Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and canno…
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arXiv research
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.
168,742 papers · 148 categories
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48 results for “topological data structure”
Topological data analysis quantifies structural dynamics using persistent homology.
problem Analyzing the shape and topology of structural dynamics data.
method Topological Data Analysis (TDA) with persistent homology to quantify shape over scales.
result Persistent homology reveals significant changes in manifold shape due to damage, not temperature.
New topological methods for hypergraph data improve community detection and pattern recognition.
problem Community detection and pattern recognition in hypergraph data.
method Introducing a new topological space structure of hypergraph data, proposing modified nearest neighbors methods.
result Improved methods for community detection and pattern recognition in hypergraph data.
A new model learns graph structures from data.
problem Learning graph topologies from data.
method Proposes a learning to optimise (L2O) approach to learn graph structures from node data.
result The proposed model learns graph structures more efficiently than classic iterative algorithms.
Paper introduces topological eigenvalue theorems for tensor analysis in multi-modal data.
problem Lack of deep understanding of tensor structures in multi-modal data fusion.
method Introduces topological perspective to tensor eigenvalue analysis, linking eigenvalues to topological features.
result Establishes new theorems that enhance understanding of tensor structures in data fusion.
Paper proposes learnable topological features for efficient phylogenetic inference.
problem Finding appropriate topological structures for phylogenetic inference tasks requires significant design effort and domain expertise.
method Combines raw node features with graph neural networks to automatically adapt to different tasks.
result Demonstrates effectiveness and efficiency on simulated and real data phylogenetic inference tasks.
PERCEPT detects changes in high-dimensional data streams using topological data analysis.
problem Detecting changes in high-dimensional data streams, especially when embedded in a low-dimensional space.
method Leverages topological data analysis to learn embedded topology as a point cloud via persistence diagrams, then applies non-parametric monitoring for detecting changes.
result Demonstrates efficient detection of online changes from high-dimensional data streams.
A faster, more stable method for optimizing topological functions.
problem Optimizing topological functions is computationally expensive and unstable.
method Introduces a novel backpropagation scheme for faster and more robust optimization.
result Produces more robust optima and stable visualizations.
TADA detects anomalies in time series using topological data analysis.
problem Detecting global changes in dependency structure between channels in multivariate time series.
method Topological Data Analysis for detecting anomalies in multivariate time series.
result The approach is more suitable for detecting global changes of correlation structures than existing methods.
A new method for graph-structured data improves transformer performance by incorporating topology.
problem Improving transformer performance on graph-structured data.
method Parameterizing topological masks as a learnable function of a weighted adjacency matrix, approximated with graph random features.
result Efficient masking algorithms provide strong performance gains for tasks on image and point cloud data.
We analyze oversquashing in topological message-passing using relational structures.
problem Oversquashing in topological message-passing remains understudied.
method A unifying axiomatic framework that bridges graph and topological message-passing.
result Potential to advance topological deep learning.
We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological structures. We compute the persistent homology associated to these structures in order…
A hierarchical clustering algorithm for data clouds without structure assumptions.
problem Exploring data clouds without making structure assumptions.
method Hierarchical topological clustering algorithm that infers persistence of outliers and clusters of arbitrary shape from data hierarchy.
result The algorithm can provide meaningful clusters in complex datasets.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
problem Investigate cosmic web evolution in CDM cosmologies.
method Apply LITE method to embed persistence diagrams into vector spaces and analyze cosmic structures.
result Discover a correlation between Persistence Energy and redshift values.
New method integrates topological knowledge into data embeddings.
problem Lack of general tools to incorporate prior topological knowledge into embeddings.
method Introduces new topological losses to topologically regularize data embeddings.
result Natural representation of simple models like clusters and flares.
Pipeline learns topological features for protein stability prediction.
problem Predicting protein stability using topological features.
method Data-driven method to learn topological features, comparing with expert features.
result Topological features achieve 92%-99% of SME-based models' performance.
This paper introduces TDA and TSI for better business analytics.
problem Nonlinear, multi-scale business datasets under-represented by traditional tools.
method Topological Data Analysis (TDA) and Topological Stability Index (TSI).
result TSI reveals structural variability in business data.
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
Entropy data replaces classical charts for smooth manifolds.
problem Establishing smooth structures on topological manifolds.
method Using entropy data to define admissible coordinate functions and reconstruct smooth atlases.
result Entropy-smooth structures are equivalent to classical smooth structures and stable under perturbations.
Reproduces IVFS for high-dimensional data structure preservation.
problem Preserving high-dimensional data structure in unsupervised feature selection.
method Inspired by random subset method, IVFS maintains data similarity through topological structure.
result IVFS outperforms SPEC and MCFS on most datasets.
In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low dimensional topological map for each of them. When it is trained as an autoencoder, th…
Regularization preserves topological data structure in autoencoders.
problem Ensuring topological data structure preservation in autoencoders.
method Regularization using Legendre nodes to preserve manifold embedding.
result Regularized autoencoders ensure one-to-one embedding of data manifolds.
Mathematical pipeline identifies structural homology of knotted proteins.
problem Quantification and classification of protein structures, especially knotted proteins, require noise-free and complete data.
method Developed a geometric framework using persistent homology to analyze protein structures.
result Persistent homology accurately represents structural homology of knotted proteins and identifies geometric features of protein entanglement.
