Machine learning classifies topological phases in leaky photonic lattices.
problem Classifying topological phases in leaky photonic lattices using limited data.
method A fully connected neural network trained on bulk intensity measurements.
result Accurate determination of topological properties from intensity distributions.
Topology aids in solving machine learning classification problems.
problem Machine learning classification problems.
method Classical topology applied to neural networks.
result Topology guides neural network architecture and training.
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: th…
Topological data analysis classifies encrypted bits with success.
problem Classifying encrypted data with traditional machine learning methods.
method Persistent homology for generating topological features, machine learning pipeline.
result Successfully classifies encrypted data, outperforming classical models.
Mathematical approach defines stability conditions for ML models.
problem Ensuring stability of machine learning models.
method Adopted topological and metric spaces theory to define stability.
result Stability of ML models depends on topological properties of classification sets.
Python library for integrating TDA with machine learning.
problem Data exploration and interpretability in machine learning.
method Integrates TDA with scikit-learn API, uses C++ for performance.
result Enhanced data exploration and interpretability in machine learning.
Introduces topological deep learning for neural network classification problems.
problem Classifying neural networks using minimal topological structures.
method Formalizes classification problems in a topological setting.
result Demonstrates conditions for the feasibility of classification problems in neural networks.
Machine learning maps knots to embeddings, revealing topological invariants.
problem Learning topological invariance in knot theory.
method Contrastive and generative machine learning techniques, auto-regressive decoder Transformer network.
result Neural networks can map different knots to the same point in an embedding vector space.
EuLearn creates diverse 3D topological datasets for machine learning.
problem Training machine learning systems to discern topological features.
method Developed novel sampling and neural network architectures for graph and manifold data.
result Incorporating topological information improves deep learning performance on EuLearn datasets.
A new method for group invariant machine learning using geometric projections.
problem Supervised group invariant and equivariant machine learning.
method Geometric topology approach involving projection of input data into a geometric space parametrizing symmetry group orbits.
result Improvement in accuracy compared to existing methods.
TDL uses topological features for deep learning models, promising new insights and solutions.
problem Lack of comprehensive theoretical foundations and practical benefits in TDL.
method Discussing open problems and potential solutions in TDL.
result TDL can complement existing graph and geometric learning methods.
This study investigates porosity and topological properties of TPMS using machine learning.
problem Understanding the relationships between porosity and topological properties of TPMS.
method Application of machine learning techniques to analyze porosity and shape factor of TPMS.
result Conjectures suggesting polynomial relationships between porosity and shape factor of TPMS.
Study shows topological features improve time series classification.
problem Classifying stochastic processes with varying noise and sampling.
method Topological data analysis features compared to statistical and raw features.
result Topological features lead to better classification performance.
Machine learning predicts topological properties of Calabi-Yau manifolds.
problem Predicting topological quantities of Calabi-Yau manifolds.
method Machine learning approach using neural networks and symbolic regressors.
result High performance scores in predicting Sasakian Hodge numbers and Crowley-Nördstrom invariant.
Machine learning and topological data analysis identify unique geometric and topological features of human papillae.
problem Identifying unique features of human papillae across individuals.
method 3D microscopic scans, machine learning, discrete differential geometry, computational topology, persistent homology.
result Persistent homology features of papillae shape predict papillae type with high accuracy and can identify individuals with high accuracy.
Unreduced PDs can perform similarly to reduced PDs in machine learning tasks.
problem Ignoring much of the information in persistence diagrams in machine learning pipelines.
method Developed methods to generate topological feature vectors from unreduced boundary matrices.
result Unreduced PDs can perform on par with, and sometimes outperform, fully-reduced PDs in machine learning tasks.
Machine learning finds knots that bound ribbon disks.
problem Detecting ribbon knots in topology.
method Bayesian optimization and reinforcement learning.
result Successfully detected many ribbon knots up to 70 crossings.
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We…
Survey on optimizing topological descriptors for machine learning.
problem Optimizing topological priors in machine learning models.
method Minimizing topologically-informed losses using gradient descent.
result Various techniques enable optimization of persistence-based loss functions.
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.
In this empirical paper, we investigate how learning agents can be arranged in more efficient communication topologies for improved learning. This is an important problem because a common technique to improve speed and robustness of learning in deep reinforcement learning and many other machine learning algorithms is t…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel…
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.
A common technique to improve learning performance in deep reinforcement learning (DRL) and many other machine learning algorithms is to run multiple learning agents in parallel. A neglected component in the development of these algorithms has been how best to arrange the learning agents involved to improve distributed…
Machine learning uncovers hidden patterns in Calabi-Yau hypersurfaces.
problem Identifying and clustering Calabi-Yau hypersurfaces from weighted-P4s.
method Supervised and unsupervised machine learning techniques.
result High accuracy in predicting topological parameters and identifying hypersurfaces.
New framework combines simple machines into complex ones for better neural network performance.
problem Improving neural network performance with limited training data.
method Developed a framework using topology and functional analysis to combine simple machines into complex ones, and used kernel methods to find optimal architectures.
result Kernel-inspired networks can outperform classical neural networks when training data is small.
