Related papers: IterLara: A Turing Complete Algebra for Big Data, …

We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…

Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…

We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…

Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…

Analytics tasks manipulate structured data with variants of relational algebra (RA) and quantitative data with variants of linear algebra (LA). The two computational models have overlapping expressiveness, motivating a common programming…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified…

Large language models (LLMs) demonstrate strong task-specific capabilities through fine-tuning, but merging multiple fine-tuned models often leads to degraded performance due to overlapping instruction-following components. Task Arithmetic…

Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common…

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…

In modern data analytics, analysts frequently face the challenge of searching for desirable entities by evaluating, for each entity, a collection of its feature relations to derive key analytical properties. This search is challenging…

Along with the proliferation of digital data collected using sensor technologies and a boost of computing power, Deep Learning (DL) based approaches have drawn enormous attention in the past decade due to their impressive performance in…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…

Previous computation models either have equivalent abilities in representing all computations but fail to provide primitive operators for programming complex algorithms or lack generalized expression ability to represent newly-added…

Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging…

Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…

We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…

Collaboration literacy requires adapting to the evolving demands of group work within complex discussions, making it difficult to develop and assess. Traditional analytics metrics capture behavioral signals while missing the semantic…

Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…