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.
Proposes a new Hodge conjecture in Bott-Chern cohomology.
Refined invariants for 4D 2-handlebodies, linking quantum groups and cohomology.
The Chern classes of a K-theory class which is represented by a vector bundle with connection admit refinements to Cheeger-Simons classes in Deligne cohomology. In the present paper we consider similar refinements in the case where the classes in K-theory are represented by geometric families of Dirac operators. In low…
Refined 1-cocycle for knots helps quantify isotopies.
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a Macdonald q,t-deformation -- refinement -- of these operators that preserves the…
Let be a flat complex vector bundle over a closed oriented odd dimensional manifold endowed with a flat connection . The refined analytic torsion for was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…
O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two refinements of Plamenevskaya's invariant, one valued in Bar-Natan's deformation of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum. We show that the first of these…
Continual learning consists in incrementally training a model on a sequence of datasets and testing on the union of all datasets. In this paper, we examine continual learning for the problem of sound classification, in which we wish to refine already trained models to learn new sound classes. In practice one does not w…
We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trad…
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or generalized spin and complex spin structures. A crucial role in our construction is play…
Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this paper, thanks to the spin extension of the permutation group we give an alterna…
What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and …
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann -invariants, which we call higher-order signatures. The higher-order genera o…
New insights into integrability and rectifiability in sub-Riemannian geometry.
Solves biased pseudo-labels in imbalanced SSL by refining them.
Refines a tangle invariant using XC-algebras.
The study refines algebraic domains with specific boundary conditions.
Study of 5D SYM theory on toric surfaces yields refined Vafa-Witten invariants.
In this paper we describe a procedure for refining the given triangulation of a 3-manifold that scales the PL-metric according to a given weight function while creating no new normal surfaces. It is known that an incompressible surface in a triangulated 3-manifold is isotopic to a normal surface that is of mini…
CAGNN learns graph embeddings without labels by clustering and refining graph topology.
We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping class group is not boundedly generated by these subgroups. In this note we enlarg…
The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de Rham cocycles -- known as differential cohomology. We will discuss the analog in the case of a group action on the manifold: The definition of equivariant characteristic fo…
In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In recent years, there has been much development for binary classification with a …
A new subdivision scheme for Heisenberg group values with central smoothness loss.
Optimal learning rate schedules derived for various tasks.
Introduces halo products and studies their geometric properties.
Develops a new theory of localization in algebraic geometry.
Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based representation of the volumetric data and then, posing the tree extraction as a graph …
New inequality for refined knot invariants in a specific space.
We present in this note a lower bound for the Calabi functional in a given Kähler class. This yields an integral inequality for constant scalar curvature metrics, which can be viewed as a refined version of Yau's Chern number inequality.
We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…
We show that totally real elliptic Lefschetz fibrations that admit a real section are classified by their "real loci" which is nothing but an -valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a \emph{necklace diagram}. On the o…
This is a survey of some of the recent developments in the theory of complex Monge-Ampere equations. The topics discussed include refinements and simplifications of classical a priori estimates, methods from pluripotential theory, variational methods for big cohomology classes, semiclassical constructions of solutions …
A new algorithm selects models for contextual bandits, reducing regret.
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the same time the number of samples into each stratum and the partition itself. More p…
Refines neural network predictions using background knowledge for improved accuracy.
New research shows label refinement and weak training have limitations for aligning LLMs.
For a closed oriented 3-manifold Y, we define an absolute grading on the Heegaard Floer homology groups of Y by homotopy classes of oriented 2-plane fields. We show that this absolute grading refines the relative one and that it is compatible with the maps induced by cobordisms. We also prove that if ξ is a contact str…
Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class…
Artificial Neural Networks (ANNs) have demonstrated remarkable utility in various challenging machine learning applications. While formally verified properties of their behaviors are highly desired, they have proven notoriously difficult to derive and enforce. Existing approaches typically formulate this problem as a p…
The purpose of these notes is to show that the methods introduced by Bauer and Furuta in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from Riemann surfaces, using the vortex equations on the latter.
This study develops a NURBS-based method for conformal surface flattening without singularities.
We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of complete minimal surfaces that includes algebraic minimal surfaces. It also provides a …
Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots, generalizing the Gauss linking integral. Their techniques were later used to construct real cohomology classes in spaces of knots and links in higher-dimensional Euclidean spaces. In previo…
The connection between Hitchin's stable forms and vector cross products is observed. Using this correspondence, we construct new examples of non-Kahler Calabi-Yau 3-folds and manifolds with G2-structure of class W3. We also generalize and refine results of Calabi and Gray in the paracomplex setting.
Spectral clustering with edge counting detects communities in sparse models.
We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.
Functorial semi-norms on singular homology give refined "size" information on singular homology classes. A fundamental example is the l^1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the l^1-semi-norm.