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.
Study families of Lie algebroids on complex spaces, introducing unfoldings.
Classifies singularities of smooth vector fields on the line.
Classifies vector fields in the kernel of a 1-form, up to equivalence.
Study deformations of Calabi-Yau foliations using Kuranishi spaces.
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…
New method for unbinned, profiled unfolding in particle physics.
New method unfolds distribution moments directly from data without binning.
Study on unfolding maps of surfaces in 3D space, proving versality conditions.
New deep-unfolded network improves video background separation.
Unfolding paths in Outer space accumulate on a simplex, not converge.
The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.
Collider data must be corrected for detector effects ("unfolded") to be compared with many theoretical calculations and measurements from other experiments. Unfolding is traditionally done for individual, binned observables without including all information relevant for characterizing the detector response. We introduc…
We show that every convex polyhedron admits a simple edge unfolding after an affine transformation. In particular there exists no combinatorial obstruction to a positive resolution of Durer's unfoldability problem, which answers a question of Croft, Falconer, and Guy. Among other techniques, the proof employs a topolog…
A simple self-supervised model for tensor RPCA using deep unfolding.
A new machine learning method handles nuisance parameters for better unfolding in particle physics.
In a previous work we proved the uniqueness and functoriality of primary unfoldings on simple Thom-Mather spaces, which is a functor to the category of smooth manifolds. In this article we extend these results for any stratified Thom-Mather pseudomanifold with arbitary finite length, through a new kind of intermediate …
A pseudo-edge graph of a convex polyhedron K is a 3-connected embedded graph in K whose vertices coincide with those of K, whose edges are distance minimizing geodesics, and whose faces are convex. We construct a convex polyhedron K in Euclidean 3-space with a pseudo-edge graph with respect to which K is not unfoldable…
This is mainly a survey article on the recent development of the theory of graph-like Legendrian unfoldings and its applications. The notion of big Legendrian submanifolds was introduced by Zakalyukin for describing the wave front propagations. Graph-like Legendrian unfoldings belong to a special class of big Legendria…
Unified framework for spectral methods, kernel learning, and manifold unfolding.
We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the Kähler geometry of a finite dimensional complex projective spaces.
Deep unfolding accelerates MCMC-based COP solvers.
New algorithms accelerate SVGD convergence using deep unfolding.
Chebyshev steps improve convergence in deep-unfolded gradient descent.
In this paper, we introduce the notions of map-germs of pedal unfolding type and normalized Legendrian map-germs; and then we show that the fundamental theorem of calculus provides a natural one to one correspondence between Whitney umbrellas of pedal unfolding type and normalized swallowtails.
Develops a Thom-Mather theory for corank 1 frontals.
Let be a closed and oriented -manifold. We define different versions of unfolded Seiberg-Witten Floer spectra for . These invariants generalize Manolescu's Seiberg-Witten Floer spectrum for rational homology -spheres. We also compute some examples when is a Seifert space.
ULES embeds dynamic networks with stability guarantees.
In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the power of neural networks. In this work, we study unfolded ISTA (Iterative Shrinkage…
Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplic…
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the underlying submanifold is isometric to a convex subset, and we provide some simple e…
New method uses Wasserstein loss for data unfolding, offering better accuracy than classical techniques.
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about the true distribution from theory or previous experiments is used for Monte-Car…
We use the construction of unfolded Seiberg-Witten Floer spectra of general 3-manifolds defined in our previous paper to extend the notion of relative Bauer-Furuta invariants to general 4-manifolds with boundary. One of the main purposes of this paper is to give a detailed proof of the gluing theorem for the relative i…
This paper develops a novel deep recurrent neural network for sequential signal reconstruction.
A new method for unfolding histograms without matrix inversion.
A very simple heuristic approach to the unfolding problem will be described. An iterative algorithm starts with an empty histogram and every iteration aims to add one entry to this histogram. The entry to be added is selected according to a criteria which includes a test and a regularization. After a relatively s…
This article is devoted to the study of smooth desingularization, which are customary employed in the definition of De Rham Intersection Cohomology with differential forms. In this paper we work with the category of Thom-Mather simple spaces. We construct a functor which sends each Thom-Mather simple space into a smoot…
Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show t…
A framework for stable dynamic network embeddings using static methods.
We introduce the notion of reticular Legendrian unfoldings in order to investigate stabilities of bifurcations of wavefronts generated by a hypersurface germ with a boundary, a corner, or an r-corner in a smooth n dimensional manifold. We define several stabilities of reticular Legendrian unfoldings and prove that they…
The paper proves ideal triangulations and disk unfolding for singular flat surfaces.
Study flat metrics from right prisms, finding non-lattice surfaces with translation coverings.
We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such, our network leverages by design that signals have a sparse representation and t…
State-free reversible VAMPnets (SRVs) are a neural network-based framework capable of learning the leading eigenfunctions of the transfer operator of a dynamical system from trajectory data. In molecular dynamics simulations, these data-driven collective variables (CVs) capture the slowest modes of the dynamics and are…
We study the intrinsic geometry of area minimizing (and also of almost minimizing) hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. For any such hypersurface we define and construct a so-called S-structure which reveals some unexpected geometric and analytic properties of the …
The paper generalizes envelope constructions for chords in circles, revealing complex singularities.
Study the geometry of bifurcation sets for specific types of functions.
Proposes a novel neural architecture for sparse coding using learned greedy pursuit.