HOLE: Homological Observation of Latent Embeddings for Neural Network Interpretability
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Abstract (arXiv)
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of Latent Embeddings), a method for analyzing and interpreting discriminative neural networks through persistent homology. HOLE extracts topological features from intermediate activations and presents them using a suite of visualization techniques, including cluster flow diagrams, blob graphs, and heatmap dendrograms. These tools facilitate the examination of representation structure and quality across layers. We evaluate HOLE using a range of discriminative models, focusing on representation quality, interpretability across layers, and robustness to input perturbations and model compression. The results indicate that topological analysis reveals patterns associated with class separation, feature disentanglement, and model robustness, providing a complementary perspective for understanding and improving deep learning systems.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 52 of its 101 references that are in the map. First posted on arXiv 8 Dec 2025.
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52 of 101 references.
References · 52
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
- 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
- 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 11,979
- 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,690
- 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
- 2013Intriguing properties of neural networkscited by 5,114
- 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,040
- 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,346
- 2017Axiomatic Attribution for Deep Networkscited by 3,350
- 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
38 more
- 2015Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingcited by 2,291
- 2013Visualizing and Understanding Convolutional Networkscited by 2,278
- 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,250
- 2019A Survey on Bias and Fairness in Machine Learningcited by 1,911
- 2017Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inferencecited by 1,548
- 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,472
- 2017Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)cited by 1,309
- 2016Pruning Filters for Efficient ConvNetscited by 1,129
- 2017SmoothGrad: removing noise by adding noisecited by 1,097
- 2020A Primer in BERTology: What we know about how BERT workscited by 807
- 2021A Survey of Quantization Methods for Efficient Neural Network Inferencecited by 798
- 2017Network Dissection: Quantifying Interpretability of Deep Visual Representationscited by 703
- 2017Learning Efficient Convolutional Networks through Network Slimmingcited by 673
- 2019Learned Step Size Quantizationcited by 604
- 2020What is the State of Neural Network Pruning?cited by 578
- 2017Learning Sparse Neural Networks through L0 Regularizationcited by 571
- 2018Quantizing deep convolutional networks for efficient inference: A whitepapercited by 507
- 2019Data-Free Quantization Through Weight Equalization and Bias Correctioncited by 328
- 2019A Multiscale Visualization of Attention in the Transformer Modelcited by 292
- 2018Scalable and accurate deep learning for electronic health recordscited by 275
- 2020Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluationcited by 183
- 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
- 2019Topological Autoencoderscited by 124
- 2017Deep Learning with Topological Signaturescited by 113
- 2018Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clusteringcited by 94
- 2020Neural Manifold Ordinary Differential Equationscited by 81
- 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
- 2018Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topologycited by 73
- 2019Summit: Scaling Deep Learning Interpretability by Visualizing Activation and Attribution Summarizationscited by 72
- 2021Intrinsic Dimension, Persistent Homology and Generalization in Neural Networkscited by 70
- 2020CNN Explainer: Learning Convolutional Neural Networks with Interactive Visualizationcited by 57
- 2017ActiVis: Visual Exploration of Industry-Scale Deep Neural Network Modelscited by 56
- 2016Towards Better Analysis of Deep Convolutional Neural Networkscited by 51
- 2021Activation Landscapes as a Topological Summary of Neural Network Performancecited by 17
- 2022Experimental Observations of the Topology of Convolutional Neural Network Activationscited by 10
- 2021Topological Measurement of Deep Neural Networks Using Persistent Homologycited by 9
- 2022Predicting the generalization gap in neural networks using topological data analysiscited by 9
- 2021Intraclass clustering: an implicit learning ability that regularizes DNNscited by 6
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