arXiv research

The paper diagnoses factor models using characteristic axes and zero-curve restrictions.

The paper diagnoses factor-model pricing errors using characteristic axes and bridge-alpha curves.

This paper diagnoses factor-model pricing errors using a new method.

The Conclusive Theorem has been established to determine the dependence of the three-axes positive-definite Finsleroid metric functions $F$ on the Finsleroid azimuthal angle $θ$ in the three-dimensional case $N=3$, provided that the condition of the angle-separation in the involved characteristic functions is implied. …

The class of the two-axes pseudo-Finslerian metrics which is specified by the condition of the angle-separation in the involved characteristic functions is proposed and studied. The complete Total Set of algebraic and differential equations is derived in all rigor which are necessary and sufficient in order that a pseu…

A new knot invariant measures crossings in three orthogonal directions.

Research in deep reinforcement learning (RL) has coalesced around improving performance on benchmarks like the Arcade Learning Environment. However, these benchmarks conspicuously miss important characteristics like abrupt context-dependent shifts in strategy and temporal sensitivity that are often present in real-worl…

Method evaluates disentanglement in DLVMs, including those not aligned with latent axes.

Paper proposes AXE loss for non-autoregressive machine translation, improving performance.

Deep learning models are full of hyperparameters, which are set manually before the learning process can start. To find the best configuration for these hyperparameters in such a high dimensional space, with time-consuming and expensive model training / validation, is not a trivial challenge. Bayesian optimization is a…

New method flattens decision boundary by targeting shortcut-aligned axes in disentangled latent space.

The paper classifies hypersurfaces in Riemannian manifolds with constant inner product and torse-forming axes.

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a quasi-geodesic wi…

Self-focal points on ellipsoids of dimension 3 or higher are rare.

AXE evaluates explanations to avoid misleading Rashomon set model selection.

Study inverse curve shortening flow on hyperbolic plane, classifying solitons.

Proposes $σ$-PCA to learn identifiable linear transformations without whitening.

In Garside groups, axes of Morse elements are strongly contracting.

Recent results using inverse scattering techniques interpret every solution $φ(x,y)$ of the sine-Gordon equation as a non-linear superposition of solutions along the axes $x=0$ and $y=0$. Here we provide a geometric method of integration, as well as a geometric interpretation. Specifically, every weakly regular surface…

This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold $\mathcal{M}$ under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of …

Simpler proof for non-basic sets in 2D.

On a Riemannian 2-torus $(T^2,g)$ we study the geodesic flow in the case of low complexity described by zero topological entropy. We show that this assumption implies a nearly integrable behavior. In our previous paper \cite{GK} we already obtained that the asymptotic direction and therefore also the rotation number ex…

We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.

We consider the problem of estimating an unknown signal $x_0$ from noisy linear observations $y = Ax_0 + z\in R^m$. In many practical instances, $x_0$ has a certain structure that can be captured by a structure inducing convex function $f(\cdot)$. For example, $\ell_1$ norm can be used to encourage a sparse solution. T…

We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.

We consider non-elementary Kleinian groups Γ, without invariant plane, generated by an elliptic and a hyperbolic element with their axes lying in one plane. We find presentations and a complete list of orbifolds uniformized by such Γ.

New approach classifies rotational Weingarten surfaces in Lorentz-Minkowski space.

Unified scheme combining softmax and ResNet for deep learning.

PRUDEX-Compass evaluates FinRL methods on 6 axes for financial market investments.

Developable ruled surfaces generated by curvature axes of curves.

Bayesian quadrature uses probabilistic models for estimating intractable integrals.

We study hypersurfaces either in the sphere \s{n+1} or in the hyperbolic space \h{n+1} whose position vector $x$ satisfies the condition $L_kx=Ax+b$, where $L_k$ is the linearized operator of the $(k+1)$-th mean curvature of the hypersurface for a fixed $k=0,...,n-1$, $A\in\R{(n+2)\times (n+2)}$ is a constant matrix an…

We study optimal double helices with straight axes (or the fattest tubes around them) computationally using three kinds of functionals; ideal ones using ropelength, best volume packing ones, and energy minimizers using two one-parameter families of interaction energies between two strands of types $r^{-α}$ and $\frac1r…

Stochastic gradient descent regularizes least squares problems by smoothing large singular values.

New CRB derived for curved models using extrinsic geometry.

New PCA method for derivatives problems.

Finite singular times for symmetric network curvature flow.

MCPCA analyzes shared factors across multiple data contexts.

New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.

We show that there is no triangulation of the infinite real Grassmannian of k-planes in R^\infty which is nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of the Grassmannian subdividing the matroid stratification. This is proved by an argument in proj…

Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…

We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.

Over-parameterized deep neural networks have proven to be able to learn an arbitrary dataset with 100$\%$ training accuracy. Because of a risk of overfitting and computational cost issues, we cannot afford to increase the number of network nodes if we want achieve better training results for medical images. Previous de…

This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements. We consider the recovery of the signal $x_o \in \mathbb{R}^N$ from $n$ random and noisy linear observations $y= Ax_o + w$, where $A$ is the measuremen…

The set of axes of hyperbolic elements in a Fuchsian group depends on the commensurability class of the group. In fact, it has been conjectured that it determines the commensurability class and this has been verified in for groups of the second kind by G. Mess and for arithemetic groups by by D. Long and A. Reid. Here …

The study confirms two cases of the convex body isoperimetric conjecture in the plane.

This paper evaluates how well neural models can solve complex tasks by breaking them into simpler ones.

Clarifies challenges in machine learning uncertainty quantification.