We construct a finitely presented group with non-quadratic Dehn function majorizable by a quadratic function on arbitrary long intervals.
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29 results for “Non-quadratic”
Paper develops methods for non-quadratic loss low-rank matrix recovery.
problem Recovery of low-rank matrices with non-quadratic losses.
method Projected gradient method with a regularity projection oracle.
result Projected gradient method converges globally and linearly.
New non-quadratic hypersurfaces found for higher dimensions.
problem Bernstein problem for affine maximal type hypersurfaces in higher dimensions.
method Constructing non-quadratic hypersurfaces for N>=3, θ\in(1/2,(N-1)/N).
result Found non-quadratic affine maximal type hypersurfaces for N>=3.
Study uses deep learning for efficient hedging of long-term financial derivatives.
problem Optimizing hedging strategies for long-term financial derivatives with various penalties and stylized facts.
method Deep reinforcement learning applied to neural networks optimizing hedging policies with quadratic and non-quadratic penalties.
result Non-quadratic global hedging policies result in significantly smaller downside risk metrics and significant hedging gains.
We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus , , namely codimension one foliations, flows, and the so-called non-quadratic foliations. We show in particular that non-quadratic foliations are rigid, in the sense that they do not admit…
New non-quadratic Euclidean complete affine maximal type hypersurfaces found for N≥2, θ∈(0,(N-1)/N].
problem Bernstein problem for affine maximal type equation.
method Constructing explicit examples of hypersurfaces.
result Found new non-quadratic Euclidean complete affine maximal type hypersurfaces for N≥2, θ∈(0,(N-1)/N].
We introduce a model for the dynamics of stock prices based on a non quadratic path integral. The model is a generalization of Ilinski's path integral model, more precisely we choose a different action, which can be tuned to different time scales. The result is a model with a very small number of parameters that provid…
Mapping Among Line Elementsmath.DG
Paper maps Hamiltonians and line elements in manifolds.
problem Mapping among generalized Hamiltonians and line elements.
method Constructing Calabi's Riemannian Line Elements and solving matrix Riccati equations.
result Analytical and exact solutions of mapping between manifolds.
Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.
problem Analyzing the growth of derivative maxima for interval diffeomorphisms with parabolic fixed points.
method Examining diffeomorphisms with only parabolic fixed points, focusing on tangency and repelling behavior.
result Maximal growth of derivative maxima is exactly quadratic for diffeomorphisms with a non-quadratic tangency to identity at a repelling fixed point.
Locally classifies 4D spherical symmetric Finsler spaces.
problem Classifying 4D spherical symmetric Finsler spaces.
method Local classification of pseudo-Finsler Berwald structures.
result Six classes of non-Riemannian SO(3)-symmetric pseudo-Finsler Berwald functions.
It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of constant phase, their points move along lines which are called rays. In non-homogeneous…
We introduce a simple algorithm, True Asymptotic Natural Gradient Optimization (TANGO), that converges to a true natural gradient descent in the limit of small learning rates, without explicit Fisher matrix estimation. For quadratic models the algorithm is also an instance of averaged stochastic gradient, where the par…
We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic functions, we provide an explicit asymptotic expansion of the moments of the averaged S…
A natural parametrization of smooth projective plane curves which tolerates the presence of sextactic points is the Forsyth-Laguerre parametrization. On a closed projective plane curve, which necessarily contains sextactic points, this parametrization is, however, in general not periodic. We show that by the introducti…
SAM optimizes deep networks by oscillating between sides of the minimum.
problem Improving performance of deep networks.
method Gradient-based optimization method that oscillates between sides of the minimum.
result SAM effectively performs gradient descent on the spectral norm of the Hessian, encouraging drift towards wider minima.
Many introductory courses in quantum mechanics include Feynman's time-slicing definition of the path integral, with a complete derivation of the propagator in the simplest of cases. However, attempts to generalize this, for instance to non-quadratic potentials, encounter formidable analytic issues in showing the succes…
New algorithm accelerates single-pass SGD for generalized linear prediction.
problem Improving single-pass non-quadratic stochastic optimization.
method Data-dependent proximal method incorporating dual-momentum acceleration.
result Momentum acceleration resolves open problem in streaming setting.
Generative approach speeds hyperparameter tuning for machine learning models.
problem Computational infeasibility of cross-validation and difficulty of fully Bayesian hyper-parameter learning.
method Combines optimization-based approximations and amortization techniques.
result Rapid evaluation of hyper-parameters over grids or ranges, supporting predictive tuning and uncertainty quantification.
On Convergence of Distributed Approximate Newton Methods: Globalization, Sharper Bounds and Beyondstat.ML
The DANE algorithm is an approximate Newton method popularly used for communication-efficient distributed machine learning. Reasons for the interest in DANE include scalability and versatility. Convergence of DANE, however, can be tricky; its appealing convergence rate is only rigorous for quadratic objective, and for …
Study confirms complex crypto market dynamics via non-linear potentials.
problem Linear models fail to capture complex financial market dynamics.
method Analyzed high-frequency crypto currency data to confirm non-linear drift and potential functions.
result Markets exhibit either single-well or double-well potentials, indicating varying levels of uncertainty or stress.
New algorithm for nonparametric IV regression using stochastic gradients.
problem Identifying causal effects in the presence of unobservable confounders.
method Functional stochastic gradient descent for NPIV regression.
result Superior stability and competitive performance compared to existing methods.
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of imag…
Graph theory criterion for Hodge theory to match linearly.
problem Matching nonlinear Hodge theory to linear on graphs.
method Minimizing edge potentials and solving nonlinear coclosed equations.
result Nonlinear selector agrees with Hodge projector on cactus graphs.
New algorithm achieves optimal regret in non-stochastic control, showing stochasticity is not beneficial.
problem Achieving optimal control in non-stochastic systems with adversarial noise.
method Novel online Newton step algorithm adapted to adversarial disturbances, using policy regret bounds.
result Optimal regret achieved in unknown dynamics, regret in known dynamics.
Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, resp…
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…
Extending Lévi-Civita's concept to non-quadratic spaces, this study finds extremal compatible linear connections.
problem Extending the Lévi-Civita connection to non-quadratic spaces.
method Hybrid conditional extremum problem, Lagrange multipliers, geometric approach.
result Existence and characterization of extremal compatible linear connections.
GNvPro efficiently trains neural networks with variable projection, improving accuracy and generalization.
problem Optimizing weights of neural networks for accurate approximation of input-target data.
method Variable projection (VarPro) extended to non-quadratic objectives, using Gauss-Newton method (GNvPro).
result GNvPro solves optimization problems more efficiently and finds better generalizing solutions.
Robustness in sparse linear models: relative efficiency based on robust approximate message passingmath.ST
Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions. When the number of parameters is of the same order as the sample size , $p \…