Related papers: An Optimizing Symbolic Algebra Approach for Genera…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
We describe the implementation of output code optimization in the open source computer algebra system FORM. This implementation is based on recently discovered techniques of Monte Carlo tree search to find efficient multivariate Horner…
In the recent years, multi-core processor designs have found their way into many computing devices. To exploit the capabilities of such devices in the best possible way, signal processing algorithms have to be adapted to an operation in…
In recent years, neuro-symbolic methods have become a popular and powerful approach that augments artificial intelligence systems with the capability to perform abstract, logical, and quantitative deductions with enhanced precision and…
In this paper, we propose a new paradigm for program optimization which is based on aggressive aggregation, i.e., on a partial evaluation-based decomposition of acyclic program fragments into a pair of computationally optimal structures: an…
This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware…
This paper presents AlphaSpace, a novel methodology designed to enhance the spatial reasoning capabilities of language models for robotic manipulation in 3D Cartesian space. AlphaSpace employs a hierarchical semantics-based tokenization…
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…
Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive…
The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…
We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form.…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
In quantum information and computation research, symbolic methods have been widely used for human specification and reasoning about quantum states and operations. At the same time, they are essential for ensuring the scalability and…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
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…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Dynamic symbolic execution (DSE) is an effective method for automated program testing and bug detection. It is increasing the code coverage by the complex branches exploration during hybrid fuzzing. DSE tools invert the branches along some…