Related papers: Solving Linear Algebra by Program Synthesis
Our goal is to build systems which write code automatically from the kinds of specifications humans can most easily provide, such as examples and natural language instruction. The key idea of this work is that a flexible combination of…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…
Large pre-trained language models such as GPT-3, Codex, and Google's language model are now capable of generating code from natural language specifications of programmer intent. We view these developments with a mixture of optimism and…
Recent breakthroughs in Large Language Models (LLMs), such as GPT-3 and Codex, now enable software developers to generate code based on a natural language prompt. Within computer science education, researchers are exploring the potential…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations.…
In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…
We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
Large Language Models (LLMs) are increasingly used to automate software development, yet most prior evaluations focus on functional correctness or high-level languages such as Python. As one of the first systematic explorations of…
Among areas of software engineering where AI techniques -- particularly, Large Language Models -- seem poised to yield dramatic improvements, an attractive candidate is Automatic Program Repair (APR), the production of satisfactory…
The capabilities of Large Language Models (LLMs) have significantly evolved, extending from natural language processing to complex tasks like code understanding and generation. We expand the scope of LLMs' capabilities to a broader context,…
We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work…
The main contribution of this thesis is the development of a new algorithm for solving convex quadratic programs. It consists in combining the method of multipliers with an infeasible active-set method. Our approach is iterative. In each…