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By a classical principle of analysis, sufficiently thin subsequences of general sequences of functions behave like sequences of independent random variables. This observation not only explains the remarkable properties of lacunary…

Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and…

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…

The task of learning to map an input set onto a permuted sequence of its elements is challenging for neural networks. Set-to-sequence problems occur in natural language processing, computer vision and structure prediction, where…

In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…

Pooling multiple neuroimaging datasets across institutions often enables improvements in statistical power when evaluating associations (e.g., between risk factors and disease outcomes) that may otherwise be too weak to detect. When there…

Most convolutional neural networks use some method for gradually downscaling the size of the hidden layers. This is commonly referred to as pooling, and is applied to reduce the number of parameters, improve invariance to certain…

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…

Traditional set prediction models can struggle with simple datasets due to an issue we call the responsibility problem. We introduce a pooling method for sets of feature vectors based on sorting features across elements of the set. This can…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

The Anscombe transform offers an approximate conversion of a Poisson random variable into a Gaussian one. This transform is important and appealing, as it is easy to compute, and becomes handy in various inverse problems with Poisson noise…

Conventional machine learning methods are predominantly designed to predict outcomes based on a single data type. However, practical applications may encompass data of diverse types, such as text, images, and audio. We introduce…

Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…

Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of…

In the past few years, deep generative models, such as generative adversarial networks \autocite{GAN}, variational autoencoders \autocite{vaepaper}, and their variants, have seen wide adoption for the task of modelling complex data…

Feature pooling layers (e.g., max pooling) in convolutional neural networks (CNNs) serve the dual purpose of providing increasingly abstract representations as well as yielding computational savings in subsequent convolutional layers. We…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…