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.
The paper introduces various canonical parameterizations for 2D-curved shapes.
There are currently two parameterizations used to derive fixed kernels corresponding to infinite width neural networks, the NTK (Neural Tangent Kernel) parameterization and the naive standard parameterization. However, the extrapolation of both of these parameterizations to infinite width is problematic. The standard p…
New parameterization for -knots simplifies their study.
Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant str…
The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first geometrical application, every surface that admits a conformal polynomic paramet…
Polynomially parameterizes knots and spheres, proving analogous results.
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data, dense 3D surface meshes are common nowadays. While meshes with higher resolution …
Two novel algorithms for conformal parameterization of multiply-connected surfaces.
The paper analyzes how over-parameterization affects GD convergence in matrix sensing problems.
Novel framework for policy optimization with general parameterization and linear convergence.
We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
Develops a method for conformal parameterization of point clouds without fixed boundaries.
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
Least squares regression shows unexpected double descent in under-parameterized models.
The paper proposes methods for volumetric parameterization of 3D solid manifolds.
This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the moduli space (2) Thurston's parameterization of the moduli space using grafting (3) …
Study shows how over-parameterized classifiers can still perform well on noisy data.
Improves adaptivity in sequence models by over-parameterizing.
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced. Applications of ML to emulate existing parameterizations, to develop new parameteri…
Gradient descent recovers low-rank matrices from corrupted measurements with double over-parameterization.
New method improves deep learning models robustness to label noise.
We study the pull-back of the 2-parameter family of quotient elastic metrics introduced in Mio-Srivastava-Joshi on the space of arc-length parameterized loops. This point of view has the advantage of concentrating on the manifold of arc-length parameterized curves, which is a very natural manifold when the analysis of …
Gradient descent slows significantly in over-parameterized single neuron learning.
New framework for better mapping of surfaces onto ellipsoids.
This paper explores adaptive methods in over-parameterized linear regression.
New methods solve tensor-on-tensor regression with unknown rank, revealing benefits of over-parameterization.
Local PCA detects intrinsic parameterization of complex thermo-chemical state-spaces.
Local convergence theory for mildly over-parameterized neural nets.
Small parameterized towers improve multi-task learning efficiency and generalization.
In this paper, we introduce a parameterized discrete curvature (-curvature) for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical discrete curvature. A discrete uniformization theorem is established for the parameterized discrete curvature, which generalizes the discrete uni…
Empirical studies show that gradient-based methods can learn deep neural networks (DNNs) with very good generalization performance in the over-parameterization regime, where DNNs can easily fit a random labeling of the training data. Very recently, a line of work explains in theory that with over-parameterization and p…
Novel approach analyzes ReLU networks' training dynamics and proposes GmP for improved optimization.
In this paper we propose a hybrid architecture of actor-critic algorithms for reinforcement learning in parameterized action space, which consists of multiple parallel sub-actor networks to decompose the structured action space into simpler action spaces along with a critic network to guide the training of all sub-acto…
This work improves the lottery ticket hypothesis by reducing over-parameterization requirement.
This paper presents a method to compute the {\it quasi-conformal parameterization} (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain onto a punctured disk associated with a given Beltrami differential. The Beltrami differential, which me…
Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm for computing the disk conformal parameterization of simply-connected open surfac…
Developed an ellipsoidal density-equalizing map for genus-0 closed surfaces.
Under-parameterization hinders deep RL's efficiency.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the…
The paper explores three methods to assign a metric to shape spaces.
We introduce a method for constructing skills capable of solving tasks drawn from a distribution of parameterized reinforcement learning problems. The method draws example tasks from a distribution of interest and uses the corresponding learned policies to estimate the topology of the lower-dimensional piecewise-smooth…
A parameterization that is a modified version of a previous work is proposed for the returns and correlation matrix of financial time series and its properties are studied. This parameterization allows easy introduction of non-stationarity and it shows several of the characteristics of the true, observed realizations, …
Over-parameterization makes optimization easier for simple neural networks, even with minor extra neurons.
The paper shows how the generalization curve can have multiple peaks, influenced by data and learning algorithm biases.
We give a parameterization of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid using Jacobi's elliptic functions. This parameterization avoids some problems present in the original depiction of these surfaces.
DEQs converge to optimal solutions with mild over-parameterization.
Over-parameterized CNNs show U-shaped test risk with depth increase.