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.
New graph embedding method improves link prediction and node classification.
Mathematical analysis of SNE and t-SNE for dimension reduction.
Urban2Vec combines street view imagery and POIs for better urban neighborhood embeddings.
t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. W…
Tubes in manifolds require wide spaces.
Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity in embedding space is not optimized in the learning. In this paper we propose a …
New framework distinguishes knots via neighborhood invariants.
Shows Euler-like vector fields come from specific embeddings.
Survey simplifies embedding theorems for manifolds.
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation…
The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…
EHNA learns node embeddings from historical network neighborhoods.
In this article, we demonstrate methods for the local removal and modification of complex tangents to embeddings of into . In particular, given any embedding of and a neighborhood of the complex tangents of the embedding, we show that there exists a (-close) totally real embedding which a…
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…
LPL optimizes embeddings to align local neighborhoods, improving cross-lingual word alignment.
Proposes a parametric t-SNE without perplexity tuning.
A multibranched surface is a 2-dimensional polyhedron without vertices. We introduce moves for multibranched surfaces embedded in a 3-manifold, which connect any two multibranched surfaces with the same regular neighborhoods in finitely many steps.
New method samples triplets from data distributions for training Triplet networks.
The study proves a tube theorem for complex hyperbolic manifolds.
Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear…
Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to the neighborhood, which may significantly degrades the flexibility of represent…
STAG injects noise into graph neural networks to improve performance.
This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970's but never published. Organizers of the Workshops in Geometric Topology (http://www.uwm.edu/~craigg/workshopgtt.htm) with the support of the National Science Foundation have facilitated the pr…
Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold.Further, an almost hyperHermitian struc…
In this paper, we study the global geometry of complete, constant mean curvature hypersurfaces embedded in n-manifolds. More precisely, we give conditions that imply properness of such surfaces and prove the existence of fixed size one-sided regular neighborhoods for certain constant mean curvature hypersurfaces in cer…
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-s…
In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth -spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.
GCNs learn by embedding similar nodes within a class and leveraging consistent neighborhood structures.
PGRec improves recommendation by modeling user-item preferences as a graph and embedding it for better predictions.
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…
We propose a dynamic neighborhood aggregation (DNA) procedure guided by (multi-head) attention for representation learning on graphs. In contrast to current graph neural networks which follow a simple neighborhood aggregation scheme, our DNA procedure allows for a selective and node-adaptive aggregation of neighboring …
Proposes a method to improve graph embedding by removing least frequent nodes.
Quantized Stochastic Primal-Dual Methods for Distributed Optimization
We propose a new metaheuristic training scheme that combines Stochastic Gradient Descent (SGD) and Discrete Optimization in an unconventional way. Our idea is to define a discrete neighborhood of the current SGD point containing a number of "potentially good moves" that exploit gradient information, and to search this …
Framework detects tipping points in complex systems using ML.
A new GNN model SPIN achieves state-of-the-art performance on diverse real-world datasets.
Study extends Nirenberg-Spencer's question to families of submanifolds.
Proposes a novel node embedding framework for graphs using Fisher Information.
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of…
Linearizability of singular foliations is preserved under a specific equivalence relation.
New method constructs Stein surfaces using topological isotopy.
The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN…
This paper sets a lower limit for the size of Weinstein's Lagrangian tubular neighborhoods.
Survey of Locally Linear Embedding and its variants.
New condition ensures submanifolds are skew in small areas.
Let be a regular neighborhood of a negative chain of -spheres (i.e. exceptional divisor of a cyclic quotient singularity), and let be a rational homology ball which is smoothly embedded in . Assume that the embedding is simple, i.e. the corresponding rational blow-up can be obtained by just a sequen…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learning tasks. However, learning structural representations of nodes is a …
The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection between germs of tubular neighborhoods of M and germs of "Euler-like" vector fields on V. We shall explain how to approach…