A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
ResNets with depth and nonlinearity avoid bad local minima.
This paper analyzes a simplified strategy for nonlinear control using local linear models and iLQR updates.
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the $\sk$-Yamabe problem for locally conformal flat manifolds when .
In this paper we establish existence and compactness of solutions to a general fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.
The theory of locally anisotropic superspaces (supersymmetric generalizations of various types of Kaluza--Klein, Lagrange and Finsler spaces) is laid down. In this framework we perform the analysis of construction of the supervector bundles provided with nonlinear and distinguished connections and metric structures. Tw…
Study shows local rigidity for hyperbolic cusped manifolds under certain metric perturbations.
This paper introduces a new method for semi-supervised learning on high dimensional nonlinear manifolds, which includes a phase of unsupervised basis learning and a phase of supervised function learning. The learned bases provide a set of anchor points to form a local coordinate system, such that each data point on…
This paper extends the single index model to handle nonlinear relationships.
Localizes curvature estimates for evolving hypersurfaces under various flows.
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from estimates. Also, the method is flexible and can be applied to a large class of equations.
Neural networks simplify uncertainty quantification of locally nonlinear systems.
Calculates local Granger causality for Gaussian and nonlinear systems.
New approach learns neural network parameters by balancing local objectives and data propagation constraints.
The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlin…
Higher order anisotropic superspaces are constructed as generalized vector superbundles provided with compatible nonlinear connection, distinguished connection and metric structures.
We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza--Klein type) spaces. The problem of definition of spinors on gen…
We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an aux…
GraphLIME explains GNN models by selecting key features locally.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
In this paper, we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high-dimensional observations. We present a metric based on local applications of canonical correlation analysis (CCA) and incorporate it in a kernel-based manifold learning technique.We show that this metr…
We define and study the invariant linear and nonlinear horizontal double complexes of a local Lie group.
Automated denoising score matching handles nonlinear diffusion processes.
New method tests independence with single nonstationary time series.
In deep learning, \textit{depth}, as well as \textit{nonlinearity}, create non-convex loss surfaces. Then, does depth alone create bad local minima? In this paper, we prove that without nonlinearity, depth alone does not create bad local minima, although it induces non-convex loss surface. Using this insight, we greatl…
A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernel-based orthogonal m…
New local method solves Yamabe problems on compact and non-compact manifolds.
The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved that all the nonsingular pairs of compatible metrics of constant Riemannian curvat…
New algorithm learns nonlinear phenomena from noisy local measurements without data exchange.
Study improves understanding of solutions to complex equations in geometry.
Study of Dirac equation with non-local nonlinearity on spheres.
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
New techniques improve the accuracy of identifying nonlinear systems from noisy data.
LNPE enhances local connections in embeddings using extended neighbor propagation.
We present an introduction to the geometry of higher order vector and co--vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by higher order nonlinear con…
New method combines variational inference with particle filtering for nonlinear data.
Breaks down complex nonlinear dynamics into simpler components.
We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains , with non-smooth boundary, in possibly non-compact manifolds. Assuming is a submanifold with corners, or is compact and locally convex with rough boundary, we prove that the restrictio…
Study finds lower bounds for solutions on Riemannian orbifolds.
Median activation functions improve GNNs by capturing local graph signal behavior.
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schrödinger equation. In this paper, we present its discrete analogue, namely, a model of defor…
The main purposes of this article are to extend our previous results on homogeneous sprays to arbitrary (generalized) sprays, to show that locally diffeomorphic exponential maps can be defined for any (generalized) spray, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. I…
Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.
We investigate the loss surface of neural networks. We prove that even for one-hidden-layer networks with "slightest" nonlinearity, the empirical risks have spurious local minima in most cases. Our results thus indicate that in general "no spurious local minima" is a property limited to deep linear networks, and insigh…
This paper presents a locally decoupled network parameter learning with local propagation. Three elements are taken into account: (i) sets of nonlinear transforms that describe the representations at all nodes, (ii) a local objective at each node related to the corresponding local representation goal, and (iii) a local…
The paper studies equations in conformal geometry with gradient and existence results.
Study horizontal discs in fat distributions, proving their existence.
We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary estimates directly from boundary estimates. In particular, the result is a generalization of the work by Escobar.