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.
SRNNs learn dynamics of physical systems from data.
New neural net learns time-reversible symplectic dynamics.
Characterizes group-equivariant neural networks for three groups.
Proposes NSSNNs to predict nonseparable Hamiltonian systems.
SSINNs learn Hamiltonian systems from data with interpretable, low-memory models.
Neural network models transform physical systems into latent Gaussian distributions.
An algorithm for efficient computation of equivariant neural network layers.
Novel method combines physics priors for energy-conserving dynamics.
New algorithm speeds up group equivariant neural networks computations.
GeoHNN models physics laws for stable, accurate predictions.
New Adam optimizer generalized for manifold training of neural networks.
Hamiltonian RNN controls hidden states gradient for long-term dependencies.
The paper develops spectral networks in symplectic topology and their relation to Lagrangian fillings.
Paper designs Poisson integrators using machine learning.
SympNets identify Hamiltonian systems from data using linear, activation, and gradient modules.
We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization and stabilization of training procedures, and also can parameterize matrices of bo…
SGNs use Hamiltonian mechanics for invertible deep generative modeling.
In this work a novel method to quantify spectral ergodicity for random matrices is presented. The new methodology combines approaches rooted in the metrics of Thirumalai-Mountain (TM) and Kullbach-Leibler (KL) divergence. The method is applied to a general study of deep and recurrent neural networks via the analysis of…
We provide a new topological interpretation of the symplectic properties of gluing equations for triangulations of hyperbolic 3-manifolds, first discovered by Neumann and Zagier. We also extend the symplectic properties to more general gluings of PGL(2,C) flat connections on the boundaries of 3-manifolds with topologic…
New approach relaxes inductive biases of physics-inspired NNs for better performance.
A symplectic manifold is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and blow-down. This theorem follows from a general Relative/Absolute correspondence for a symple…
Study on symplectic Dirac operators on foliations, estimating eigenvalues.
We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably we show that several symplectic manifolds do not admit log-symplectic structures and several log-symplectic manifolds do not admit symplectic structures, for example #m CP^2 # n bar(CP^2)…
Symplectic 4-manifolds can be divided into three parts with a special structure.
Smooth symplectic manifolds can be approximated by PL symplectic manifolds.
We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This description is particularly nice if the group is Hamiltonian, that is, if the left c…
Solves symplectic and conformal symplectic group actions equivalence problem.
We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that cohomologically symplectic solvmanifolds are symplectic.
We present some methods to construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or non-symplectic cyclic isotropy point sets. All such actions are not compatible with any symplectic form.
Anti-symplectic involutions connect a sphere in a symplectic surface.
New insights into symplectic loops and their flux groups.
We use the minimal coupling procedure of Sternberg and Weinstein and our pseudo-symplectic capacity theory to prove that every closed symplectic submanifold in any symplectic manifold has an open neighborhood with finite (-sensitive) Hofer-Zehnder symplectic capacity. Consequently, the Weinstein conjecture holds n…
Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify symplectically ruled log-symplectic manifolds (both orientable and non-orientab…
Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.
Study on symplectic semi-characteristic using cohomology and vector fields.
A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms. The main results are: * If a symplectic form represents a bounded cohomology cl…
Extends symplectic flow results to foliations.
Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.
New models for symplectic structures on classifying stacks.
We introduce a method to resolve a symplectic orbifold into a smooth symplectic manifold. Then we study how the formality and the Lefschetz property of the symplectic resolution are compared with that of the symplectic orbifold. We also study the formality of the symplectic blow-up of a symplectic orbifold along symple…
Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic manifold admitting a flat symplectic connection and an infinitesimal automorphism that is not symplectic.
We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic and singularities. We use discrete symplectic invariants to distinguish symplectic singularities of the curves. We also give the geometric description of symplectic classes.
Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres is replaced with a rational homology ball , . Subsequently, Symington [Sy] defined this procedure in the symplectic category, where a symplectic (given…
Symplectic structures simplified for compact manifolds.
Constructs infinite-dimensional Siegel disc as symplectic and Kaehler quotient.
The study of flat symplectic Lie algebras and groups.
In this paper, we introduce the notion of a pre-symplectic algebroid, and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebroids. This result is the geometric generalization of the relation between left-symmetric algebras and symplectic (Frobenius) Lie algebras. A…
In [11], I. M. Gelfand, V. Retakh, and M. Shubin defined the symplectic sectional curvature of a torsion-free connection preserving a symplectic form. The present article defines the corresponding notion of constant symplectic sectional curvature and characterizes this notion in terms of the curvature tensor of the sym…