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Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the…
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…
Despite continued advancement in machine learning algorithms and increasing availability of large data sets, there is still no universally acceptable solution for automatic sleep staging of human sleep recordings. One reason is that a…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…
Neural networks have achieved remarkable success in many cognitive tasks. However, when they are trained sequentially on multiple tasks without access to old data, their performance on early tasks tend to drop significantly. This problem is…
It is well-known that in inverse problems, end-to-end trained networks overfit the degradation model seen in the training set, i.e., they do not generalize to other types of degradations well. Recently, an approach to first map images…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime…
In ghost imaging scheme, an illuminated light is split into test and reference beams which pass through two different optical systems respectively and an image is constructed by the second-order correlation between the two light beams.…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
We investigate modeling coreference resolution under a fixed memory constraint by extending an incremental clustering algorithm to utilize contextualized encoders and neural components. Given a new sentence, our end-to-end algorithm…
Deep neural networks have been proven effective in a wide range of tasks. However, their high computational and memory costs make them impractical to deploy on resource-constrained devices. To address this issue, quantization schemes have…
Initialization of parameters in deep neural networks has been shown to have a big impact on the performance of the networks (Mishkin & Matas, 2015). The initialization scheme devised by He et al, allowed convolution activations to carry a…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
Autoencoders have been extensively used in the development of recent anomaly detection techniques. The premise of their application is based on the notion that after training the autoencoder on normal training data, anomalous inputs will…
We prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work Erath and Praetorius [SIAM J. Numer. Anal., 54 (2016), pp.…