This paper uses machine learning to select kernels for machine learning models on various devices.
problem Traditional kernel auto-tuning is limited for machine learning research with changing network topologies and hyperparameters.
method Combines auto-tuning and machine learning to select kernels for SYCL on various devices.
result Initial results show high performance kernel selection with little developer effort.
Machine learning reveals hidden features in knot classification.
problem Classifying the topology of closed curves.
method Investigating shortcut methods used by ML for knot classification.
result Developed a dataset and code to remove non-topological features.
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.
This review explores TDA and TDL beyond persistent homology.
problem Limitations of persistent homology in capturing topological invariants and homotopic evolution.
method Spectral representations, sheaf theory, Mayer topology, interaction topology, differential topology, geometric topology.
result Review of topological tools for various data types.
Graph Laplacians and machine learning predict properties of finite graphs.
problem Understanding properties of finite graphs using spectral and topological methods.
method Combining graph Laplacians, spectral inequalities, machine learning, and topological data analysis.
result Neural networks can accurately predict graph properties like Ricci-flatness and spectral gaps.
Chatter detection has become a prominent subject of interest due to its effect on cutting tool life, surface finish and spindle of machine tool. Most of the existing methods in chatter detection literature are based on signal processing and signal decomposition. In this study, we use topological features of data simula…
Paper uses topological data analysis for time series classification.
problem Classifying univariate time series data, especially physiological signals.
method Persistent homology for feature engineering, followed by machine learning.
result Higher accuracy achieved with fewer features compared to traditional methods.
This paper refines understanding of decentralized learning by considering graph topology.
problem Current theory fails to predict performance in decentralized learning settings.
method Quantifies how graph topology influences convergence in decentralized learning.
result Graph topology significantly impacts convergence in decentralized learning, contrary to spectral gap theory.
Fog learning distributes ML model training across heterogeneous devices and networks.
problem Challenges with conventional federated learning in heterogeneous networks.
method Intelligent distribution of ML model training across nodes from edge devices to cloud servers.
result Enhanced federated learning with multi-layer hybrid framework considering network, heterogeneity, and proximity.
Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection' fusion of Gaussian estimators in networks. It then gives two examples in which ta…
Persistent homology enhances graph classification by capturing long-range graph properties.
problem Lack of formal assessment of persistent homology in graph learning.
method Brief introduction and theoretical discussion of persistent homology in graph context, followed by empirical analysis.
result Persistent homology improves graph classification, especially for data with prominent topological structures.
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization method for measures in Euclidean spaces and use it for reflecting underlying chan…
We introduce a theory-driven mechanism for learning a neural network model that performs generative topology design in one shot given a problem setting, circumventing the conventional iterative process that computational design tasks usually entail. The proposed mechanism can lead to machines that quickly response to n…
This paper proposes a new method for automatically selecting the optimal kernel bandwidth in density estimation.
problem The challenge of selecting the optimal kernel bandwidth in unsupervised density estimation.
method The approach uses a topology-based loss function for automated bandwidth selection.
result Demonstrates the potential of the topology-based approach across different dimensions.
A method for vectorizing persistence diagrams simplifies topological data analysis.
problem Challenges in integrating persistence diagrams into machine learning pipelines.
method Quantized Persistence and Integral transforms of Diagrams (Qupid) using binning and discrete transforms.
result Qupid preserves highly competitive performances compared to state-of-the-art methods across various classification tasks.
We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning. Our string of innovations are 1) robust topological features are used to encode behavioral information, 2) statistical models are fitted to distributions over these topological …
Agent learns to navigate uncertain 3D maps using a hybrid planner.
problem Planning in 3D environments with uncertain topological maps.
method Hierarchical strategy combining graph planner and local policy, data-driven learning with neural network.
result Machine learning can overcome missing information in probabilistic topological maps.
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.
The paper explores statistical and topological properties of sliced probability divergences.
problem Understanding the topological, statistical, and computational consequences of slicing divergences.
method Deriving theoretical properties of sliced probability divergences, including metric axioms preservation and weak continuity.
result Sliced divergences share similar topological properties and have stable sample complexity.
Strong regulations in the financial industry mean that any decisions based on machine learning need to be explained. This precludes the use of powerful supervised techniques such as neural networks. In this study we propose a new unsupervised and semi-supervised technique known as the topological hierarchical decomposi…
Study evaluates synthetic data augmentation for small datasets, highlighting inconsistencies in traditional metrics.
problem Inconsistent validation of synthetic data generated for small sample sizes.
method Proposes a normalized Bottleneck distance metric to evaluate synthetic tabular data.
result Common metrics like propensity scoring and MMD fail for small datasets, showing instability and high variability.
Paper tackles dynamic graph topology identification in time-varying graphs.
problem Dynamic graph topology identification in time-varying graphs.
method Proposes an online algorithm for time-varying optimization, with intrinsic temporal regularization.
result Demonstrates performance on Gaussian graphical model problem.