Introduction to Geometric Deep Learning
Taking inspiration from Gabriel Peyre's Numerical Tours
In particular:
[BONUS]
We can eventually try to re-implement some matlab code on specific wavelet families:
- https://wavelet-tour.github.io/softwares/
- Here a collection of a large variety of geometric multiscale transforms
The notion of wavelets and multiscale separation is also used to build neural networks (i.e. Scattering Networks)
- See Kymatio for some implementations
- In general the work of Stephane Mallat's Lab both on Scholar and Github (scattered among lab members, for example see this)
- Introduction to Graphs and applications w/ NetworkX
This content is largely based on
- "Complessita' nei sistemi sociali" course at UniTo
- NetworkX Gallery Examples
More in detail:
- Create an empty graph, adding nodes and edges and drawing
- Graph properties: Eccentricity, Radius, Diameter, Center, Periphery, Density, Average Shortest Path
- Centrality Measures: Degree, Betweenness, Closeness, PageRank
- Random Walks & PageRank
- Clustering & Community Detection
- Beam Search
- Disparity Filtering
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Introduction to Manifolds and applications w/ Geomstats
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To get an idea of the motivations behind learning about and on manifolds, please take a look at this awesome notebook from Adele Myers and collaborators :)
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Also, for some more definitions, there is this notebook
More in detail:
- Three different & intuitive definitions of a Manifold
- An Example: the hypersphere
- Manifolds as a Class? w/ Geomstats
- The Parent Class: Manifold
- OpenSet and LevelSet
- VectorSpace
- ProductManifold
- What is a connection
- 1st Example: EMG data and SemiPositiveDefinite Matrices
- 2nd Example: Zachary's Karate Club and Hyperbolic Embeddings
ARC Challenge - Abstraction Reasoning Corpus
- Core knowledge a short story
- Previous Edition on Kaggle
- Some notebooks with solutions