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Semantic representations can be framed as a structured, dynamic knowledge space through which humans navigate to retrieve and manipulate meaning. To investigate how humans traverse this geometry, we introduce a framework that represents…
Representing molecular structures effectively in chemistry remains a challenging task. Language models and graph-based models are extensively utilized within this domain, consistently achieving state-of-the-art results across an array of…
The design of complex man-made systems mostly involves a conceptual modeling phase; therefore, it is important to ensure an appropriate analysis method for these models. A key concept for such analysis is the development of a diagramming…
Recently, large language models (LLMs) have been widely researched in the field of graph machine learning due to their outstanding abilities in language comprehension and learning. However, the significant gap between natural language tasks…
In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…
Large language model (LLM) tokenizers act as structured compressors: by mapping text to discrete token sequences, they determine token count (and thus compute and context usage) and the statistical structure seen by downstream models.…
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…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
In complex engineering systems, the dependencies among components or development activities are often modeled and analyzed using Design Structure Matrix (DSM). Reorganizing elements within a DSM to minimize feedback loops and enhance…
Large language models (LLMs) have demonstrated remarkable mathematical capabilities, largely driven by chain-of-thought (CoT) prompting, which decomposes complex reasoning into step-by-step solutions. This approach has enabled significant…
Machine learning for tabular data remains constrained by poor schema generalization, a challenge rooted in the lack of semantic understanding of structured variables. This challenge is particularly acute in domains like clinical medicine,…
A prevalent theme throughout science and engineering is the ongoing paradigm shift away from isolated systems towards open and interconnected systems. Port-Hamiltonian theory developed as a synthesis of geometric mechanics and network…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
Engineering projects for railway infrastructure typically involve many subsystems which need consistent views of the planned and built infrastructure and its underlying topology. Consistency is typically ensured by exchanging and verifying…
Both topos theory and automata theory are known for their multi-faceted nature and relationship with topology, algebra, logic, and category theory. This paper aims to clarify the topos-theoretic aspects of automata theory, particularly…
Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of…
The Unified Modeling Language (UML) is rapidly emerging as a de-facto standard for modelling OO systems. Given this role, it is imperative that the UML have a well- defined, fully explored semantics. Such semantics is required in order to…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…