arXiv research

Adding supplementary axes improves neural network learnability and accuracy.

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.

New method corrects least-squares temporal difference for better lambda-return estimation.

Bayesian optimization finds best hyperparameters for deep learning models.

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

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

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

We survey the use of continued fraction expansions in the algebraical and topological study of complex analytic singularities. We also prove new results, firstly concerning a geometric duality with respect to a lattice between plane supplementary cones and secondly concerning the existence of a canonical plumbing struc…

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.

This is supplementary material for the main Geodesics article by the authors. In Appendix A, we present some general results on the construction of Gaussian random fields. In Appendix B, we restate our Shape Theorem, specialized to the setting of this article. In Appendix C, we state some straightforward consequences o…

We prove that the criterion for Markov equivalence provided by Zhao et al. (2005) may involve a set of features of a graph that is exponential in the number of vertices.

AXE evaluates explanations to avoid misleading Rashomon set model selection.

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…

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

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. …

This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".

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

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

We make evident a curvature tensor for every vector sub-bundle of an arbitrary manifold tangent bundle which reduces to the curvature tensor of an Ehresmann connection in the case of the horizontal sub-bundle of the tangent bundle to the total space of the nonlinear fiber bundle on which the connection is defined. Then…

On the Grassmann manifold G (m, n) of m-dimensional subspaces of an n-dimensional projective space P^n, a certain supplementary construction called the normalization is considered. By means of this normalization, one can construct the structure of a Riemannian or semi-Riemannian manifold or an affine connection on G(m,…

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 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…

Mathisson's 'new mechanics' of a relativistic spinning particle is shown to follow, in the case of planar motion, from only general requirements of relativistic invariance and of the dependence on third order derivatives along with the 'variationality' feature. The Hamiltonian counterpart ultimately recovers the Dixon …

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 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.

For CR structures in dimension three, the CR pluriharmonic functions are characterized by the vanishing of a third order operator. This third order operator, after composition with the divergence operator, gives the fourth order analogue of the Paneitz operator. In this short note, we give criteria under which the kern…

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.

In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (arxiv:1209.2045) we described all smooth solutions of the two-function tt*-Toda equations in terms of asymptotic data, holomorphic data, and monodromy data. In this supplementary article we focus on the holomorphic data and its interpret…

Motivation: Drug discovery demands rapid quantification of compound-protein interaction (CPI). However, there is a lack of methods that can predict compound-protein affinity from sequences alone with high applicability, accuracy, and interpretability. Results: We present a seamless integration of domain knowledges and …

Study on 4D Einstein manifolds with improved boundary regularity.

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 PCA method for derivatives problems.

Finite singular times for symmetric network curvature flow.

MCPCA analyzes shared factors across multiple data contexts.