Topological twists for 4d N=2 theories depend on spacetime type, gerbe connections, and generalized spin-c structures.
problem Defining topologically twisted partition functions for 4d N=2 theories.
method Topological twisting for general 4d N=2 theories, introducing generalized spin-c structures.
result Topological partition functions depend on spacetime type, gerbe connections, and generalized spin-c structures.
Topological Flow Matching: A Generative Modeling Framework for Structured Spaces
problem Handling structured spaces in generative modeling
method Introducing topological flow matching
result Captures the structure of the underlying domain while preserving desirable properties
Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This 4-neighbourhood topological simplicity makes the application of convolutional masks straightf…
Combines geometry and topology for analyzing hierarchical datasets.
problem Analyzing complex, hierarchical datasets with irregular structures.
method Combines manifold learning and topological data analysis.
result Superior classification results compared to state-of-the-art methods.
PLLay adds topological layers to deep learning models efficiently.
problem Efficiently incorporating topological features into deep learning models.
method Persistence landscapes for differentiable topological features.
result PLLay improves model learnability and robustness.
TDA improves stock portfolio selection by analyzing data structure.
problem Traditional portfolio selection methods fail to handle stock market data complexities.
method Two-stage method involving time series generation and clustering with TDA features.
result TDA-based portfolio outperforms other methods consistently over different time frames.
FCM clustering adapts to persistence diagrams for topological data analysis.
problem Integrating topological data into machine learning workflows.
method Adapting Fuzzy c-Means to persistence diagrams.
result FCM clustering captures topological structure without additional processing.
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of to…
The paper sets limits on neural network sizes based on dataset shapes.
problem Understanding the size of neural networks needed for accurate predictions.
method Examined how the shape of data influences neural network complexity.
result Established upper limits on neural network width based on dataset topology.
Persistent homology reveals a topological signature of grokking in neural networks.
problem Understanding how neural networks learn and generalize from modular arithmetic tasks.
method Persistent homology on point clouds derived from embedding matrices of models trained on modular arithmetic.
result A sharp increase in first homology persistence indicates grokking, with a dominant long-lived topological feature and structured secondary features.
Novel algorithm learns sparse signal representations over topological spaces.
problem Sparse representation of signals over combinatorial topological spaces.
method Leveraging Hodge theory, the paper embeds topology into a dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, and optimizes the dictionary coefficients and sparse signal representation via iterative alternating algorithms.
result Efficiently learned sparse representations and underlying relational structure of topological signals.
CT improves neural network performance on cell complex data.
problem Improving predictive performance of neural networks on complex data.
method Introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes.
result CT achieves state-of-the-art performance on cell complex datasets without complex enhancements.
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theo…
Survey on hyperplane arrangements and their topology.
problem Topology of hyperplane arrangements.
method Focus on the relationship between topology and real structure.
result Relationship between topology and real structure of hyperplane arrangements.
Kontsevich's classes distinguish smooth structures on fiber bundles.
problem Distinguishing smooth structures on fiber bundles.
method Using Kontsevich's characteristic classes and real blow-up construction.
result Kontsevich's classes are determined by the topology of the 2-point configuration space bundle.
In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite the success of recent deep learning methods for diffusion, we find that they often…
Detects singularities in complex data to improve machine learning models.
problem Real-world data often contains non-manifold structures (singularities) that can mislead machine learning models.
method Develops a topological framework to quantify local intrinsic dimension and Euclidicity score for multiple scales.
result Identifies singularities and captures local geometric complexity in image data.
Current paper addresses topology issues in PBSHM to enable transfer learning.
problem Absence of meaningful topology on graph space hinders rigorous analysis.
method Introduced parametric families of structures, defined open sets, and continuous variation between fibres.
result Enabled rigorous transfer learning in PBSHM by addressing topology issues.
Study uses big data to analyze quantum invariants.
problem Investigate structural properties of Jones polynomial.
method Exploratory and topological data analysis, including coloring, rank increase, categorification.
result Contrasts behavior of Jones polynomial under various enhancements.
Paper tackles uncertainty in GNNs for graph data.
problem Uncertainty in GNNs' predictions for graph data.
method CF-T2NN, tensor decomposition, topological learning.
result CF-T2NN improves reliability and interpretability of GNN outcomes.
Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learningmath.DG
New method for manifold topological learning avoids remeshing issues.
problem Persistent homology on manifolds is numerically inconsistent.
method Persistent de Rham-Hodge Laplacians in Eulerian representation.
result Avoids numerical inconsistency over multiscale manifolds.
Data science enhances knot theory by analyzing invariant relations.
problem Understanding the complex relations between knot invariants.
method Topological data analysis applied to knot theory.
result New insights into long-standing conjectures about knots.
A new algorithm reduces the size of datasets for TDA.
problem Processing large datasets with high dimensions in TDA is computationally infeasible.
method Introduced Characteristic Lattice Algorithm (CLA) for data reduction.
result CLA reduces dataset size while preserving geometric and topological features.
In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally inexpensive way. CWGAN consists of a generator and a discriminator, both of which are…
Paper proposes a method to improve circular coordinate representation for detecting changes in high-dimensional datasets.
problem Detecting changes in high-dimensional datasets with preserved topological structures.
method Adapt circular coordinate framework using a generalized penalty function instead of an L2 penalty.
result Circular coordinates with generalized penalty can detect changes in high-dimensional datasets under different sampling schemes.