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In this article, we develop a new approach to the Poincar\'e--Dulac normal form theory for a system of differential equations near a singular point. Using the continuous averaging method, we construct a normalization flow that moves a…

This thesis presents novel contributions in two primary areas: advancing the efficiency of generative models, particularly normalizing flows, and applying generative models to solve real-world computer vision challenges. The first part…

Normalizing flows model probability distributions by learning invertible transformations that transfer a simple distribution into complex distributions. Since the architecture of ResNet-based normalizing flows is more flexible than that of…

It is a common assumption that the activation of different layers in neural networks follow Gaussian distribution. This distribution can be transformed using normalization techniques, such as batch-normalization, increasing convergence…

Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in…

Convolutional neural networks (CNNs) have recently been very successful in a variety of computer vision tasks, especially on those linked to recognition. Optical flow estimation has not been among the tasks where CNNs were successful. In…

Deep convolutional neural networks (CNNs) have achieved breakthrough performance in many pattern recognition tasks such as image classification. However, the development of high-quality deep models typically relies on a substantial amount…

Recently, computational modeling has shifted towards the use of deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by…

It has previously been reported that the representation that is learned in the first layer of deep Convolutional Neural Networks (CNNs) is highly consistent across initializations and architectures. In this work, we quantify this…

Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…

Accurate pipe roughness estimation in large-scale water distribution networks is often hindered by the high cost of traditional field methods. This study investigates whether network partitioning, by utilizing hydraulic and graph-derived…

This study focuses on the novel application of a normalizing flow as a method of domain adaptation. Normalizing flows offer a way to transform data points between two different distributions. The present study investigates a method of…

In this paper, we propose Selective Output Smoothing Regularization, a novel regularization method for training the Convolutional Neural Networks (CNNs). Inspired by the diverse effects on training from different samples, Selective Output…

We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then…

Sampling-based motion planning is the predominant paradigm in many real-world robotic applications, but its performance is immensely dependent on the quality of the samples. The majority of traditional planners are inefficient as they use…

We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open…

Fair representation learning is an attractive approach that promises fairness of downstream predictors by encoding sensitive data. Unfortunately, recent work has shown that strong adversarial predictors can still exhibit unfairness by…

Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…