Mathematics of Shape Learning
PhD student project
Context
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Artificial Neural Networks (ANN): nonlinear interpolation technique inspired by biological neural networks
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Convolutional Neural Networks (CNN): type of ANN mainly used for image classification
- 2010–2012 CNN + GPU implementation \(\Rightarrow\) CNN Revolution!
- Quickly adopted by tech companies, today used in your computer, phone, car, ... (more to come)
Why does it work so well?
- New field: Mathematics of AI
- WASP AI/Math: initiative to make Sweden a leading country in this fast growing field
Problem addressed in project
- Today's CNN-based image classifiers identifies a cat and an elephant with very high probability
- [Geirhos, et al. 2019] Cat "painted" with elephants skin identified with very high probability as elephant
Conclusion: CNN's "see" texture where we see shape
Can we trust CNN's with human tasks?
- Approach: use Shape Analysis to construct and analyze new NN better suited for shape recognition
- Mathematics involved: Riemannian geometry, analysis, numerics, mathematical hydrodynamics, stochastic analysis