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Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
We propose a new structure for the complex-valued autoencoder by introducing additional degrees of freedom into its design through a widely linear (WL) transform. The corresponding widely linear backpropagation algorithm is also developed…
Inverse problem is ubiquitous in science and engineering, and Bayesian methodologies are often used to infer the underlying parameters. For high dimensional temporal-spatial models, classical Markov chain Monte Carlo (MCMC) methods are…
We study stochastic gradient descent {\em without replacement} (\sgdwor) for smooth convex functions. \sgdwor is widely observed to converge faster than true \sgd where each sample is drawn independently {\em with replacement}…
The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
This paper contributes to the study of a new and remarkable family of stochastic processes that we will term class $\Sigma^{r}(H)$. This class is potentially interesting because it unifies the study of two known classes: the class…
The hyperbolic spin chain is used to elucidate the notion of spontaneous symmetry breaking for a non-amenable internal symmetry group, here SO(1,2). The noncompact symmetry is shown to be spontaneously broken -- something which would be…
Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the…
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…
We formulate $\lambda$-deformed $\sigma$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter $\lambda$ and for…
De-homogenization is becoming an effective method to significantly expedite the design of high-resolution multiscale structures, but existing methods have thus far been confined to simple static compliance minimization. There are two…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…
Automatically determining the number of intrinsic mode functions (IMFs) and their center frequencies in Variational Mode Decomposition (VMD) remains an open mathematical challenge. Existing methods rely on heuristic settings,…
In this paper, a generic extension of variational mode decomposition (VMD) algorithm for multivariate or multichannel data sets is presented. We first define a model for multivariate modulated oscillations that is based on the presence of a…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
Feature detection is an important procedure for image matching, where unsupervised feature detection methods are the detection approaches that have been mostly studied recently, including the ones that are based on repeatability requirement…
We study Gaussian random functions on the complex plane whose stochastics are invariant under the Weyl-Heisenberg group (twisted stationarity). The theory is modeled on translation invariant Gaussian entire functions, but allows for…