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We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…

The Linear Threshold Model (LTM) is widely used to study the propagation of collective behaviors as complex contagions. However, its dependence on discrete states and timesteps restricts its ability to capture the multiple time-scales…

Large reasoning models (LRMs) generate extended solutions, yet it remains unclear whether these traces reflect substantive internal computation or merely verbosity and overthinking. Although recent hidden-state analyses suggest that…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

We show how Markov mixed membership models (MMMM) can be used to predict the degradation of assets. We model the degradation path of individual assets, to predict overall failure rates. Instead of a separate distribution for each hidden…

We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

Motion prediction is a challenging task for autonomous vehicles due to uncertainty in the sensor data, the non-deterministic nature of future, and complex behavior of agents. In this paper, we tackle this problem by representing the scene…

A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…

Methods for out-of-distribution (OOD) detection that scale to 3D data are crucial components of any real-world clinical deep learning system. Classic denoising diffusion probabilistic models (DDPMs) have been recently proposed as a robust…

Motivated by machine learning applications in networks of sensors, internet-of-things (IoT) devices, and autonomous agents, we propose techniques for distributed stochastic convex learning from high-rate data streams. The setup involves a…

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of…

This paper deals with a distributed state estimation problem for jointly observable multi-agent systems operated over various time-varying network topologies. The results apply when the system matrix of the system to be observed contains…

In this work, we extend the idea of Quantum Markov chains [S. Gudder. Quantum Markov chains. J. Math. Phys., 49(7), 2008] in order to propose Quantum Hidden Markov Models (QHMMs). For that, we use the notions of Transition Operation…

Observations from dynamical systems often exhibit irregularities, such as censoring, where values are recorded only if they fall within a certain range. Censoring is ubiquitous in practice, due to saturating sensors, limit-of-detection…

In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and…

We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations. Stochastically driven flow models are…

Out-of-time-order correlators (OTOCs) have proven to be a useful tool for studying thermalisation in quantum systems. In particular, the exponential growth of OTOCS, or scrambling, is sometimes taken as an indicator of chaos in quantum…