Related papers: Application-tailored Linear Algebra Algorithms: A …
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…
We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral…
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…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
Lifelong learning can be viewed as a continuous transfer learning procedure over consecutive tasks, where learning a given task depends on accumulated knowledge --- the so-called knowledge base. Most published work on lifelong learning…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
The organizer of a machine learning competition faces the problem of maintaining an accurate leaderboard that faithfully represents the quality of the best submission of each competing team. What makes this estimation problem particularly…
Machine learning algorithms have difficulties to generalize over a small set of examples. Humans can perform such a task by exploiting vast amount of background knowledge they possess. One method for enhancing learning algorithms with…
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…
Genetic algorithms constitute a family of black-box optimization algorithms, which take inspiration from the principles of biological evolution. While they provide a general-purpose tool for optimization, their particular instantiations can…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
Algorithm portfolio and selection approaches have achieved remarkable improvements over single solvers. However, the implementation of such systems is often highly customised and specific to the problem domain. This makes it difficult for…
Optimal use of computing resources requires extensive coding, tuning and benchmarking. To boost developer productivity in these time consuming tasks, we introduce the Experimental Linear Algebra Performance Studies framework (ELAPS), a…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
Because loops execute their body many times, compiler developers place much emphasis on their optimization. Nevertheless, in view of highly diverse source code and hardware, compilers still struggle to produce optimal target code. The sheer…
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…
Compiler optimization decisions are often based on hand-crafted heuristics centered around a few established benchmark suites. Alternatively, they can be learned from feature and performance data produced during compilation. However,…
When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…
Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area…
The space and run-time requirements of broad coverage grammars appear for many applications unreasonably large in relation to the relative simplicity of the task at hand. On the other hand, handcrafted development of application-dependent…