Related papers: Bisimulation maps in presheaf categories
The Bayesian brain hypothesis, predictive processing and variational free energy minimisation are typically used to describe perceptual processes based on accurate generative models of the world. However, generative models need not be…
This paper describes methods for comparative evaluation of the interpretability of models of high dimensional time series data inferred by unsupervised machine learning algorithms. The time series data used in this investigation were logs…
Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Symbolic execution is a powerful program analysis technique that allows for the systematic exploration of all program paths. Path explosion, where the number of states to track becomes unwieldy, is one of the biggest challenges hindering…
The topic of provable deep neural network robustness has raised considerable interest in recent years. Most research has focused on adversarial robustness, which studies the robustness of perceptive models in the neighbourhood of particular…
This review synthesizes advances in predictive processing within the sensory cortex. Predictive processing theorizes that the brain continuously predicts sensory inputs, refining neuronal responses by highlighting prediction errors. We…
We discuss the back and forth technique in the context of presheaf model theory. The essence of the back and forth technique lies in showing the relationship between various hierarchies which calibrate similarity between two models and,…
State-of-the-art saliency prediction methods develop upon model architectures or loss functions; while training to generate one target saliency map. However, publicly available saliency prediction datasets can be utilized to create more…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…
Autonomous vehicles (AVs) are now operating on public roads, which makes their testing and validation more critical than ever. Simulation offers a safe and controlled environment for evaluating AV performance in varied conditions. However,…
This paper studies the reduction (abstraction) of finite-state transition systems for control synthesis problems. We revisit the notion of alternating simulation equivalence (ASE), a more relaxed condition than alternating bisimulations, to…
Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages. It is known to be sound, and sometimes complete, with respect to context equivalence. In this paper we show that…
For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We…
This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of $\varepsilon$-perturbed bisimulation…
Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on social media platforms, and order book dynamics. This paper…
We propose that the sheaf condition on a presheaf of design spaces provides a mathematical model for multi-view consistency in the architecture of cyber-physical systems (CPS). In model-based systems engineering, multiple engineering views…
A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty.…
Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living…