mlsanityData to 14 Oct 2026

Activation Landscapes as a Topological Summary of Neural Network Performance

arXiv 2110.10136 ↗First posted 19 Oct 2021cs.LG math.ATcited by 18

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Abstract (arXiv)

We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize this information using persistence landscapes. The resulting feature map provides both an informative visual- ization of the network and a kernel for statistical analysis and machine learning. We observe that the topological complexity often increases with training and that the topological complexity does not decrease with each layer.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 26 of its 52 references that are in the map. First posted on arXiv 19 Oct 2021.

Builds on

26 of 52 references.

References · 26

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14 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 4; 2025: 5; 2026: 2.

18 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  2. 2022Topology and geometry of data manifold in deep learningcited by 12
  3. 2022Experimental Observations of the Topology of Convolutional Neural Network Activationscited by 10
  4. 2023Deep neural networks architectures from the perspective of manifold learningcited by 5
  5. 2024Deep Learning as Ricci Flowcited by 4
  6. 2024MOUNTAINEER: Topology-Driven Visual Analytics for Comparing Local Explanationscited by 4
  7. 2024Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Cloudscited by 2
  8. 2025Topological Signatures of ReLU Neural Network Activation Patternscited by 2
  9. 2023Importance attribution in neural networks by means of persistence landscapes of time seriescited by 1
  10. 2023Estimating class separability of text embeddings with persistent homologycited by 1
  11. 2023Topological Parallax: A Geometric Specification for Deep Perception Modelscited by 1
  12. 2023Addressing caveats of neural persistence with deep graph persistencecited by 1
6 more
  1. 2025Topology of Out-of-Distribution Examples in Deep Neural Networkscited by 1
  2. 2025A Quotient Homology Theory of Representation in Neural Networkscited by 1
  3. 2025HOLE: Homological Observation of Latent Embeddings for Neural Network Interpretabilitycited by 1
  4. 2025Topology-Aware Activation Functions in Neural Networkscited by 0
  5. 2026Topological Simplification in Predictive Coding Networkscited by 0
  6. 2026Constructive Bounds for the Topological Expressivity of Neural Networkscited by 0