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.
Topological attention improves forecasting of univariate time series.
A new method for graph-structured data improves transformer performance by incorporating topology.
Attention-based models have recently shown great performance on a range of tasks, such as speech recognition, machine translation, and image captioning due to their ability to summarize relevant information that expands through the entire length of an input sequence. In this paper, we analyze the usage of attention mec…
CRAUM-Net improves salient object detection with context and uncertainty modeling.
This is a survey article for the forthcoming `A Concise Encyclopedia of Knot Theory.' We focus on the topology of spatial graphs with few vertices and edges, paying particular attention to Brunnian -graphs.
Graph Attention Networks improve image classification with superpixels.
Reformulates binary classification on manifolds using Yang-Mills-Higgs theory.
Study local and global aspects of complex plane curve embeddings.
Topologically protected vortex knots and links are proposed and proven.
Paper introduces a conformer-based system for streaming language identification in long-form speech.
Improved neural transducer model outperforms attention model on longer sequences.
TGAT learns node embeddings for evolving graphs, capturing both static and temporal features.
The interplay between inter-neuronal network topology and cognition has been studied deeply by connectomics researchers and network scientists, which is crucial towards understanding the remarkable efficacy of biological neural networks. Curiously, the deep learning revolution that revived neural networks has not paid …
GISST interprets GNNs by combining attention and sparsity for graph structure and node feature importance.
We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that the Lie group action must have odd cohomogeneity. We pay special attention to mani…
Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence diagrams. How do we summarize them, average them or cluster them? One approach -- th…
CT improves neural network performance on cell complex data.
Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We consider problems of estim…
In recent years a lot of attention has been paid to topological spaces which are a bit more general than smooth manifolds - orbifolds. Orbifolds are intuitively speaking manifolds with some singularities. The formal definition is also modelled on that of manifolds, an orbifold is a topological space which locally is ho…
Study on minimal torsion topological generators for mapping class groups of infinite-type surfaces.
AdaCAD improves semi-supervised classification by focusing on intra-class nodes.
Bayesian supertrees method uses variational Bayes for overlapping taxon subsets.
We consider the quantum Teichmuller space of the punctured surface introduced by Chekhov-Fock-Kashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmuller space of the surface. In order to apply it in 3-dimensional topology, we put more attention to the details involv…
Develops a mean-field theory for multi-head self-attention under cross-entropy training.
The Turaev genus of a knot is a topological measure of how far a given knot is from being alternating. Recent work by several authors has focused attention on this interesting invariant. We discuss how the Turaev genus is related to other knot invariants, including the Jones polynomial, knot homology theories, and ribb…
Advanced methods of applying deep learning to structured data such as graphs have been proposed in recent years. In particular, studies have focused on generalizing convolutional neural networks to graph data, which includes redefining the convolution and the downsampling (pooling) operations for graphs. The method of …
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces ov…
We describe loss surfaces using topological Betti numbers.
A new topology improves decentralized learning efficiency and accuracy.
Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. …
We study the problem of prescribing the Paneitz curvature on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of suc…
Study of symplectic manifolds degenerating into singular spaces.
This paper presents an innovative and generic deep learning approach to monitor heart conditions from ECG signals.We focus our attention on both the detection and classification of abnormal heartbeats, known as arrhythmia. We strongly insist on generalization throughout the construction of a deep-learning model that tu…
Pulli kolam is a ubiquitous art form in south India. It involves drawing a line looped around a collection of dots (pullis) place on a plane such that three mandatory rules are followed: all line orbits should be closed, all dots are encircled and no two lines can overlap over a finite length. The mathematical foundati…
Power system studies require the topological structures of real-world power networks; however, such data is confidential due to important security concerns. Thus, power grid synthesis (PGS), i.e., creating realistic power grids that imitate actual power networks, has gained significant attention. In this letter, we cas…
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generaliz…
Expander graphs have been a focus of attention in computer science in the last four decades. In recent years a high dimensional theory of expanders is emerging. There are several possible generalizations of the theory of expansion to simplicial complexes, among them stand out coboundary expansion and topological expand…
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
New method identifies network dynamics and noise structure.
Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects of this relationship, as well as the tests of this conjecture performed over th…
Unified analysis for decentralized SGD across various topologies and updates.
A3T-GCN improves traffic forecasting by capturing spatial and temporal dependencies.
Proposes a graph pooling method leveraging node proximity for hierarchical graph representation learning.
Enhances GNNs by improving input data quality from topology and labels.
This work identifies and mitigates topological bias in HGNNs using meta-weighting and debiasing.
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections and estimate system parameters of a recurrent network, given a sequence of node …
Distance, normals, and double normals for real plane curves with singularities
A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface M endowed with an anti-holomorphic involution which determines topologically the o…