Related papers: On the equivalence between Implicit Regularization…

Architectural Design Rewriting (ADR, for short) is a rule-based formal framework for modelling the evolution of architectures of distributed systems. Rules allow ADR graphs to be refined. After equipping ADR with a simple logic, we equip…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Randomized experiments are considered the gold standard for estimating causal effects. However, out of the set of possible randomized assignments, some may be likely to produce poor effect estimates and misleading conclusions. Restricted…

Implicit Neural Representations (INRs) have emerged as promising surrogates for large 3D scientific simulations due to their ability to continuously model spatial and conditional fields, yet they face a critical fidelity-speed dilemma: deep…

How to improve discriminative feature learning is central in classification. Existing works address this problem by explicitly increasing inter-class separability and intra-class similarity, whether by constructing positive and negative…

Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…

We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…

In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional spacetime and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales,…

Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…

A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…

Sufficient dimension reduction (SDR) methods aim to identify a dimension reduction subspace (DRS) that preserves all the information about the conditional distribution of a response given its predictor. Traditional SDR methods determine 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…

Implicit neural representation has opened up new possibilities for inverse rendering. However, existing implicit neural inverse rendering methods struggle to handle strongly illuminated scenes with significant shadows and indirect…

The purpose of this work is to implement physics-based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. The ConvDecoder neural network was trained with a…

In this work, we develop a discretisation method for the mixed formulation of the magnetostatic problem supporting arbitrary orders and polyhedral meshes. The method is based on a global discrete de Rham (DDR) sequence, obtained by patching…

We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models SM_p for p>> 1. We explain how to compute the NS and Ramond fields conformal blocks in the leading order in 1/p and follow…

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

Image super-resolution (SR) has attracted increasing attention due to its wide applications. However, current SR methods generally suffer from over-smoothing and artifacts, and most work only with fixed magnifications. This paper introduces…