem in the computer security domain. On the one hand, malicious parties may recover interpretable source codes from the software products to gain commercial advantages. On the…