相关论文: On the equivalence between Implicit Regularization…

A Lorentz and gauge symmetry preserving regularization method is discussed in four dimension based on momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom of shift of the loop momentum to define the…

Continual learning (CL) remains one of the long-standing challenges for deep neural networks due to catastrophic forgetting of previously acquired knowledge. Although rehearsal-based approaches have been fairly successful in mitigating…

High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular classes of convex ones and concave ones. A long debate has been on whether one class dominates…

Implicit neural representation (INR) has become the standard approach for arbitrary-scale image super-resolution (ASSR). To date, no empirical study has systematically examined the effectiveness of existing methods, nor investigated the…

The distributed recursion (DR) algorithm is an effective method for solving the pooling problem that arises in many applications. It is based on the well-known P-formulation of the pooling problem, which involves the flow and quality…

Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by…

This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems,…

Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…

Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…

Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Comutative (NC) \phi^4 scalar theory in 4-dimensions, we explictly analyze, to one-loop, the IR and UV divergences of non-planar diagrams having quadratic…

Compressed sensing (CS) methods in magnetic resonance imaging (MRI) offer rapid acquisition and improved image quality but require iterative reconstruction schemes with regularization to enforce sparsity. Regardless of the difficulty in…

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly…

The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…

We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…

We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…

There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…

Contrastive Reinforcement Learning (CRL) provides a promising framework for extracting useful structured representations from unlabeled interactions. By pulling together state-action pairs and their corresponding future states, while…

We introduce a novel Pseudo-Negative Regularization (PNR) framework for effective continual self-supervised learning (CSSL). Our PNR leverages pseudo-negatives obtained through model-based augmentation in a way that newly learned…

Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized…