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Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field…

We consider a self-supervised approach to anomaly detection in tabular data. Random transformations are applied to the data, and then each transformation is identified based on its output. These predicted transformations are used to…

The property of the conformal algebra to contain the Schr\"odinger algebra in one less space dimension is extended to the supersymmetric case. More precisely, we determine the counterpart of any field theory admissible super conformal…

We provide new adaptive first-order methods for constrained convex optimization. Our main algorithms AdaACSA and AdaAGD+ are accelerated methods, which are universal in the sense that they achieve nearly-optimal convergence rates for both…

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…

We continue our study of the AGT correspondence between instanton counting on C^2/Z_p and Conformal field theories with the symmetry algebra A(r,p). In the cases r=1, p=2 and r=2, p=2 this algebra specialized to: A(1,2)=H+sl(2)_1 and…

In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The proposed method integrates deep adaptive sampling…

Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…

We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

The adaptive gradient online learning method known as AdaGrad has seen widespread use in the machine learning community in stochastic and adversarial online learning problems and more recently in deep learning methods. The method's…

Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to some random subspace of the parameters, constructing and…

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…

Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field…

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…