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This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis.
Sur les points singuliers d’une forme de Pfaff complètement intégrable ou d’une fonction numérique [On the singular points of a completely integrable Pfaff form or of a numerical function]
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SLINK: An optimally efficient algorithm for the single-link cluster method
R. Sibson · 1973
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Efficiency of a good but not linear set union algorithm
R. E. Tarjan · 1975
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Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. correlation with molecular orbital energies and hydrophobicity
A. K. Debnath, R. L. Lopez de Compadre, G. Debnath, A. J. Shusterman, and C. Hansch · 1991
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Fewnomials
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A density-based algorithm for discovering clusters in large spatial databases with noise
M. Ester, H.-P. Kriegel, J. Sander, and X. Xu · 1996
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HVS: A heuristic for variable selection in multilayer artificial neural network classifier
M. Yacoub and Y. Bennani · 1997
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Gradient-based learning applied to document recognition
Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner · 1998
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Early Stopping - But When? , pages 55–69
L. Prechelt · 1998
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Computing persistent homology of directed flag complexes
D. Lütgehetmann, D. Govc, J. P. Smith, and R. Levi · 1999
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A minimum spanning tree algorithm with inverse-Ackermann type complexity
B. Chazelle · 2000
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Topology
J. R. Munkres · 2000
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Topological estimation using witness complexes
V. de Silva and G. Carlsson · 2004
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NAS-Bench-NLP: Neural architecture search benchmark for natural language processing, 2020
N. Klyuchnikov, I. Trofimov, E. Artemova, M. Salnikov, M. Fedorov, and E. Burnaev · 2006
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The minimal spanning tree and the upper box dimension
G. Kozma, Z. Lotker, and G. Stupp · 2006
Earlier work this paper cites.
Stability of persistence diagrams
D. Cohen-Steiner, H. Edelsbrunner, and J. Harer · 2007
Earlier work this paper cites.
Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
G. Singh, F. Memoli, and G. Carlsson · 2007
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On the local behavior of spaces of natural images
G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian · 2008
Earlier work this paper cites.
Learning multiple layers of features from tiny images
A. Krizhevsky · 2009
Earlier work this paper cites.
Active learning literature survey
B. Settles · 2009
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Zigzag persistence
G. Carlsson and V. de Silva · 2010
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Barycenters in the Wasserstein space
M. Agueh and G. Carlier · 2011
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The MNIST database of handwritten digit images for machine learning research [best of the web]
L. Deng · 2012
Earlier work this paper cites.
Neurips 2020 Competition: Predicting generalization in deep learning, 2020a
Y. Jiang, P. Foret, S. Yak, D. M. Roy, H. Mobahi, G. K. Dziugaite, S. Bengio, S. Gunasekar, I. Guyon, and B. Neyshabur · 2012
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Imagenet classification with deep convolutional neural networks
A. Krizhevsky, I. Sutskever, and G. E. Hinton · 2012
Earlier work this paper cites.
On the complexity of neural network classifiers: A comparison between shallow and deep architectures
M. Bianchini and F. Scarselli · 2013
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Banknote Authentication
V. Lohweg · 2013
Earlier work this paper cites.
Linear-size approximations to the Vietoris–Rips filtration
D. R. Sheehy · 2013
Earlier work this paper cites.
Persistence stability for geometric complexes
F. Chazal, V. de Silva, and S. Oudot · 2014
Earlier work this paper cites.
Confidence sets for persistence diagrams
B. T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan, and A. Singh · 2014
Earlier work this paper cites.
Generative adversarial nets
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
Earlier work this paper cites.
Homotopy theory for digraphs, 2014
A. Grigor’yan, Y. Lin, Y. Muranov, and S.-T. Yau · 2014
Earlier work this paper cites.
Auto-encoding variational Bayes
D. P. Kingma and M. Welling · 2014
Earlier work this paper cites.
Assessing the clinical utility of cancer genomic and proteomic data across tumor types
Y. Yuan, E. M. Van Allen, L. Omberg, N. Wagle, A. Amin-Mansour, A. Sokolov, L. A. Byers, Y. Xu, K. R. Hess, L. Diao, L. Han, X. Huang, M. S. Lawrence, J. N. Weinstein, J. M. Stuart, G. B. Mills, L. A. Garraway, A. A. Margolin, G. Getz, and H. Liang · 2014
Earlier work this paper cites.
Statistical topological data analysis using persistence landscapes
P. Bubenik · 2015
Earlier work this paper cites.
Comparing persistence diagrams through complex vectors
B. Di Fabio and M. Ferri · 2015
Earlier work this paper cites.
Explaining and harnessing adversarial examples, 2015
I. J. Goodfellow, J. Shlens, and C. Szegedy · 2015
Earlier work this paper cites.
Deep learning face attributes in the wild
Z. Liu, P. Luo, X. Wang, and X. Tang · 2015
Earlier work this paper cites.
