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Safe and reliable state estimation techniques are a critical component of next-generation robotic systems. Agents in such systems must be able to reason about the intentions and trajectories of other agents for safe and efficient motion…

We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb R^d)$. In other words, we establish a…

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…

Modern robotic perception is highly dependent on neural networks. It is well known that neural network-based perception can be unreliable in real-world deployment, especially in difficult imaging conditions. Out-of-distribution detection is…

Flow matching has emerged as a powerful generative framework, with recent few-step methods achieving remarkable inference acceleration. However, we identify a critical yet overlooked limitation: these models suffer from severe diversity…

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise.…

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth…

A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. To date, only limited progress has been made understanding…

We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…

Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Diffusion models (DMs) have emerged as powerful generative models for solving inverse problems, offering a good approximation of prior distributions of real-world image data. Typically, diffusion models rely on large-scale clean signals to…

The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior…

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…

Residual connections and normalization layers have become standard design choices for graph neural networks (GNNs), and were proposed as solutions to the mitigate the oversmoothing problem in GNNs. However, how exactly these methods help…

Recently proposed normalizing flow models such as Glow have been shown to be able to generate high quality, high dimensional images with relatively fast sampling speed. Due to their inherently restrictive architecture, however, it is…

Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work we provide sharp results for the implicit regularization…

Convolutional rectifier networks, i.e. convolutional neural networks with rectified linear activation and max or average pooling, are the cornerstone of modern deep learning. However, despite their wide use and success, our theoretical…

Diffusion and flow-based generative models have shown strong potential for image restoration. However, image denoising under unknown and varying noise conditions remains challenging, because the learned vector fields may become inconsistent…