arXiv research

Promotes spectral functionals to noncommutative fields and proves a theorem.

In this work we prove a residue formula for Morita-Futaki-Bott invariant with respect any holomorphic vector fields with isolated (possibly degenerated) singularities in terms of Grothendieck's residues.

We prove a holomorphic residue localization formula for odd holomorphic vector fields on compact complex supermanifolds whose fermionic and bosonic dimensions coincide. Under isolated non-degeneracy hypotheses on the reduced zero set, we give an explicit local residue formula.

Study shows how deep residual networks can be analyzed as shallow network ensembles for optimization.

We prove residual formulas for vector fields defined on compact complex orbifolds with isolated singularities and give some applications of these on weighted projective spaces.

Enhanced image denoising with MWRDCNN using residual dense blocks.

Spatial Adapter adds structured spatial representation to frozen predictors.

Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are …

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…

Given a compatible vector field on a compact connected almost-complex manifold, we show in this article that the multiplicities of eigenvalues among the zero point set of this vector field have intimate relations. We highlight a special case of our result and reinterpret it as a vanishing-type result in the framework o…

Study Transformer layers under cross-entropy training using mean field control.

Sharp stability threshold found for deep residual architectures.

Residual networks with depthwise hyperparameter scaling transfer optimal hyperparameters across width and depth.

Field theory explains optimal scaling in ResNets for signal propagation.

Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In…

SRFRN accelerates image super-resolution using shallow residual units.

New spectral functionals related to noncommutative residue and torsion Dirac operators.

Explains complex analytic invariants of vector fields and foliations.

Deep heteroskedastic models overfit, showing a phase transition with regularization strength.

New spectral torsion defined for rescaled Dirac operators.

Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…

The paper explores a new method for landmark matching using sub-Riemannian geometry and neural networks.

Model predicts option movements using residual transactions for better market timing.

Introduces a neural network-based method for efficient state and parameter estimation in complex systems.

The paper computes metrics and Einstein tensors on even-dimensional manifolds.

Proves a Baum--Bott formula for foliations by curves with logarithmic terms.

This paper proposes a deep speech enhancement method which exploits the high potential of residual connections in a wide neural network architecture, a topology known as Wide Residual Network. This is supported on single dimensional convolutions computed alongside the time domain, which is a powerful approach to proces…

New method learns PDE solutions from low-fidelity data.

Improved far-field speaker verification for short utterances in noisy conditions.

New framework analyzes deep neural networks using feature probabilities.

Reducing volatility proxy improves apparent market correlation dynamics.

We speed up Gaussian process cross-validation calculations and improve model diagnostics.

Groups with specific properties have vanishing $\ell^2$-Betti numbers.

The study analyzes deep linear networks from random initialization, capturing dynamics and hyperparameter effects.

A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy o…

New methods explain NE embeddings by identifying key variables.

PIE-PINN estimates elastic properties from noisy, low-res displacement data.

The study examines discrete subgroups of PSL2 over non-archimedean fields.

The paper establishes analogs of Stallings' theorem for group homomorphisms and their nilpotent quotients.

Deep Gaussian processes on manifolds improve performance on complex data.

On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are obtained by fixing at each singularity the polar part of the connection. We prove that…

In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to estimate high-dimensional factor models, using the empirical spectral density of …

It is shown that, up to isometry, all but finitely many closed, orientable hyperbolic 3-manifolds with a given trace field $K$ admit 0.34 as a Margulis number. This is deduced from a more technical result giving a condition under which $\max(d(P,x\cdot P),d(P,y\cdot P))\ge0.34$ for every $P\in\HH^3$, where $x$ and $y$ …

Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.

Let $M$ be a compact and connected smooth manifold endowed with a smooth action of a finite group $Γ$, and let $f$ be a $Γ$-invariant Morse function on $M$. We prove that the space of $Γ$-invariant Riemannian metrics on $M$ contains a residual subset ${\mathcal Met}_f$ with the following property. Let $g\in{\mathcal Me…

Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…