arXiv research

The center of mass in General Relativity is hard to define due to coordinate freedom.

Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.

Novel deep learning method predicts reaction coordinates and future MD trajectories.

Transformers reduce redundancy by focusing on invariant relational quantities.

Proof of local well-posedness for a specific boundary condition in general relativity.

In this paper, we explore degrees of freedom in deep sigmoidal neural networks. We show that the degrees of freedom in these models is related to the expected optimism, which is the expected difference between test error and training error. We provide an efficient Monte-Carlo method to estimate the degrees of freedom f…

We give the first example of systolic freedom over torsion coefficients. The phenomenon is a bit unexpected (contrary to a conjecture of Gromov's) and more delicate than systolic freedom over the integers.

Neural network learns atomic coordinates from Patterson maps in a simplified case.

The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetim…

The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it ma…

Measuring supernova neutrinos removes spacetime's conformal freedom.

Measures neural network complexity via effective degrees of freedom.

Paper proves robust M-estimators' coordinates' normality in high dimensions.

Classifies solutions in multisymplectic field theories using geometric gauge freedom.

This paper investigates the model degrees of freedom in k-means clustering. An extension of Stein's lemma provides an expression for the effective degrees of freedom in the k-means model. Approximating the degrees of freedom in practice requires simplifications of this expression, however empirical studies evince the a…

Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected beha…

A new distribution family extends the $\alpha$-stable distribution with a degree of freedom parameter.

The paper models financial order books using geometric shears and directional liquidity.

Unified finetuning of all quantization degrees of freedom achieves state-of-the-art 4-bit quantization.

3D dust map of the Milky Way improves resolution and accuracy.

While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed under nonlinear Lorentz-conformal mappings. Squares are transformed into curvili…

We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, w…

Fewer degrees of freedom can train deep networks, showing a sharp phase transition.

In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes finite transformation law highly complicated, both technically and conceptually. In…

The paper examines parallel one forms on Riemannian and Finslerian manifolds.

Following the spirit of a previous work of ours, we investigate the group of those General Coordinate Transformations (GCTs) which preserve manifest spatial homogeneity. In contrast to the case of Bianchi Type Models we, here, permit an isometry group of motions $G_{4}=SO(3)\otimes T_{r}$, where $T_{r}$ is the translat…

The paper argues for using more degrees of freedom in empirical financial analysis to improve conclusions.

We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We a…

EPGP surrogate outperforms finite elements in solving wave equations.

Presented spherical symmetric teleparallel geometry frames and field equations.

A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of parameters. Its computation and properties are well understood when dealing with di…

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …

Geometrically describes pseudo-gauge freedom in relativistic hydrodynamics.

Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains "slow" de…

Directly simulates squared Bessel processes efficiently.

Deep neural networks reduce loan portfolio risk.

A new method joins two arcs with a degree of freedom.

We developed a perturbation model for affine gravity theories.

Space exploration missions have seen use of increasingly sophisticated robotic systems with ever more autonomy. Deep learning promises to take this even a step further, and has applications for high-level tasks, like path planning, as well as low-level tasks, like motion control, which are critical components for missi…

New method uses scalars to approximate physics functions.

A new property fixes look-ahead bias in backtesting and trading pipelines.

Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifold admits metrics of arbitrarily small total volume, and possessing the following property: every m-dimensional submanifold of less than unit m-volume is necessarily torsion in homology. This result is different from the case o…

Developed a new thresholding method that connects soft and hard thresholding.

Develops unisolvent weights for Nédélec second family finite elements in 2D.

We prove the simultaneous (k,n-k)-systolic freedom, for a pair of adjacent integers k smaller than n/2, of a simply connected n-manifold X. Our construction, related to recent results of I. Babenko, is concentrated in a neighborhood of suitable k-dimensional submanifolds of X. We employ calibration by differential form…

In this paper we are investigating variational homogeneous second order differential equations by considering the questions of how many different variational principles exist for a given spray. We focus our attention on h(2)-variationality; that is, the regular Lagrange function is homogeneous of degree two in the dire…

We simplify supergravity in 10D using geometric insights.

For an integrable Hamiltonian with $d\ (d\geq 2)$ degrees of freedom, we show the conditions on perturbations, for which invariant tori can be destructed.