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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…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
We present a technique for automatically transforming kernel-based computations in disparate, nested loops into a fused, vectorized form that can reduce intermediate storage needs and lead to improved performance on contemporary hardware.…
In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in $\mathbb{R}^2$ computed using tools of algebraic topology. However, this multi-set structure…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Recent vision-language model (VLM)-based approaches have achieved impressive results on image vectorization tasks. However, they are typically evaluated on synthetic benchmarks, where clean SVGs are rasterized at high resolution and then…
Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior…
Linear codes over finite fields parameterized by functions have proven to be a powerful tool in coding theory, yielding optimal and few-weight codes with significant applications in secret sharing, authentication codes, and association…
Predicting program behavior and reasoning about code execution remain significant challenges in software engineering, particularly for large language models (LLMs) designed for code analysis. While these models excel at understanding static…
High-quality visualizations are an essential part of robotics research, enabling clear communication of results through figures, animations, and demonstration videos. While Blender is a powerful and freely available 3D graphics platform,…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently…
Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean…
The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for…
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
In this position paper, we present a prototype of a visualizer for functional programs. Such programs, whose evaluation model is the reduction of an expression to a value through repeated application of rewriting rules, and which tend to…
Researchers in the humanities are among the many who are now exploring the world of big data. They have begun to use programming languages like Python or R and their corresponding libraries to manipulate large data sets and discover brand…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…