Going deeper with convolutions
C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich · 2015
Earlier work this paper cites.
GUDHI User and Reference Manual
The GUDHI Project · 2015
Earlier work this paper cites.
Spread: A measure of the size of metric spaces
S. Willerton · 2015
Earlier work this paper cites.
Persistence-based pooling for shape pose recognition
T. Bonis, M. Ovsjanikov, S. Oudot, and F. Chazal · 2016
Earlier work this paper cites.
The Structure and Stability of Persistence Modules , volume 10 of SpringerBriefs in Mathematics
F. Chazal, V. de Silva, M. Glisse, and S. Oudot · 2016
Earlier work this paper cites.
Deep Learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
Earlier work this paper cites.
Deep residual learning for image recognition
K. He, X. Zhang, S. Ren, and J. Sun · 2016
Earlier work this paper cites.
Unsupervised representation learning with deep convolutional generative adversarial networks
A. Radford, L. Metz, and S. Chintala · 2016
Earlier work this paper cites.
Persistence images: A stable vector representation of persistent homology
H. Adams, T. Emerson, M. Kirby, R. Neville, C. Peterson, P. Shipman, S. Chepushtanova, E. Hanson, F. Motta, and L. Ziegelmeier · 2017
Cited alongside, same era.
Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
Cited alongside, same era.
Sliced Wasserstein kernel for persistence diagrams
M. Carrière, M. Cuturi, and S. Oudot · 2017
Cited alongside, same era.
Topological data analysis of financial time series: Landscapes of crashes
M. Gidea and Y. Katz · 2017
Cited alongside, same era.
Improved training of Wasserstein GANs
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. Courville · 2017
Cited alongside, same era.
Gans trained by a two time-scale update rule converge to a local nash equilibrium
M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochreiter · 2017
Experimental stability analysis of neural networks in classification problems with confidence sets for persistence diagrams
N. Akai, T. Hirayama, and H. Murase · 2021
Later among the works it cites.
Effective gene expression prediction from sequence by integrating long-range interactions
Ž. Avsec, V. Agarwal, D. Visentin, J. R. Ledsam, A. Grabska-Barwinska, K. R. Taylor, Y. Assael, J. Jumper, P. Kohli, and D. R. Kelley · 2021
Later among the works it cites.
Ripser: Efficient computation of Vietoris–Rips persistence barcodes
U. Bauer · 2021
Later among the works it cites.
Intrinsic dimension, persistent homology and generalization in neural networks
T. Birdal, A. Lou, L. J. Guibas, and U. Simsekli · 2021
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Optimizing persistent homology based functions
M. Carrière, F. Chazal, M. Glisse, Y. Ike, H. Kannan, and Y. Umeda · 2021
Later among the works it cites.
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Cited alongside, same era.
dsprites: Disentanglement testing sprites dataset
L. Matthey, I. Higgins, D. Hassabis, and A. Lerchner · 2017
Cited alongside, same era.
Feature visualization
C. Olah, A. Mordvintsev, and L. Schubert · 2017
Cited alongside, same era.
Cliques of neurons bound into cavities provide a missing link between structure and function
M. W. Reimann, M. Nolte, M. Scolamiero, K. Turner, R. Perin, G. Chindemi, P. Dłotko, R. Levi, K. Hess, and H. Markram · 2017
Cited alongside, same era.
Fashion-MNIST: A novel image dataset for benchmarking machine learning algorithms, 2017
H. Xiao, K. Rasul, and R. Vollgraf · 2017
Cited alongside, same era.
Algebraic stability of zigzag persistence modules
M. Botnan and M. Lesnick · 2018
Cited alongside, same era.
Structure and stability of the one-dimensional Mapper
M. Carrière and S. Oudot · 2018
Cited alongside, same era.
F. Ding, J.-S. Denain, and J. Steinhardt · 2021
Later among the works it cites.
A survey of topological machine learning methods
F. Hensel, M. Moor, and B. Rieck · 2021
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Imagenette dataset
J. Howard · 2021
Later among the works it cites.
Methods and analysis of the first competition in predicting generalization of deep learning
Y. Jiang, P. Natekar, M. Sharma, S. K. Aithal, D. Kashyap, N. Subramanyam, C. Lassance, D. M. Roy, G. K. Dziugaite, S. Gunasekar, I. Guyon, P. Foret, S. Yak, H. Mobahi, B. Neyshabur, and S. Bengio · 2021
Later among the works it cites.
Rebooting ACGAN: Auxiliary classifier GANs with stable training
M. Kang, W. J. Shim, M. Cho, and J. Park · 2021
Later among the works it cites.
Neural network with smooth activation functions and without bottlenecks is almost surely a Morse function
S. V. Kurochkin · 2021
Later among the works it cites.
Topological uncertainty: Monitoring trained neural networks through persistence of activation graphs
T. Lacombe, Y. Ike, M. Carrière, F. Chazal, M. Glisse, and Y. Umeda · 2021
Later among the works it cites.
