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Hybrid programs combine digital control with differential equations, and naturally appear in a wide range of application domains, from biology and control theory to real-time software engineering. The entanglement of discrete and continuous…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
The past decade has witnessed a surge of endeavors in statistical inference for high-dimensional sparse regression, particularly via de-biasing or relaxed orthogonalization. Nevertheless, these techniques typically require a more stringent…
Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…
This work targets the development of an efficient abstraction method for formal analysis and control synthesis of discrete-time stochastic hybrid systems (SHS) with linear dynamics. The focus is on temporal logic specifications, both over…
Many important functional and security properties--including non-interference, determinism, and generalized non-interference (GNI)--are hyperproperties, i.e., properties relating multiple executions of a program. Existing separation logics…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for…
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
This paper addresses a novel task of anticipating 3D human-object interactions (HOIs). Most existing research on HOI synthesis lacks comprehensive whole-body interactions with dynamic objects, e.g., often limited to manipulating small or…
Most existing interpretable methods explain a black-box model in a post-hoc manner, which uses simpler models or data analysis techniques to interpret the predictions after the model is learned. However, they (a) may derive contradictory…
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure.…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
Human-object interaction (HOI) detection aims to comprehend the intricate relationships between humans and objects, predicting $<human, action, object>$ triplets, and serving as the foundation for numerous computer vision tasks. The…
In the last two decades, Interactive White Boards (IWBs) have been widely available as a pedagogic tool. The usability of these boards for teaching disciplines where complex drawings are needed, we consider debatable in multiple regards. In…
Human-Object Interaction (HOI) detection is a fundamental task in image understanding. While deep-learning-based HOI methods provide high performance in terms of mean Average Precision (mAP), they are computationally expensive and opaque in…
Splitting is a method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretization. In this paper, our goal is to use temporal splitting…