Related papers: Automatic Differentiation: Inverse Accumulation Mo…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…
The two-dimensional Jacobian Conjecture says that a $\mathbb{C}$-algebra endomorphism $F:\mathbb{C}[x,y] \to \mathbb{C}[x,y]$ that has an invertible Jacobian is an automorphism. We show that if a $\mathbb{C}$-algebra endomorphism…
The Jacobian Conjecture uses the equation $det(Jac(F))\in k^*$, which is a very short way to write down many equations putting restrictions on the coefficients of a polynomial map $F$. In characteristic $p$ these equations do not suffice to…
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…
This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…
We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the…
We propose a procedure to reconstruct characteristic features of an unknown stochastic system from the long-time full counting statistics of some of the system's transitions that are monitored by a detector. The full counting statistics is…
The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few.…
We prove that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an n-1-element p-basis of its ring of constants. In the case of two variables we characterize these…
Newton-Raphson controller is a powerful prediction-based variable gain integral controller. Basically, the classical model-based Newton-Raphson controller requires two elements: the prediction of the system output and the derivative of the…
Understanding why gradient-based training in deep networks exhibits strong implicit bias remains challenging, in part because tractable singular-value dynamics are typically available only for balanced deep linear models. We propose an…
The paper deals with the distribution of singular values of the input-output Jacobian of deep untrained neural networks in the limit of their infinite width. The Jacobian is the product of random matrices where the independent rectangular…
Change-of-variables (CoV) formulas allow to reduce complicated probability densities to simpler ones by a learned transformation with tractable Jacobian determinant. They are thus powerful tools for maximum-likelihood learning, Bayesian…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
The direct sampling method proposed by Walker et al. (JCGS 2011) can generate draws from weighted distributions possibly having intractable normalizing constants. The method may be of interest as a useful tool in situations which require…
Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…
We describe the relation between block Jacobi matrices and minimization problems for discrete time optimal control problems. Using techniques developed for the continuous case, we provide new algorithms to compute spectral invariants of…