arXiv research

Paper develops methods for non-quadratic loss low-rank matrix recovery.

We construct a finitely presented group $G$ with non-quadratic Dehn function $f$ majorizable by a quadratic function on arbitrary long intervals.

New non-quadratic hypersurfaces found for higher dimensions.

Study uses deep learning for efficient hedging of long-term financial derivatives.

We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus $T^n$, $n\geq 2$, 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].

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…

Generative approach speeds hyperparameter tuning for machine learning models.

New algorithm for nonparametric IV regression using stochastic gradients.

Paper maps Hamiltonians and line elements in manifolds.

Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.

Locally classifies 4D spherical symmetric Finsler spaces.

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 $p$ is of the same order as the sample size $n$, $p \…

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…

New algorithm achieves optimal regret in non-stochastic control, showing stochasticity is not beneficial.

SAM optimizes deep networks by oscillating between sides of the minimum.

GNvPro efficiently trains neural networks with variable projection, improving accuracy and generalization.

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.

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.

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.

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.

Introduces Fitzpatrick losses, tighter than Fenchel-Young losses.

We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determ…

We present the Tamed Cross Entropy (TCE) loss function, a robust derivative of the standard Cross Entropy (CE) loss used in deep learning for classification tasks. However, unlike other robust losses, the TCE loss is designed to exhibit the same training properties than the CE loss in noiseless scenarios. Therefore, th…

Unified surrogate loss framework for multi-label learning with strong consistency guarantees.

This paper introduces new loss functions for balanced multi-class classification.

We present $α$-loss, $α\in [1,\infty]$, a tunable loss function for binary classification that bridges log-loss ($α=1$) and $0$-$1$ loss ($α= \infty$). We prove that $α$-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal y…

This work broadens calibeating to various proper losses using Bregman divergence.

This work generalizes calibeating for a broader range of proper losses using Bregman divergence.

Proposes squentropy loss for improved classification accuracy and model calibration.

New loss function calibrates WW-hinge loss for multiclass SVM.

The study analyzes a model for aggregate losses with dependent and overdispersed inter-losses times.

Symmetric losses improve classifier robustness from corrupted labels.

Two new algorithms improve performance in adversarial bandits with unbounded losses.

Paper explores connections between loss functions and consistency in binary classification and regression.

Paper introduces a new topological loss for better convergence.

Novel loss functions improve decision tree learning from noisy data.

Theoretical analysis of cross-entropy loss functions and their robustness.

This paper improves operational risk modeling by selecting better loss severity distributions.

This paper improves loss functions for deep learning with noisy labels.