Diffeomorphism-based feature learning using Poincaré inequalities on augmented input space Article Swipe
We propose a gradient-enhanced algorithm for high-dimensional function approximation. The algorithm proceeds in two steps: firstly, we reduce the input dimension by learning the relevant input features from gradient evaluations, and secondly, we regress the function output against the pre-learned features. To ensure theoretical guarantees, we construct the feature map as the first components of a diffeomorphism, which we learn by minimizing an error bound obtained using Poincaré Inequality applied either in the input space or in the feature space. This leads to two different strategies, which we compare both theoretically and numerically and relate to existing methods in the literature. In addition, we propose a dimension augmentation trick to increase the approximation power of feature detection. A generalization to vector-valued functions demonstrate that our methodology directly applies to learning autoencoders. Here, we approximate the identity function over a given dataset by a composition of feature map (encoder) with the regression function (decoder). In practice, we construct the diffeomorphism using coupling flows, a particular class of invertible neural networks. Numerical experiments on various high-dimensional functions show that the proposed algorithm outperforms state-of-the-art competitors, especially with small datasets.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://hal.science/hal-04364208
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4390308277
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4390308277Canonical identifier for this work in OpenAlex
- Title
-
Diffeomorphism-based feature learning using Poincaré inequalities on augmented input spaceWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-12-26Full publication date if available
- Authors
-
Romain Verdière, Clémentine Prieur, Olivier ZahmList of authors in order
- Landing page
-
https://hal.science/hal-04364208Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://hal.science/hal-04364208Direct OA link when available
- Concepts
-
Diffeomorphism, Feature (linguistics), Poincaré conjecture, Space (punctuation), Inequality, Mathematics, Artificial intelligence, Computer science, Pure mathematics, Mathematical analysis, Philosophy, Operating system, LinguisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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