arXiv research

New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.

The study examines stable regions in weighted manifolds with boundary properties.

We prove by Hilbert-Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves, and of Hasset on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solved a questi…

No stable discrete maps into certain curved spaces exist.

Stable capillary surfaces in weighted balls are disks.

A new method normalizes flow mixtures for better inference across different data types.

We present an explicit construction of the moduli spaces of rank 2 stable parabolic bundles of parabolic degree 0 over the Riemann sphere, corresponding to "optimum" open weight chambers of parabolic weights in the weight polytope. The complexity of the different moduli space' weight chambers is understood in terms of …

Generative Adversarial Networks (GANs) are powerful models for learning complex distributions. Stable training of GANs has been addressed in many recent works which explore different metrics between distributions. In this paper we introduce Fisher GAN which fits within the Integral Probability Metrics (IPM) framework f…

The moduli space $Δ_{g,w}$ of tropical $w$-weighted stable curves of volume $1$ is naturally identified with the dual complex of the divisor of singular curves in Hassett's spaces of $w$-weighted stable curves. If at least two of the weights are $1$, we prove that $Δ_{0,w}$ is homotopic to a wedge sum of spheres, possi…

Study on stable minimal hypersurfaces under Ricci curvature constraints.

In this paper, we study stable weighted minimal hypersurfaces in manifolds with nonnegative Bakry-Emery Ricci curvature. We will give some geometric and topological applications. In particular, we give some partial classification of complete 3-manifolds with nonnegative Bakry-Emery Ricci curvature assuming that $f$ is …

The paper evaluates functions of stable Lévy processes and their extrema efficiently.

Many complex ecosystems, such as those formed by multiple microbial taxa, involve intricate interactions amongst various sub-communities. The most basic relationships are frequently modeled as co-occurrence networks in which the nodes represent the various players in the community and the weighted edges encode levels o…

Stable unactivated neurons reduce expressiveness in ReLU networks.

We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under suitable scaling on the weights, is a stochastic process whose finite-dimension…

Study improves understanding of Ricci curvature in manifolds.

NROWAN-DQN improves stability and exploration in noisy networks.

In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multi…

Soft diamond regularizers improve deep learning performance and sparsity.

In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian manifold which admits a stable solution. Furthermore, under the non-negativity of …

Adaptive estimation of alpha-Stable distribution and Hurst exponent for nonstationary time series.

Algorithm identifies optimal stable matching in uncertain two-sided markets.

We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $Σ^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize Gaussian weighted area and preserve Gaussian weighted volume. We sho…

Let $M$ be a weighted manifold with boundary $\partial M$, i.e., a Riemannian manifold where a density function is used to weight the Riemannian Hausdorff measures. In this paper we compute the first and the second variational formulas of the interior weighted area for deformations by hypersurfaces with boundary in $\p…

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…

Deep neural networks with heavy-tailed weights converge to stable distributions.

This paper analyzes deep Stable neural networks, showing convergence rates under different growth settings.

In this paper we consider a class of weighted-volume preserving curvature flows acting on hypersurfaces that are trapped within two parallel hyperplanes and satisfy an orthogonal boundary condition. In the author's thesis the stability of cylinders under the flows was considered; it was found that they are stable provi…

Let $Ω$ be an open half-space or slab in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\exp(ω(p)-c|p|^2)$, where $c>0$ and $ω$ is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to $\partialΩ$. In this work we follow a varia…

Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.

Maximizes probability of completing investment schedules with optimal portfolio weights.

Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.

Stability of weighted extremal manifolds proven through blowups.

Price fluctuations of commodities like cotton and wheat are thought to display probability distributions of returns that follow a Lévy stable distribution. Recent analysis of stocks and foreign exchange markets show that the probability distributions are not Lévy stable, a plausible result since commodity markets have …

New nonparametric estimators improve causal effect estimation.

Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights, the minimal number of singular fibers of codimension 2 of stable maps into the re…

New concept of attitude towards probability introduced in risk sharing problems.

Proposes a new framework for investing that adapts to market regimes.

Let $Σ$ be a compact immersed surface with constant weighted mean curvature $H_f$ in a weighted manifold $(M^3,g,f)$. In this paper we obtain upper bounds for the first eigenvalue of the weighted Jacobi operator on $Σ$ in terms of $H_f$ and the curvature of the ambient. As consequence we obtain that there is no stable …

Improved portfolio optimization method reduces risk and improves performance.

Develops RES metrics for stable rare-event forecasting evaluation.

Study shows instability of Kähler Ricci solitons and stability of orbifold singularities.

The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.

Dynamic Vocabulary Pruning stabilizes LLM training by removing low-probability tokens.

The paper proposes a new method for covariate balancing using IPM to improve causal inference.

Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation. Generalization with high probability has been established in a landmark paper of Bousque…

We consider returns of two Korean stock market indices, KOSPI and KOSDAQ index. Central parts of the probability distribution function of returns are well fitted by the Lorentzian distribution function. However, tail parts of the probability distribution function follow a power law behavior well. We found that the prob…

Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.