Related papers: Implicitization of Hypersurfaces
We propose a calculus for modeling implicit programming that supports first-class, overlapping, locally scoped, and higher-order instances with higher-kinded types. We propose a straightforward generalization of the well-established System…
Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Precise representations of 3D faces are beneficial to various computer vision and graphics applications. Due to the data discretization and model linearity, however, it remains challenging to capture accurate identity and expression clues…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
In the pursuit of explaining implicit regularization in deep learning, prominent focus was given to matrix and tensor factorizations, which correspond to simplified neural networks. It was shown that these models exhibit an implicit…
The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and the strong duality holds. We describe here two…
Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT…
We present two algorithms that compute the Newton polytope of a polynomial defining a hypersurface H in C^n using numerical computation. The first algorithm assumes that we may only compute values of f - this may occur if f is given as a…
Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…
It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In~this paper we will investigate in more detail the case of canal surfaces that are often…
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based…
Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…
In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…