arXiv research

Stability of weighted extremal manifolds proven through blowups.

We investigate the $m$-relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement $K$-convexity of the $m$-relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the $K$-convexity of the weig…

This paper gives an exposition of relative weight filtrations on completions of mapping class groups associated to a stable degeneration of marked genus g curves. These relative weight filtrations have been constructed using Galois theory (with Matsumoto) and Hodge theory (with Pearlstein and Terasoma). It is shown tha…

We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the nonnegative weighted Ricci cur…

We develop a relative version of Kostant's harmonic theory and use this to prove a relative version of Kostant's theorem on Lie algebra (co)homology. These are associated to two nested parabolic subalgebras in a semisimple Lie algebra. We show how relative homology groups can be used to realize representations with low…

Under the assumption of asymptotic relative Chow-stability for polarized algebraic manifolds $(M, L)$, a series of weighted balanced metrics $ω_m$, $m \gg 1$, called polybalanced metrics, are obtained from complete linear systems $|L^m|$ on $M$. Then the asymptotic behavior of the weights as $m \to \infty$ will be stud…

Paper develops Lie theory for Rota-Baxter operators on Lie algebras and groups.

Proposes a multi-objective Q-network for dynamic weights in deep RL.

We consider the $\mathfrak{aff}(n|1)-$module structure on the spaces of differential bilinear operators acting on the superspaces of weighted densities. We classify $\mathfrak{aff}(n|1)-$invariant binary differential operators acting on the spaces of weighted densities. This result allows us to compute the first $\math…

New method constructs relative invariants for group actions on extended manifolds.

Improved atomistic model predicts molecular properties using weighted skip-connections.

In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4. In the case of formal Hamiltonian vector fields on R^2, we computed the relative Gel'fand-Kalinin-Fuks cohomology groups of weight <20 in the paper by Mikami-Nakae-Kodama. The main strategy…

Researchers address the generation of differential invariants for geometric structures.

In this paper we study the relative Chow and $K$-stability of toric manifolds in the toric sense. First, we give a criterion for relative $K$-stability and instability of toric Fano manifolds in the toric sense. The reduction of relative Chow stability on toric manifolds will be investigated using the Hibert-Mumford cr…

For a polarized Kähler manifold $(X, L)$, we show the equivalence between relative balanced embeddings introduced by Mabuchi and $σ$-balanced embeddings introduced by Sano, answering a question of Hashimoto. We give a GIT characterization of the existence of a $σ$-balanced embedding, and relate the optimal weight $σ$ t…

New tests detect asphericity in complex pairs, simplifying previous proofs.

In this paper we prove general inequalities involving the weighted mean curvature of compact submanifolds immersed in weighted manifolds. As a consequence we obtain a relative linear isoperimetric inequality for such submanifolds. We also prove an extrinsic upper bound to the first non zero eigenvalue of the drift Lapl…

New surface area measures defined for ball-convex bodies, leading to entropy and inequalities.

In "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations", arXiv:0910.3414, (October 2009) by D.Kotschick and S.Morita, the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields without constant vector fields on 2n-plane were characterized b…

A new method uses nearest neighbors for importance weighting.

Equivalence found between certain Kahler and Sasaki metrics.

The abstract develops weighted Ricci curvature in Lorentz-Finsler geometry and extends singularity theorems.

Residual Network (ResNet) is the state-of-the-art architecture that realizes successful training of really deep neural network. It is also known that good weight initialization of neural network avoids problem of vanishing/exploding gradients. In this paper, simplified models of ResNets are analyzed. We argue that good…

Improved robustness in ASR systems with speaker adaptation.

Novel spectral embedding considers node weights for graph analysis.

Defines new stability conditions for Sasaki manifolds and extremal metrics.

Diffusion models accurately recover mixture weights from generated samples despite score function insensitivity.

A new model clusters network nodes based on relative edge weights.

Study on local elasticity in neural network training, improving detection of class-specific changes.

Blowups of Kähler manifolds can inherit extremal metrics.

New method finds profitable investment opportunities by considering additional financial variables.

This work explores the importance of model weights and Hessian bias in pruning.

The study extends SPT to account for real-world transaction costs, improving portfolio performance.

Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…

In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fe…

The writers propose a mathematical Method for deriving risk weights which describe how a borrower's income, relative to their debt service obligations (serviceability) affects the probability of default of the loan. The Method considers the borrower's income not simply as a known quantity at the time the loan is made, …

We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and the corresponding market weights. These models substantially extend volatility stabilized market models considered by Robert Fernholz and Ioannis Karatzas in …

Proves invariance of weighted extremal Kähler metrics under smooth blowups.

The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.

We consider a self-adjoint non-negative operator $H$ in a Hilbert space $\mathsf{L}^2(X,{\rm d}μ)$. We assume that the semigroup $(\mathrm{e}^{-t H})_{t>0}$ is defined by an integral kernel, $p$, which allows an estimate of the form $p(t,x,x)\le F_1(x)F_2(t)$ for all $(x,t)\in X\times\mathbb{R_+}$; we refer to $F_1$ as…

Paper proves a sharp weighted Isoperimetric inequality for substatic manifolds.

Study geometric and topological properties of Finsler manifolds with weighted Ricci curvature bounds.

We introduce a pathwise approach to analyze the relative performance of an equity portfolio with respect to a benchmark market portfolio. In this energy-entropy framework, the relative performance is decomposed into three components: a volatility term, a relative entropy term measuring the distance between the portfoli…

Prior-weighted logistic regression has become a standard tool for calibration in speaker recognition. Logistic regression is the optimization of the expected value of the logarithmic scoring rule. We generalize this via a parametric family of proper scoring rules. Our theoretical analysis shows how different members of…

A new approach optimizes weights in DLP for better risk-adjusted performance.

Weight normalization speeds up matrix sensing problems.

This research shows loss weighting remains effective in last layer retraining despite model overparameterization.

RGRR allocates between QQQ and DIA based on relative states, improving Sharpe and CAGR.