TopoAct: Visually exploring the shape of activations in deep learning
A. Rathore, N. Chalapathi, S. Palande, and B. Wang · 2021
Later among the works it cites.
Persistent homology and the upper box dimension
B. Schweinhart · 2021
Later among the works it cites.
Activation landscapes as a topological summary of neural network performance
M. Wheeler, J. Bouza, and P. Bubenik · 2021
Later among the works it cites.
Intelligent health care: Applications of deep learning in computational medicine
S. Yang, F. Zhu, X. Ling, Q. Liu, and P. Zhao · 2021
Later among the works it cites.
Understanding deep learning (still) requires rethinking generalization
C. Zhang, S. Bengio, M. Hardt, B. Recht, and O. Vinyals · 2021
Later among the works it cites.
Topological detection of trojaned neural networks
S. Zheng, Y. Zhang, H. Wagner, M. Goswami, and C. Chen · 2021
Later among the works it cites.
Evaluating the disentanglement of deep generative models through manifold topology
S. Zhou, E. Zelikman, F. Lu, A. Y. Ng, G. E. Carlsson, and S. Ermon · 2021
Later among the works it cites.
Representation topology divergence: A method for comparing neural network representations
S. Barannikov, I. Trofimov, N. Balabin, and E. Burnaev · 2022
Later among the works it cites.
Computational Topology: An Introduction
H. Edelsbrunner and J. L. Harer · 2022
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An adversarial robustness perspective on the topology of neural networks
M. Goibert, E. Dohmatob, and T. Ricatte · 2022
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Mathematical Aspects of Deep Learning
P. Grohs and G. Kutyniok · 2022
Later among the works it cites.
A framework for differential calculus on persistence barcodes
J. Leygonie, S. Oudot, and U. Tillmann · 2022
Later among the works it cites.
M. Masden · 2022
Later among the works it cites.
Topological data analysis in biomedicine: A review
Y. Skaf and R. Laubenbacher · 2022
Later among the works it cites.
A review on AI Safety in highly automated driving
M. Wäschle, F. Thaler, A. Berres, F. Pölzlbauer, and A. Albers · 2022
Later among the works it cites.
Quantitative performance assessment of CNN units via topological entropy calculation
Y. Zhao and H. Zhang · 2022
Later among the works it cites.
https://www.kaggle.com/datasets/mlg-ulb/creditcardfraud/data
Credit Card Fraud Detection: Anonymized credit card transactions labeled as fraudulent or genuine · 2023
Closest in time.
Metric space magnitude and generalisation in neural networks, 2023
R. Andreeva, K. Limbeck, B. Rieck, and R. Sarkar · 2023
Closest in time.
Disentanglement learning via topology, 2023
N. Balabin, D. Voronkova, I. Trofimov, E. Burnaev, and S. Barannikov · 2023
Closest in time.
Decorrelating neurons using persistence
R. Ballester, C. Casacuberta, and S. Escalera · 2023
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An introduction to multiparameter persistence, 2023
M. B. Botnan and M. Lesnick · 2023
Closest in time.
Generalization bounds using data-dependent fractal dimensions
B. Dupuis, G. Deligiannidis, and U. Simsekli · 2023
Closest in time.
Caveats of neural persistence in deep neural networks
L. Girrbach, A. Christensen, O. Winther, Z. Akata, and A. S. Koepke · 2023
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Topp&r: Robust support estimation approach for evaluating fidelity and diversity in generative models
P. J. Kim, Y. Jang, J. Kim, and J. Yoo · 2023
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Architectures of topological deep learning: A survey on topological neural networks, 2023
M. Papillon, S. Sanborn, M. Hajij, and N. Miolane · 2023
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Understanding Deep Learning
S. J. D. Prince · 2023
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Experimental observations of the topology of convolutional neural network activations
E. Purvine, D. Brown, B. Jefferson, C. Joslyn, B. Praggastis, A. Rathore, M. Shapiro, B. Wang, and Y. Zhou · 2023
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TopoBERT: Exploring the topology of fine-tuned word representations
A. Rathore, Y. Zhou, V. Srikumar, and B. Wang · 2023
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On the expressivity of persistent homology in graph learning, 2023
B. Rieck · 2023
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Topological singularity detection at multiple scales
J. Von Rohrscheidt and B. Rieck · 2023
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GRIL: A 2 2 -parameter persistence based vectorization for machine learning
C. Xin, S. Mukherjee, S. N. Samaga, and T. K. Dey · 2023
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Visualizing and analyzing the topology of neuron activations in deep adversarial training
Y. Zhou, Y. Zhou, J. Ding, and B. Wang · 2023
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On the use of persistent homology to control the generalization capacity of a neural network
A. Barbara, Y. Bennani, and J. Karkazan · 2024
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Topological dynamics of functional neural network graphs during reinforcement learning
M. Muller, S. Kroon, and S. Chalup · 2024
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