Related papers: Systematic Analytic Regularization in $\varphi^4$ …
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
A range of defense methods have been proposed to improve the robustness of neural networks on adversarial examples, among which provable defense methods have been demonstrated to be effective to train neural networks that are certifiably…
Deep Neural Networks (DNNs) generalization is known to be closely related to the flatness of minima, leading to the development of Sharpness-Aware Minimization (SAM) for seeking flatter minima and better generalization. In this paper, we…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…
The analysis of ocean surface is widely performed using synthetic aperture radar (SAR) imagery as it yields information for wide areas under challenging weather conditions, during day or night, etc. Speckle noise constitutes however the…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Deep learning models have been successfully used in computer vision and many other fields. We propose an unorthodox algorithm for performing quantization of the model parameters. In contrast with popular quantization schemes based on…
Improving generalization is one of the main challenges for training deep neural networks on classification tasks. In particular, a number of techniques have been proposed, aiming to boost the performance on unseen data: from standard data…
We introduce an approach for calculating the quantum loop corrections in the $\phi^4$ theory. Differential regularization and background-field method are essential tools and are used to calculate the effective action of the theory to…
In an effort to improve generalization in deep learning and automate the process of learning rate scheduling, we propose SALR: a sharpness-aware learning rate update technique designed to recover flat minimizers. Our method dynamically…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
In this article, the problem of identifying the source term in transport processes given by a complete parabolic equation is studied mathematically from noisy measurements taken at an arbitrary fixed time. The problem is solved analytically…
In this paper, SAR image reconstruction with joint phase error estimation (autofocusing) is formulated as an inverse problem. An optimization model utilising a sparsity-enforcing Cauchy regularizer is proposed, and an alternating…
Precisely modeling complex systems like cyber-physical systems is challenging, which often render model-based system verification techniques like model checking infeasible. To overcome this challenge, we propose a method called LAR to…
Given a compact linear operator $\K$, the (pseudo) inverse $\K^\dagger$ is usually substituted by a family of regularizing operators $\R_\alpha$ which depends on $\K$ itself. Naturally, in the actual computation we are forced to approximate…
Explicit analytic expressions for the electron self-energy and the vertex correction in quantum electrodynamics are derived at one loop using the recently proposed regularization scheme known as denominator regularization, assisted by its…
This paper focuses on linear regression models with non-conjugate sparsity-inducing regularizers such as lasso and group lasso. Although the empirical Bayes approach enables us to estimate the regularization parameter, little is known on…
We propose modifications to the functional form of the SCAN density functional to eliminate numerical instabilities. This is necessary to allow reliable, automatic generation of pseudopotentials (including PAW potentials). The regularized…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…