Related papers: A Gaussian Comparison Theorem for Training Dynamic…
We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…
We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…
We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…
We study the dynamics of on-line learning in large perceptrons, for the case of training sets with a structural bias of the input vectors, by deriving exact and closed macroscopic dynamical laws using non-equilibrium statistical mechanical…
This paper establishes the theoretical foundations for the asymptotic separability of Gaussian Mixture Models (GMMs) in high dimensions by extending the classical Feldman-H\'ajek theorem. We first prove that a countable mixture of Gaussian…
A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This…
Learning motion policies from expert demonstrations is an essential paradigm in modern robotics. While end-to-end models aim for broad generalization, they require large datasets and computationally heavy inference. Conversely, learning…
Recently, Gaussian processes have been used to model the vector field of continuous dynamical systems, referred to as GPODEs, which are characterized by a probabilistic ODE equation. Bayesian inference for these models has been extensively…
Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…
Maneuvering target tracking is a challenging problem for sensor systems because of the unpredictability of the targets' motions. This paper proposes a novel data-driven method for learning the dynamical motion model of a target.…
Score matching has become a central training objective in modern generative modeling, particularly in diffusion models, where it is used to learn high-dimensional data distributions through the estimation of score functions. Despite its…
Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved,…
Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…
In probabilistic classification, a discriminative model based on the softmax function has a potential limitation in that it assumes unimodality for each class in the feature space. The mixture model can address this issue, although it leads…
We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity. In particular, this result explains the counterintuitive phenomenon that…
Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…
Training deep learning neural networks often requires massive amounts of computational ressources. We propose to sequentially monitor network predictions to trigger retraining only if the predictions are no longer valid. This can reduce…
Systematic Generalization refers to a learning algorithm's ability to extrapolate learned behavior to unseen situations that are distinct but semantically similar to its training data. As shown in recent work, state-of-the-art deep learning…
We present a deep learning model for data-driven simulations of random dynamical systems without a distributional assumption. The deep learning model consists of a recurrent neural network, which aims to learn the time marching structure,…