Related papers: Janossy Pooling: Learning Deep Permutation-Invaria…

Inspired by the Hardy-Littlewood maximal function, we propose a novel pooling strategy which is called maxfun pooling. It is presented both as a viable alternative to some of the most popular pooling functions, such as max pooling and…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…

Filtering and smoothing with a generalised representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using…

We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…

Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…

Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce…

Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization…

We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling…

Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed…

We introduce a novel matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a hierarchical, multi-layer, correlational architecture designed for matching images and was inspired by…

We introduce a parametric form of pooling, based on a Gaussian, which can be optimized alongside the features in a single global objective function. By contrast, existing pooling schemes are based on heuristics (e.g. local maximum) and have…

We present a generative model that is defined on finite sets of exchangeable, potentially high dimensional, data. As the architecture is an extension of RealNVPs, it inherits all its favorable properties, such as being invertible and…

Palm distributions play a central role in the study of point processes and their associated summary statistics. In this paper, we characterize the Palm distributions of the superposition of independent point processes, establishing a simple…

Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional…

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…

This work addresses flexibility in deep learning by means of transductive reasoning. For adaptation to new data and tasks, e.g., in continual learning, existing methods typically involve tuning learnable parameters or complete re-training…

For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest…

In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…