A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method converts and optimizes sampling schedules for generative models.
Optimizes diffusion processes for target distributions.
ESOP uses Bayesian optimization to find optimal lock-down schedules.
Defines circumcenter of mass for polytopes without triangulation.
Proves critical points of ADM mass correspond to specific initial data sets.
New optimizer SF-NorMuon matches tuned AdamW across various horizons.
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP conver…
This paper optimizes diffusion schedules for better sampling from data distributions.
Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standard sphere. The Hawking mass gives a well-known lower bound, and an upper bound is obtained by estimating the mass of a static vacuum extensi…
The semicontinuity phenomenon of the ADM mass under pointed (i.e., local) convergence of asymptotically flat metrics is of interest because of its connections to nonnegative scalar curvature, the positive mass theorem, and Bartnik's mass-minimization problem in general relativity. In this paper, we extend a previously …
First we review the definition of a negative point mass singularity. Then we examine the gravitational lensing effects of these singularities in isolation and with shear and convergence from continuous matter. We review the Inverse Mean Curvature Flow and use this flow to prove some new results about the mass of a sing…
New metrics found in hyperbolic manifolds as volume-minimizers.
Hybrid classical-quantum framework optimizes portfolio rebalancing with reduced transaction costs.
Dropout schedules can be optimized to significantly reduce model test loss.
Provides an overview of Bartnik's quasi-local mass.
We provide larger step-size restrictions for which gradient descent based algorithms (almost surely) avoid strict saddle points. In particular, consider a twice differentiable (non-convex) objective function whose gradient has Lipschitz constant L and whose Hessian is well-behaved. We prove that the probability of init…
MAS scores cluster size consistency from points, robust to label changes.
Two distinct phases of deep learning training improve model generalization.
Survey of mass partition problems in geometry and topology.
A natural question in mathematical general relativity is how the ADM mass behaves as a functional on the space of asymptotically flat 3-manifolds of nonnegative scalar curvature. In previous results, lower semicontinuity has been established by the first-named author for pointed convergence, and more generally by…
New geometric inequality for mass from immersed submanifolds.
In this paper, we will study the limiting behavior of the Brown-York mass of the coordinate spheres in an asymptotically flat manifold. Limiting behaviors of volumes of regions related to coordinate spheres are also obtained, including a discussion on the isoperimetric mass introduced by Huisken \cite{Huisken}. We will…
The paper shows how to create scalar flat metrics with very large ADM mass.
Proposes a new method for predicting uncertain net electricity demand.
The ADM mass, viewed as a functional on the space of asymptotically flat Riemannian metrics of nonnegative scalar curvature, fails to be continuous for many natural topologies. In this paper we prove that lower semicontinuity holds in natural settings: first, for pointed Cheeger--Gromov convergence (without any symmetr…
For a closed surface M with metric g, the Robin mass m(p) at the point p is the value of the Green function G(p,q) at p=q after the logarithmic singularity has been removed. The Laplacian-mass is the average value of the Robin mass, minus the value of the Robin mass for the round sphere of the same area. The Laplacian-…
Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed Cheeger--Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. I…
We consider the two body problem with central interaction on two point homogeneous spaces from point of view of the invariant differential operators theory. The representation of the two particle Hamiltonian in terms of the radial differential operator and invariant operators on the symmetry group is found. The connect…
We introduce a framework for studying the effects of self-interaction on the construction of point particle initial data in General Relativity. Within this framework we rigorously prove the vanishing mass claim made by Arnowitt, Deser and Misner regarding point sources. We identify a geometric structure and a scaling p…
The paper proves stability of the positive mass theorem using intrinsic flat convergence.
New positive mass theorem for hyperbolic 3-manifolds using Green functions.
New method schedules learning rate without stopping time, outperforming existing methods.
This paper proposes a method to select project schedules with the lowest risk.
The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Th…
The paper calculates mass and volume of Einstein metrics in four dimensions.
We define barycentric coordinates on a Riemannian manifold using Karcher's center of mass technique applied to point masses for n+1 sufficiently close points, determining an n-dimensional Riemannian simplex defined as a "Karcher simplex." Specifically, a set of weights is mapped to the Riemannian center of mass for the…
We point out a duality between steady incompressible Euler flows and solutions of the strongly coupled Faddeev-Skyrme sigma model with potential (mass) term. We supplement this result with various applications and several explicit examples.
Rigidity results for Hawking mass in curved spaces with bounds on Bartnik capacity.
Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.
Optimizes financial auditor schedules to reduce time and costs.
This article asks how planning scholarship may effectively gain impact in planning practice through media exposure. In liberal democracies the public sphere is dominated by mass media. Therefore, working with such media is a prerequisite for effective public impact of planning research. Using the example of megaproject…
Let be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point is called the mass endomorphism in associated to the metric due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a gen…
ScheduleFree+ improves large language model training without schedules or learning rates.
In this paper, we show that the Chen-Nester-Tung (CNT) quasi-local energy is closely related to the Wang-Yau (WY) quasi-local mass. As a particular example, we compute the second variation of the CNT quasi-local energy for axially symmetric Kerr-like spacetimes with axially symmetric embeddings at the obvious critical …
Cosine schedule is optimal for discrete diffusion models.
Optimal learning rate schedules derived for various tasks.
The paper optimizes interpolation schedules in generative models to improve sampling accuracy.
Proves existence of Yamabe metrics on conical 4-manifolds using min-max method.