Related papers: Application-tailored Linear Algebra Algorithms: A …
The main purpose of this book is to propose an introduction to the modern tools of algebraic complexity. To remain as simple as possible while providing meaningful examples, we chose to focus on effective linear algebra; this is certainly…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
While deep learning is a powerful tool for natural language processing (NLP) problems, successful solutions to these problems rely heavily on large amounts of annotated samples. However, manually annotating data is expensive and…
We describe an augmented intelligence system for simplifying and enhancing the modeling experience for operations research. Using this system, the user receives a suggested formulation of an optimization problem based on its description. To…
Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…
We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully…
A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…
Domain specific accelerators present new challenges and opportunities for code generation onto novel instruction sets, communication fabrics, and memory architectures. In this paper we introduce an intermediate representation (IR) which…
Deep search agents, which aim to answer complex questions requiring reasoning across multiple documents, can significantly speed up the information-seeking process. Collecting human annotations for this application is prohibitively…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…
Sequential computation via autoregressive generation can make difficult tasks learnable, but the generation order of intermediate states strongly affects whether training succeeds. We address the problem of discovering a learning-friendly…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
Since the mid-1990s, researchers have been trying to use machine-learning based approaches to solve a number of different compiler optimization problems. These techniques primarily enhance the quality of the obtained results and, more…
A class or taxonomic hierarchy is often manually constructed, and part of our knowledge about the world. In this paper, we propose a novel algorithm for automatically acquiring a class hierarchy from a classifier which is often a large…
Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an…
Guiding large language models with a selected set of human-authored demonstrations is a common practice for improving LLM applications. However, human effort can be costly, especially in specialized domains (e.g., clinical diagnosis), and…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…