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.
Moving between 3-manifold triangulations is NP-hard
Hamilton's Ricci flow (RF) equations were recently expressed in terms of a sparsely-coupled system of autonomous first-order nonlinear differential equations for the edge lengths of a d-dimensional piecewise linear (PL) simplicial geometry. More recently, this system of discrete Ricci flow (DRF) equations was further s…
This paper finds all prime alternating knots with minimal warping degree two.
We construct the first explicit example of a simplicial 3-ball B_{15,66} that is not collapsible. It has only 15 vertices. We exhibit a second 3-ball B_{12,38} with 12 vertices that is collapsible and evasive, but not shellable. Finally, we present the first explicit triangulation of a 3-sphere S_{18, 125} (with only 1…
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…
Topic models, and more specifically the class of Latent Dirichlet Allocation (LDA), are widely used for probabilistic modeling of text. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its spe…
New method for matching bipartite and unipartite graphs without collapsing.
Classifies actions of tori on manifolds up to diffeomorphisms.
Spectral clustering with edge counting detects communities in sparse models.
Paper shows how to represent Milnor's triple linking number using chord diagrams and doodle invariants.
Study financial contagion and risk in sparse networks with directed edges.
ACERL embeds networks into a low-dimensional space preserving structural and semantic properties.
New method handles structural uncertainty in graphs better than existing models.
Enhances neural architecture search efficiency and prevents performance collapse.
Sparse connectivity improves generalization in neural networks below the Edge of Stability.
Graph Neural Networks (GNNs) have proved to be an effective representation learning framework for graph-structured data, and have achieved state-of-the-art performance on many practical predictive tasks, such as node classification, link prediction and graph classification. Among the variants of GNNs, Graph Attention N…
We analyze the degree-two part of the Torelli group's associated graded.
This paper extends neural collapse to regression problems, revealing key features and structures.
New CRM models for sparse networks with linear edge growth.
Study detects edge correlation between unlabeled random graphs.
Gradient descent on LSE objectives implicitly performs EM, leading to collapse without volume control.
Latent Dirichlet Allocation (LDA) is a topic model widely used in natural language processing and machine learning. Most approaches to training the model rely on iterative algorithms, which makes it difficult to run LDA on big corpora that are best analyzed in parallel and distributed computational environments. Indeed…
VINNAS uses variational inference to avoid mode collapse in neural architecture search.
New analysis shows how attention masks and LayerNorm prevent rank collapse in transformers.
Grokking occurs at numerical stability edge, requiring regularization to prevent.
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint cl…
New metrics improve scRNA-seq perturbation modeling by reducing mode collapse.
FedDST trains sparse sub-networks to improve efficiency in federated learning.
Architectures for sparse hierarchical representation learning have recently been proposed for graph-structured data, but so far assume the absence of edge features in the graph. We close this gap and propose a method to pool graphs with edge features, inspired by the hierarchical nature of chemistry. In particular, we …
Proposes a Bayesian approach for automatic node selection in sparse neural networks.
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a general model of cascades, including the voter model and the independent cascad…
New method aggregates nodes in sparse graphical models.
MMCGAN uses explicit manifold learning to improve GAN performance.
The paper studies strict equivalence in multi-virtual linkoids with new invariants.
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the LASSO coefficient to obtain an appropriate number of edges in the adjacency matr…
We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental group. In degree two we clarify the relation between hyperbolic and atoroidal cla…
We propose a dynamic edge exchangeable network model that can capture sparse connections observed in real temporal networks, in contrast to existing models which are dense. The model achieved superior link prediction accuracy on multiple data sets when compared to a dynamic variant of the blockmodel, and is able to ext…
Efficiently estimates longitudinal networks by merging sparse networks.
We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over multiple samples, for little more computational cost than drawing a single addit…
Study on GD and SGD over diagonal networks, focusing on stepsizes and regularisation.
Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors,…
We calculate the twisted Reidemeister torsion of the complement of an iterated torus knot associated with a representation of its fundamental group to the complex special linear group of degree two. We also show that the twisted Reidemeister torsions associated with various representations appear in the asymptotic expa…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and valu…
Evidential Softmax preserves multimodality in sparse probability distributions for generative models.
New algorithm estimates edge density of random graphs robustly, achieving optimal breakdown point.
The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns typical mass univariate methods. Furthermore most network estimation methods cannot d…
New pruning method for sparse additive models speeds up causal structure learning.
We introduce a new method for estimating the growth of various quantities arising in dynamical systems. We apply our method to polygonal billiards on surfaces of constant curvature. For instance, we obtain power bounds of degree two plus epsilon in length for the number of billiard orbits between almost all pairs of po…