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.
Generalized Tanaka prolongation ensures convergence of formal embeddings of complex manifolds.
We continue the study the Dolbeault dga of the formal neighborhood of an arbitary closed embedding of complex manifolds previously defined by the author in \cite{DolbeaultDGA}. The special case of the diagonal embedding has been studied in \cite{Diagonal}. We describe the Dolbeault dga explicitly in terms of the formal…
Generalizes embedding formalism for CFTs on curved backgrounds.
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is…
The paper explores how semantic independence can be captured in text embeddings using partial orthogonality.
In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the training data and the networks' structure. A longer version of this paper with more…
Spaces over BO are equivalent to thickened manifolds.
The Fisher information metric is an important foundation of information geometry, wherein it allows us to approximate the local geometry of a probability distribution. Recurrent neural networks such as the Sequence-to-Sequence (Seq2Seq) networks that have lately been used to yield state-of-the-art performance on speech…
Embedding large and high dimensional data into low dimensional vector spaces is a necessary task to computationally cope with contemporary data sets. Superseding latent semantic analysis recent approaches like word2vec or node2vec are well established tools in this realm. In the present paper we add to this line of res…
Inspired by a work of Kapranov, we define the notion of Dolbeault complex of the formal neighborhood of a closed embedding of complex manifolds. This construction allows us to study coherent sheaves over the formal neighborhood via complex analytic approach, as in the case of usual complex manifolds and their Dolbeault…
Embeds hyperbolic plane into 3D space with detailed geometric analysis.
We investigate modular embeddings for semi-arithmetic Fuchsian groups. First we prove some purely algebro-geometric or even topological criteria for a regular map from a smooth complex curve to a quaternionic Shimura variety to be covered by a modular embedding. Then we set up an adelic formalism for modular embeddings…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of dif…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to large graphs. We therefore propose a framework for parallel computat…
We study a certain class of embedded two-foams that arise from gluing discs into ribbon torus knots along nonintersecting torus meridians. We exhibit several equivalent diagrammatic formalisms for these objects and identify several of their invariants, including a unique prime decomposition.
New insights show embedding lengths correlate with semantic properties.
DiSeNE generates interpretable node embeddings without supervision.
We focus our attention on the link prediction problem for knowledge graphs, which is treated herein as a binary classification task on neural embeddings of the entities. By comparing, combining and extending different methodologies for link prediction on graph-based data coming from different domains, we formalize a un…
Renormalized volume invariant for knots in 3-sphere computed.
The action of Batalin-Vilkovisky Delta-operator on semidensities in an odd symplectic superspace is defined. This is used for the construction of integral invariants on surfaces embedded in an odd symplectic superspace and for more clear interpretation of the Batalin-Vilkovisky formalism geometry.
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inferenc…
Heterogeneous information network (HIN) embedding has gained increasing interests recently. However, the current way of random-walk based HIN embedding methods have paid few attention to the higher-order Markov chain nature of meta-path guided random walks, especially to the stationarity issue. In this paper, we system…
The abstract manifold cannot have uniformly quasiregular self-maps.
This work proposes a geometric approach to equivariant message passing on Riemannian manifolds.
Generalizes holographic method to higher codimension submanifolds.
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-r…
Word embeddings are commonly obtained as optimizers of a criterion function of a text corpus, but assessed on word-task performance using a different evaluation function of the test data. We contend that a possible source of disparity in performance on tasks is the incompatibility between classes of transformat…
Our work proves robustness of embedding schemes to discrete changes in text.
We address the following natural extension problem for group actions: Given a group , a subgroup , and an action of on a metric space, when is it possible to extend it to an action of the whole group on a (possibly different) metric space? When does such an extension preserve interesting properties o…
We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in …
New method embeds dynamic networks with stability for node behavior.
This paper introduces lattice representations for efficient discrete learning.
New energy measure for isolated systems in general relativity.
Develops a new framework for temporal anchoring in deep embedding spaces.
BC-Aligner maintains backward compatibility of embeddings after frequent updates.
Proves a theorem for comparing surfaces in 3D space.
This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the usual infinite boundary and a corner where the two meet. On the finite boundary …
New walk extraction strategies improve node embeddings in KGs.
The abstract discusses convergent realizations of Lie subalgebras in control theory.
New algorithm tackles dynamic query routing to multiple embedding models.
Using standard analysis only, we present an extension of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesim…
We solve the vector embedding problem by minimizing total distortion under constraints.
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formalism in which self-adjoint (Schroedinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we …
Formalizes concepts as latent variables in hierarchical models for high-dimensional data.
Quantum kernels can be efficiently embedded into classical feature spaces.
Researchers solve a question about embedding knots into Legendrian structures.
Study the spaces of Legendrian knots and links with maximal Thurston-Bennequin invariant.
Estimates peer influence effects using embeddings for social networks.