Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
By Alberto Bietti, Julien Mairal. 2017
98 citations recorded by the source corpus.
Subfields: Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Vision and Pattern Recognition
- Simon Lacoste-Julien
- Alberto Bietti
- Julien Mairal
- Grégoire Mialon
- François Soumis
- Yassine Yaakoubi
- Yee Whye Teh
- Luc Van Gool
In Representation & Self-Supervised Learning
- Alberto Bietti
- Julien Mairal
- Grégoire Mialon
- Simon Lacoste-Julien
- François Soumis
- Yassine Yaakoubi
- Benjamin Bloem-Reddy
- François Rousseau
Citations in the corpus
- Structured Convolutional Kernel Networks for Airline Crew Scheduling (2021, methodology): “We review CKNs, with the same notation as in Mairal (2016); Bietti & Mairal (2019).”
- On Regularization and Robustness of Deep Neural Networks (2018, methodology): “(2)—it turns out that this is the same set as above, since Φ is homogeneous (Bietti and Mairal, 2018) and X = R—we obtain a lower bound based on the Lipschitz constant of f :”
- A Group-Theoretic Framework for Data Augmentation (2019, background): “A related line of work focuses on representation learning and demonstrates the benefits of invariant feature representations [3, 50, 13, 1, 67, 53, 10, 2].”
- Residual Networks as Flows of Diffeomorphisms (2019, background): “Recent works have been done in this direction connecting RKHS and deep networks [6].”
- On the Inductive Bias of Neural Tangent Kernels (2019, methodology): “In contrast to the kernels studied in [11], which for instance cover the limiting kernels that arise from training only the last layer of a ReLU CNN, we find that the obtained NTK kernel mappings for the ReLU activation lack a desired Lipschitz property which is needed for stability to deformations ”
- Probabilistic Symmetries and Invariant Neural Networks (2020, background): “Bietti and Mairal (2019) takes some initial steps in this direction.”
- A Kernel Perspective for Regularizing Deep Neural Networks (2018, unknown): “By constructing an appropriate multi-layer hierarchical kernel, Bietti & Mairal (2019) show that the corresponding RKHS H contains a CNN with the same architecture and parameters as f , but with activations that are smooth approximations of ReLU.”