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Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand…

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and…

This thesis pretends to be another step in the development of numerical research in disordered systems. Specifically, we will focus on spin glasses which have demonstrated to be a fertile field from both, experimental and theoretical…

We propose a connection between self-similar, focusing dynamics in nonlinear partial differential equations (PDEs) and macroscopic dynamic features of the glass transition. In particular, we explore the divergence of the appropriate…

Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…

A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…

The use of learned dynamics models, also known as world models, can improve the sample efficiency of reinforcement learning. Recent work suggests that the underlying causal graphs of such dynamics models are sparsely connected, with each of…

Topic models and all their variants analyse text by learning meaningful representations through word co-occurrences. As pointed out by Williamson et al. (2010), such models implicitly assume that the probability of a topic to be active and…

Motivated by results of the topological theory of glasses accounting for geometric frustration, we develop the simplest possible continuum mechanical model of defect dynamics in metallic glasses that accounts for topological, energetic, and…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

In model-based reinforcement learning, generative and temporal models of environments can be leveraged to boost agent performance, either by tuning the agent's representations during training or via use as part of an explicit planning…

We summarize studies of growing lengths in different aging systems. The article is structured as follows. We recall the definition of a number of observables, typically correlations and susceptibilities, that give access to dynamic and…

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…

We present a many body approach for non-equilibrium behavior and self-generated glassiness in strongly correlated quantum systems. It combines the dynamical mean field theory of equilibrium systems with the replica theory for classical…

Three properties of the Edwards-Anderson model with mobile bonds are investigated which are characteristic of kinetic glasses. First is two-time relaxation in aged systems, where a significant difference is observed between spin and bond…

The static and dynamic susceptibilities for a general class of mean field random orthogonal spherical spin glass models are studied. We show how the static and dynamical properties of the linear and nonlinear susceptibilities depend on the…

We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms.…

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…

Generative models of brain activity have been instrumental in testing hypothesized mechanisms underlying brain dynamics against experimental datasets. Beyond capturing the key mechanisms underlying spontaneous brain dynamics, these models…