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.
DeepJet improves jet flavor classification and quark-gluon tagging.
Classification of jets with deep learning has gained significant attention in recent times. However, the performance of deep neural networks is often achieved at the cost of interpretability. Here we propose an interpretable network trained on the jet spectrum which is a two-point correlation function of the…
Paper proves flexibility of specific relations using convex integration.
A key question for machine learning approaches in particle physics is how to best represent and learn from collider events. As an event is intrinsically a variable-length unordered set of particles, we build upon recent machine learning efforts to learn directly from sets of features or "point clouds". Adapting and spe…
Optimal transport calibrates machine learning models for particle physics simulations.
Classifies Kähler metrics with constant holomorphic curvature.
Precise scientific analysis in collider-based particle physics is possible because of complex simulations that connect fundamental theories to observable quantities. The significant computational cost of these programs limits the scope, precision, and accuracy of Standard Model measurements and searches for new phenome…
Paper introduces Modular Jets for diagnosing model decompositions in pipelines.
The paper finds two types of metric lines in curve spaces.
We are interested in the local extrinsic geometry of smooth surfaces in 4-space, and classify jets of Monge forms by projective transformations according to -types of their central projections.
Recent literature on deep neural networks for tagging of highly energetic jets resulting from top quark decays has focused on image based techniques or multivariate approaches using high-level jet substructure variables. Here, a sequential approach to this task is taken by using an ordered sequence of jet constituents …
We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smoo…
Tensor networks improve b-jet classification in high-energy physics.
We describe a strategy for constructing a neural network jet substructure tagger which powerfully discriminates boosted decay signals while remaining largely uncorrelated with the jet mass. This reduces the impact of systematic uncertainties in background modeling while enhancing signal purity, resulting in improved di…
We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó's TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the -action on Heegaard Fl…
Lisa Traynor has described an example of a two-component Legendrian `circular helix link' in the 1-jet space of the circle (with its canonical contact structure) that is topologically but not Legendrian isotopic to that same link with the order of the two components reversed. We give a complete classification of the Le…
We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification of Monge forms and bifurcations of parabolic curves and flecnodal curves.
This study classifies metric lines in jet space.
Quantum GNNs outperform classical GNNs in jet tagging.
Moment Pooling reduces latent space dimensions in machine learning models.
We introduce jet topics: a framework to identify underlying classes of jets from collider data. Because of a close mathematical relationship between distributions of observables in jets and emergent themes in sets of documents, we can apply recent techniques in "topic modeling" to extract jet topics from data with mini…
We study D3-brane theories that are dually described as deformations of two different superconformal theories with massless monopoles and dyons. These arise at the self-intersection of a seven-brane in F-theory, which cuts out a link on a small three-sphere surrounding the self-intersection. The spectru…
Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliate manifold morphisms are presented. Although the paper has mainly a survey character, it also includes new results: jets modulo multifoliations are introd…
Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. W…
We present a new flavor of Variational Autoencoder (VAE) that interpolates seamlessly between unsupervised, semi-supervised and fully supervised learning domains. We show that unlabeled datapoints not only boost unsupervised tasks, but also the classification performance. Vice versa, every label not only improves class…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An ad…
A Jet groupoid R_q over a manifold X is a special Lie groupoid consisting of q-jets of local diffeomorphisms from X to X. As a subbundle of the q-th order jet bundle of the trivial bundle X times X, a jet groupoid can be considered as a nonlinear system of partial differential equations (PDE). This leads to the concept…
Equivariant neural network simplifies particle physics models.
We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable 1-forms on $R^3
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…
Jet spaces on Carnot groups have a canonical Lie group structure.
Wind speed prediction improved using a novel deep ensemble learning model inspired by jet aerodynamics.
Jets from boosted heavy particles have a typical angular scale which can be used to distinguish them from QCD jets. We introduce a machine learning strategy for jet substructure analysis using a spectral function on the angular scale. The angular spectrum allows us to scan energy deposits over the angle between a pair …
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space . A generalized theorem of characterization of our jet geometrical KCC-invariants is also presented.
We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integral homology spheres. Combining these inequalities with the known classifications of non-zero degree maps between Seifert fibered spaces, we prove that a map f from Y' to Y between Seifert homology spheres yie…
AI helps build particle physics theories more efficiently.
VAE improves anomaly detection for jet tagging at the LHC.
Finite-gap solutions approximate jets of initial data for certain BKM systems.
We show that the local equivalence problem for second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also show that, modulo Cartan duality and point transformations, the Painlevé-I equati…
In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geome…
Study jets of flat partial connections in foliations.
We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries - in parti…
Establishes jet transversality for regular maps from flexible manifolds.
Jet bundles as higher-order polarised -contact manifolds
In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras in dimensions 3 and 4. The classification in dimension~4 is closely connected with normal forms of nondegenerate elliptic …
A holonomic knot is a knot in 3-space which arises as the 2-jet extension of a smooth function on the circle. A holonomic knot associated to a generic function is naturally framed by the blackboard framing of the knot diagram associated to the 1-jet extension of the function. There are two classical invariants of frame…
In this paper we introduce a natural definition for the affine maps between two Finsler manifolds and and we give some geometrical properties of these affine maps. Starting from the equations of the affine maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet space $J^1(TM;…
Study shows no periodic geodesics in jet space.