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Tensor completion aims at imputing missing entries from a partially observed tensor. Existing tensor completion methods often assume either multi-linear or nonlinear relationships between latent components. However, real-world tensors have…
Operations Research (OR) is vital for decision-making in many industries. While recent OR methods have seen significant improvements in automation and efficiency through integrating Large Language Models (LLMs), they still struggle to…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
For decades, SQL has been the default language for composing queries, but it is increasingly used as an artifact to be read and verified rather than authored. With Large Language Models (LLMs), queries are increasingly machine-generated,…
Abstract Meaning Representation (AMR) is a graphical meaning representation language designed to represent propositional information about argument structure. However, at present it is unable to satisfyingly represent non-veridical…
Incorporating external knowledge bases in traditional retrieval-augmented generation (RAG) relies on parsing the document, followed by querying a language model with the parsed information via in-context learning. While effective for…
Modern research in code generators for dense linear algebra computations has shown the ability to produce optimized code with a performance which compares and often exceeds the one of state-of-the-art implementations by domain experts.…
Domain specific accelerators present new challenges and opportunities for code generation onto novel instruction sets, communication fabrics, and memory architectures. In this paper we introduce an intermediate representation (IR) which…
The attention mechanism is an important reason for the success of transformers. It relies on computing pairwise relations between tokens. To reduce the high computational cost of standard quadratic attention, linear attention has been…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
Large Language Models (LLMs) have shown to be capable of various tasks, yet their capability in interpreting and reasoning over tabular data remains an underexplored area. In this context, this study investigates from three core…
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…
With the rapid development and widespread application of Large Language Models (LLMs), multidimensional evaluation has become increasingly critical. However, current evaluations are often domain-specific and overly complex, limiting their…
The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
The main goal of this paper is to explore latent topic analysis (LTA), in the context of quantum information retrieval. LTA is a valuable technique for document analysis and representation, which has been extensively used in information…
Iterative methods for computing matrix functions have been extensively studied and their convergence speed can be significantly improved with the right tuning of parameters and by mixing different iteration types. Handtuning the design…
Performance-critical industrial applications, including large-scale program, network, and distributed system analyses, rely on fixed-point computations. The introduction of recursive common table expressions (CTEs) using the WITH RECURSIVE…
We present ORCA (Omni Research on Calculation in AI) Benchmark - a novel benchmark that evaluates large language models (LLMs) on multi-domain, real-life quantitative reasoning using verified outputs from Omni's calculator engine. In 500…
Retrieval-augmented Generation (RAG) extends large language models (LLMs) with external knowledge but faces key challenges: restricted effective context length and redundancy in retrieved documents. Pure compression-based approaches reduce…