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This study proposes Interaction Tensor SHAP (IT-SHAP), a tensor algebraic formulation of the Shapley Taylor Interaction Index (STII) that makes its computational structure explicit. STII extends the Shapley value to higher order…
We introduce CLARGA, a general-purpose multimodal fusion architecture for multimodal representation learning that works with any number and type of modalities without changing the underlying framework. Given a supervised dataset, CLARGA can…
This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous- and discrete-time nonlinear systems. Unlike other existing tools, the main…
Large Language Models (LLMs) encode meanings of words in the form of distributed semantics. Distributed semantics capture common statistical patterns among language tokens (words, phrases, and sentences) from large amounts of data. LLMs…
Combining large language models with logical reasoning enhances their capacity to address problems in a robust and reliable manner. Nevertheless, the intricate nature of logical reasoning poses challenges when gathering reliable data from…
An automated resource analysis technique is introduced, targeting a Call-By-Push-Value abstract machine, with memory prediction as a practical goal. The machine has a polymorphic and linear type system enhanced with a first-order logical…
Text analytical tasks like word embedding, phrase mining, and topic modeling, are placing increasing demands as well as challenges to existing database management systems. In this paper, we provide a novel algebraic approach based on…
In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using…
Querying tables with unstructured data is challenging due to the presence of text (or image), either embedded in the table or in external paragraphs, which traditional SQL struggles to process, especially for tasks requiring semantic…
Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be…
Solving arithmetic tasks is a simple and fundamental skill, yet modern Large Language Models (LLMs) have great difficulty with them. We introduce the Integrated Gated Calculator (IGC), a module that enables LLMs to perform arithmetic by…
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
Tabular reasoning involves interpreting natural language queries about tabular data, which presents a unique challenge of combining language understanding with structured data analysis. Existing methods employ either textual reasoning,…
Machine reading comprehension (MRC) that requires discrete reasoning involving symbolic operations, e.g., addition, sorting, and counting, is a challenging task. According to this nature, semantic parsing-based methods predict interpretable…
A foundation is investigated for the application of loosely structured data on the Web. This area is often referred to as Linked Data, due to the use of URIs in data to establish links. This work focuses on emerging W3C standards which…
Despite advances in language and speech technologies, no open-source system enables full speech-to-speech, multi-turn dialogue with integrated tool use and agentic reasoning. We introduce AURA (Agent for Understanding, Reasoning, and…
Retrieval-Augmented Generation (RAG) has demonstrated considerable effectiveness in open-domain question answering. However, when applied to heterogeneous documents, comprising both textual and tabular components, existing RAG approaches…
Automatic amortized resource analysis (AARA) is a type-based technique for inferring concrete (non-asymptotic) bounds on a program's resource usage. Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs.…
Numerical reasoning over text is a challenging task of Artificial Intelligence (AI), requiring reading comprehension and numerical reasoning abilities. Previous approaches use numerical reasoning programs to represent the reasoning process.…
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…