mlsanityData to 7 Oct 2026

Decision boundaries and convex hulls in the feature space that deep learning functions learn from images

arXiv 2202.04052 ↗First posted 5 Feb 2022cs.CV cs.AI cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and learn from images. However, there is not sufficient understanding about this low-dimensional space based on theory or empirical evidence. For image classification models, their last hidden layer is the one where images of each class is separated from other classes and it also has the least number of features. Here, we develop methods and formulations to study that feature space for any model. We study the partitioning of the domain in feature space, identify regions guaranteed to have certain classifications, and investigate its implications for the pixel space. We observe that geometric arrangements of decision boundaries in feature space is significantly different compared to pixel space, providing insights about adversarial vulnerabilities, image morphing, extrapolation, ambiguity in classification, and the mathematical understanding of image classification models.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 25 of its 42 references that are in the map. First posted on arXiv 5 Feb 2022.

Builds on

25 of 42 references.

References · 25

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13 more
  1. 2018Are adversarial examples inevitable?cited by 113
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Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 3; 2024: 0; 2025: 1.

5 papers.

  1. 2023Reverse engineering adversarial attacks with fingerprints from adversarial examplescited by 4
  2. 2023Scalable Attribution of Adversarial Attacks via Multi-Task Learningcited by 2
  3. 2025SHRUG-FM: Reliability-Aware Foundation Models for Earth Observationcited by 2
  4. 2022Over-parameterization: A Necessary Condition for Models that Extrapolatecited by 1
  5. 2023An Ambiguity Measure for Recognizing the Unknowns in Deep Learningcited by 1