New model predicts persistent weather patterns better than persistence model.
problem Improving weather forecasting accuracy for persistent patterns.
method Mixture of experts model using ordinal neural network.
result The model outperforms persistence and other models for longer time horizon predictions.
New model predicts energy prices volatility by smoothing time variation and persistence.
problem Separate study of volatility's time variation and persistence.
method Dynamic persistence model that allows shocks with heterogeneous persistence to vary smoothly over time.
result Significantly improves volatility forecasts over state-of-the-art models.
New framework detects time-varying economic persistence.
problem Time-varying persistence in economic shocks.
method Localized regression techniques to identify evolving heterogeneity.
result Substantial persistence variations align with macroeconomic events.
Persistently trained EBMs generate images and estimate complex densities.
problem Challenges in ML learning for energy-based models, especially non-convergence of MCMC.
method Introduce diffusion data, learn a joint EBM through persistent training with enhanced sampling.
result First simultaneous achievement of stability, post-training image generation, and superior out-of-distribution detection for image data.
Develops 2-categorical methods for multi-parameter persistence.
problem Fundamental limitations of traditional persistence modules.
method 2-categorical structures to capture hierarchical interactions.
result New invariants effectively characterize multidimensional topological features.
Persistence landscapes map diagrams into function spaces for statistical and machine learning applications.
problem Mapping persistence diagrams into function spaces for statistical and machine learning.
method Introducing persistence landscapes, weighted persistence landscapes, and Poisson-weighted persistence landscape kernels.
result Persistence landscapes allow for the application of statistical and machine learning tools, and are stable and invertible.
Persistent neurons improve neural network optimization by leveraging previous solutions.
problem Improving neural network optimization under different initialization and data distributions.
method Persistent neurons use information from previous converged solutions to explore new landscapes and avoid local minima.
result Persistent neurons converge to more optimal solutions and improve model performance under various initializations.
Approaches for approximating persistent homology for large datasets.
problem Inability to compute persistent homology for large datasets.
method Multiple subsampling framework for statistical approximation of persistent homology.
result Derivation of finite sample convergence rates for empirical means of persistent homology.
Generates random persistence diagrams for data analysis.
problem Generating random persistence diagrams for data analysis.
method Based on pairwise interacting point processes and RJ-MCMC algorithm.
result Demonstrates the efficacy and utility of RPDG in materials science.
Proposes deep graph persistence to address neural persistence issues in deep learning.
problem Variance of weights and lack of spatial structure in deep neural networks impact neural persistence.
method Extends neural persistence to the whole network, considering interactions between layers.
result Deep graph persistence alleviates variance-related issues and captures persistent paths through the network.
Modeling poverty transitions in India over 54 years, showing rising but persistent poverty.
problem Understanding and addressing poverty dynamics in India over long periods.
method Stochastic model of Geometric Brownian Motion with reallocation (RGBM).
result Annual poverty transitions are common, but poverty persists, especially among the poorest.
The paper examines how long-memory dynamics, rough-volatility, and persistence affect equity volatility forecasting.
problem The study investigates how long-memory dynamics, rough-volatility, and persistence impact equity volatility forecasting.
method The paper combines semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions.
result Persistence measures improve out-of-sample volatility forecasts, particularly during periods of elevated market volatility and in volatility-managed portfolio applications.
Paper presents a more accurate method for nonparametric density estimation using FMMPL and SIR.
problem Improving nonparametric density estimation for complex datasets.
method Finite mixture model of nonparametric density estimation using sampling importance resampling.
result FMMPL provides more accurate results with less space complexity.
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
Paper proves k-means clustering works on persistence diagrams.
problem Complex geometry of persistence diagram space.
method Proves convergence of k-means on persistence diagram space. result Performance of k-means on persistence diagrams and measures is superior. Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
Paper shows how LSTM can remember long sequences by attending to persisted information.
problem LSTMs struggle with long sequences due to fading information and bias towards recent data.
method The paper introduces a mechanism that allows LSTMs to attend to information in memory based on how long it was persisted by the gating mechanism.
result The method improves LSTM's ability to process long sequences by retrieving information proportionally to its persistence in memory.
A new method for stable vector representation of persistence diagrams.
problem Finding a stable vector representation of persistence diagrams for ML tasks.
method Persistence B-spline Grid (PBSG) based on data fitting.
result The PBSG method is stable with respect to the 1-Wasserstein distance metric.
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.
This paper demonstrates the flaws of co-persistence theory proposed by Bollerslev and Engle (1993) which cause the theory can hardly be applied. With the introduction of the half-life of decay coefficient as the measure of the persistence, and both the weak definition of persistence and co-persistence in variance, this…
Differentiable topology layer for machine learning models.
problem Regularizing and incorporating topological priors in machine learning models.
method Computes persistent homology based on level set and edge-based filtrations.
result Demonstrates three novel applications of the topology layer in machine learning.
New methods found persistent tangles in knots.
problem Persistent tangles in knot diagrams.
method Non-trivial colorings for tangles.
result Any knot with non-trivial coloring has persistent tangles.
