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Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology

Authors: Bastian Rieck, Matteo Togninalli, Christian Bock, Michael Moor, Max Horn, Thomas Gumbsch, Karsten M. Borgwardt - International Conference on Learning Representations, ICLR 2019 cited by 148

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

Introduction toAlgorithmsIntroduction to AlgorithmsIntroduction toAlgorithmsIntroduction to AlgorithmsExtending PersistenceUsing Poincaré and…Extending Persistence Using Poincaré and Lefschetz DualityPersistent homology ofcomplex networksPersistent homology of complex networksDropout: a simple way toprevent neural networks…Dropout: a simple way to prevent neural networks from overfittingSequence to SequenceLearning with Neural…Sequence to Sequence Learning with Neural NetworksVisualizing andUnderstanding…Visualizing and Understanding Convolutional NetworksBatch Normalization:Accelerating Deep…Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate ShiftDeep Residual Learningfor Image RecognitionDeep Residual Learning for Image RecognitionClique CommunityPersistence: A…Clique Community Persistence: A Topological Visual Analysis Approach for Complex NetworksMethods for Interpretingand Understanding Deep…Methods for Interpreting and Understanding Deep Neural NetworksOn Characterizing theCapacity of Neural…On Characterizing the Capacity of Neural Networks using Algebraic TopologyA Topology Layer forMachine LearningA Topology Layer for Machine LearningCharacterizing the Shapeof Activation Space in…Characterizing the Shape of Activation Space in Deep Neural NetworksPath Homologies of DeepFeedforward NetworksPath Homologies of Deep Feedforward NetworksTopological Measurementof Deep Neural Networks…Topological Measurement of Deep Neural Networks Using Persistent HomologyA note on stochasticsubgradient descent for…A note on stochastic subgradient descent for persistence-based functionals: convergence and practical aspectsFuzzy c-Means Clusteringfor Persistence DiagramsFuzzy c-Means Clustering for Persistence DiagramsA topological encodingconvolutional neural…A topological encoding convolutional neural network for segmentation of 3D multiphoton images of brain vasculature using persistent homologyLearning Topology:Bridging Computational…Learning Topology: Bridging Computational Topology and Machine LearningAn Introduction toTopological Data…An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data ScientistsTopological Uncertainty:Monitoring Trained…Topological Uncertainty: Monitoring Trained Neural Networks through Persistence of Activation GraphsA Fast and Robust Methodfor Global Topological…A Fast and Robust Method for Global Topological Functional OptimizationArtificial TextDetection via Examining…Artificial Text Detection via Examining the Topology of Attention MapsNeural Persistence: AComplexity Measure for…Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic TopologyEarlier referencesFocus paperCiting papersOlderNewer

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