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In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
Several efficient distributed algorithms have been developed for matrix-matrix multiplication: the 3D algorithm, the 2D SUMMA algorithm, and the 2.5D algorithm. Each of these algorithms was independently conceived and they trade-off memory…
In this study, we investigate the use of Large Language Models (LLMs) for the interactive and automated production of customs circuit layouts described in natural language. Our proposed layout automation process leverages a…
A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…
Auto-vectorization is a fundamental optimization for modern compilers to exploit SIMD parallelism. However, state-of-the-art approaches still struggle to handle intricate code patterns, often requiring manual hints or domain-specific…
Volumetric design is the first and critical step for professional building design, where architects not only depict the rough 3D geometry of the building but also specify the programs to form a 2D layout on each floor. Though 2D layout…
This paper presents an investigation of the capabilities of Generative Pre-trained Transformers (GPTs) to auto-generate graphical process models from multi-modal (i.e., text- and image-based) inputs. More precisely, we first introduce a…
We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
In this work, we extend modular techniques for computing Gr\"obner bases involving rational coefficients to (two-sided) ideals in free algebras. We show that the infinite nature of Gr\"obner bases in this setting renders the classical…
Vectorization is a compiler optimization that replaces multiple operations on scalar values with a single operation on vector values. Although common in traditional compilers such as rustc, clang, and gcc, vectorization is not common in the…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We present MMCORE, a unified framework designed for multimodal image generation and editing. MMCORE leverages a pre-trained Vision-Language Model (VLM) to predict semantic visual embeddings via learnable query tokens, which subsequently…
Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network…