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
Persistence diagrams from random matrices follow RMT universality, offering a new spectral diagnostic.
problem Understanding spectral properties of random matrices using topological data analysis.
method Applying Morse theory to persistence diagrams of quadratic forms restricted to unit spheres.
result Persistence entropy outperforms traditional level spacing ratios in discriminating random matrix ensembles.
New method for analyzing multiparameter persistence modules from smooth functions.
problem Analyzing multiparameter persistence modules from smooth functions.
method Generalized Morse theory applied to cobordism and Cerf theory.
result Complete description of persistence modules as direct sums of indecomposables.
Develops robust persistence diagrams using kernel methods.
problem Persistence diagrams are sensitive to data perturbations.
method Constructs robust persistence diagrams from superlevel filtrations of robust density estimators using reproducing kernels.
result Robust persistence diagrams are consistent estimators in bottleneck distance.
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.
This paper interprets critical scales in persistent homology for compact metric spaces.
problem Understanding critical scales in persistent homology for general compact metric spaces.
method Analyzing local minima of the distance function and their impact on persistence.
result Each decrease in zero-dimensional persistence and increase in one-dimensional persistence is induced by local minima of the distance function.
Introduces a new space of Radon measures for better understanding persistence diagrams.
problem Lack of optimal transport-based formalism for persistence diagrams.
method Formalizes persistence diagrams as Radon measures on the upper half plane via optimal partial transport.
result Characterizes convergence and barycenters of persistence diagrams.
MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
New geometric insights reveal the persistence distribution in spin systems.
problem Determining the full persistence probability distribution in non-Markovian stochastic processes.
method Exact Fredholm Pfaffian structure and Painlevé VI system analysis.
result Recovery of the universal persistence exponent and its geometric interpretation.
Study on embedding persistence diagrams into Hilbert spaces, focusing on metric distortion.
problem Understanding metric properties of persistence diagrams in Hilbert spaces.
method Investigate embedding persistence diagrams into separable Hilbert spaces using bi-Lipschitz maps.
result Impossible to find a bi-Lipschitz embedding into finite-dimensional Hilbert spaces.
Kernel for multi-parameter persistent homology connects TDA with ML.
problem Connecting persistent homology with machine learning for multivariate data.
method Integrating a one-parameter kernel weighted along straight lines.
result Stable and efficiently computable kernel for multi-parameter persistence.
We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index…
Persistent homology can recognize knotting in curves.
problem Recognizing knotting in curves
method Compute one-dimensional persistent homology, extract cycle representatives, and assign a hypergraph curvature-based score.
result Systematic differences between knotted and unknotted structures are revealed.
This article analyzes the relationship between co-persistence and hedging which indicates co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persis…
Persistent homology detects curvature from sampled points.
problem Understanding the geometric information encoded in short intervals of persistent homology.
method Persistent homology computations and average persistence landscapes.
result Persistent homology detects curvature of disks from sampled points.
New model adds persistent memory to self-attention layers for improved performance.
problem Improving transformer performance by removing feed-forward layers.
method Augmenting self-attention layers with persistent memory vectors.
result The model outperforms standard transformers on language modeling benchmarks.
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a …
A new approach to reinforcement learning improves policy performance by adjusting control frequency.
problem Improving reinforcement learning performance by optimizing control frequency.
method Introducing action persistence and a novel algorithm, PFQI, to learn optimal value function at a given persistence.
result PFQI effectively learns optimal value function with action persistence, improving reinforcement learning performance.
Given a compact geodesic space X we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of X to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
A new method compares persistent cycles in topological data.
problem Comparing persistent homology representations of two spaces.
method Direct comparison of individual persistent cycles based on persistence intervals and spatial placement.
result Demonstrated the effectiveness of the method in topological inference.
Improved persistence spheres map measures to functions, stable under partial transport.
problem Representing and comparing measures in topological machine learning.
method Persistence spheres map measures to continuous functions on the sphere, stable under 1-Wasserstein partial transport.
result Persistence spheres provide a stable, parameter-free representation of measures, improving upon existing methods.
Embeds persistence diagrams into Hilbert spaces to use kernel methods.
problem No inner product structure on persistence diagrams.
method Shows non-embeddability of persistence diagrams into Hilbert spaces.
result Persistence diagrams with bottleneck distance do not coarse embed into Hilbert spaces.
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, …
Improved modeling of persistence diagrams for data analysis.
problem Determining significant outliers in persistence diagrams.
method Modification of the RST (Replicating Statistical Topology) model using MCMC Metropolis-Hastings algorithm.
result The modified RST model improves the goodness of fit in persistence diagram analysis.
Persistency of excitation ensures correct parameter estimation in neural networks.
problem Ensuring correct parameter estimation in neural networks during training.
method Analyzed gradient descent dynamics in a two-layer neural network and proposed a new algorithm.
result Conditions for persistent excitation of network weights are difficult to satisfy in multi-layer networks.
TopInG improves graph interpretability using persistent homology.
problem Lack of interpretability in Graph Neural Networks (GNNs).
method TopInG uses persistent homology to identify persistent rationale subgraphs in graphs.
result TopInG improves predictive accuracy and interpretability compared to state-of-the-art methods.