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.
Framework expands particle filtering to estimate states beyond prior boundaries.
New phenomenon found in Gothen components' boundary.
Estimates scalar curvature without nonnegativity, showing gap phenomenon on manifolds.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.
Bayesian approach for solving systems of linear PDEs with boundary conditions.
Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating from deep networks being "too linear" (Goodfellow et al., 2014). We show here t…
Transformer pretraining yields strong EB performance without explicit adaptation.
BPVAE enhances VAE robustness to OOD inputs.
A seminal result in geometric group theory is that a 1-ended hyperbolic group has a locally connected visual boundary. As a consequence, a 1-ended hyperbolic group also has a path connected visual boundary. In this paper, we study when this phenomenon occurs for CAT(0) groups. We show if a 1-ended CAT(0) group with iso…
We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We prove, in particular, that small energy controls C1 boundary regularity. We examin…
The paper discovers new ways Riemann surfaces can degenerate.
New method uses Gaussian processes for solving linear PDEs with boundary conditions.
We make systematic developments on Lawson-Osserman constructions relating to the Dirichlet problem (over unit disks) for minimal surfaces of high codimension in their 1977 Acta paper. In particular, we show the existence of boundary functions for which infinitely many analytic solutions and at least one nonsmooth Lipsc…
The aim of this paper is to study a possible "boundary phenomenon" for Spinc Dirac operators in a special case. If you parametrise Spinc Dirac operators by a family of connections on a Spinc 4-manifold with boundary, this boundary inherits also a family of Spinc Dirac operators which has a spectral section (in the sens…
Paper studies curvature of stable surfaces meeting at a common boundary.
The paper explores new phenomena in boundaries of relatively hyperbolic groups.
Categorifies Stokes coefficients in Chern-Simons theory models.
New static vacuum metrics confirmed for near Euclidean boundary data.
Study shows cliff-learning in transfer learning from foundation models.
In this paper, we prove that nonnegative polyharmonic functions on the upper half space satisfying a conformally invariant nonlinear boundary condition have to be the "\emph{polynomials} plus \emph{bubbles}" form. The nonlinear problem is motivated by the recent studies of boundary GJMS operators and the -curvature …
Consider a set represented by an inequality. An interesting phenomenon which occurs in various settings in mathematics is that the interior of this set is the subset where strict inequality holds, the boundary is the subset where equality holds, and the closure of the set is the closure of its interior. This paper disc…
The paper studies free boundary minimal surfaces with many boundaries and their convergence to closed minimal surfaces.
Catastrophic forgetting is the notorious vulnerability of neural networks to the change of the data distribution while learning. This phenomenon has long been considered a major obstacle for allowing the use of learning agents in realistic continual learning settings. A large body of continual learning research assumes…
We prove a phenomenon of concentration of total curvature for stable minimal surfaces in the product space H^2xR; where H^2 is the hyperbolic plane. Under some geometric conditions on the asymptotic boundary of an oriented stable minimal surface immersed in H^2xR, it has infinite total curvature. In particular, we infe…
This paper examines how the choice of prior distribution affects likelihoods of out-of-distribution inputs in deep generative models.
The paper identifies a new geometric and spectral phenomenon in the critical hyperbolic catenoid family.
We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result is a manifestation of the so-called Hopf rigidity phenomenon which was recen…
The n-strand braid group can be defined as the fundamental group of the configuration space of n unlabeled points in a closed disk based at a configuration where all n points lie in the boundary of the disk. Using this definition, the subset of braids that have a representative where a specified subset of these points …
Non-uniqueness found in option valuation for certain α values.
Research shows conditional existence of foliations by CMC and Willmore type half-spheres near a boundary point.
Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.
We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not arise from ``generic'' degenerations is often negligible in problems involving …
Fast algorithm solves BVPs in linear time with probabilistic uncertainty.
Recently Auckly-Kim-Melvin-Ruberman showed that for any finite subgroup G of SO(4) there exists a contractible 4-manifold with an effective G-action on its boundary so that the twists associated to the non-trivial elements of G do not extend to diffeomorphisms of the entire manifold. We use a Heegaard Floer theoretic a…
Theoretical study explains grokking in neural networks.
As has been observed by Morse \cite{Mo}, any generic vector field on a compact smooth manifold with boundary gives rise to a stratification of the boundary $\d X$ by compact submanifolds $\{\d_j^\pm X(v)\}_{1 \leq j \leq \dim(X)}$, where $\textup{codim}(\d_j^\pm X(v))= j$. Our main observation is that this stra…
This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. The presentation is intended to complement [GS], presenting the essential ideas rather than the analytical det…
We show that the twisted Kähler-Ricci flow on a complex manifold X converges to a flow of moving free boundaries, in a certain scaling limit. This leads to a new phenomenon of singularity formation and topology change which can be seen as a complex generalization of the extensively studied formation of shocks in Hamilt…
This work shows that Gaussian is the only prior for optimal linear estimation in loss.
In this paper, we consider the problem of predicting demographics of geographic units given geotagged Tweets that are composed within these units. Traditional survey methods that offer demographics estimates are usually limited in terms of geographic resolution, geographic boundaries, and time intervals. Thus, it would…
Cold posteriors improve Bayesian neural networks by reducing overestimation of aleatoric uncertainty.
Noise in SGD affects overparameterized models, favoring sparse solutions.
Survey of integrating physics knowledge into machine learning models.
In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic geometric partial differential equations. Examples include Willmore surfaces, stationary solitons for the surface diffusion flow, and …
Paper analyzes weak-to-strong generalization in CNNs, identifying data-scarce and data-abundant regimes.
Deep neural networks' decision boundaries move closer to natural images during training.
SSMs can be poisoned with clean labels, leading to generalization failure.