Geometric deep learning the erlangen programme to ml
Quote
- symmetry as wide or as narrow as you may define
- one idea by
Origins
- Euclid
- Ecuclides elements
- 300 bc
End of Euclid’s monopoly
- Poncelet
- Lobachevsky
- Gauss
Nineteeth centruy zoo
Erlangen Programme
- Euclidean
- Affine
- Projective
Revolution in Physics
- E. Noether
- H. Weyl
- C. N Yang
- R L Mills
Phyiscs is all about symmetry
20 CENTURY ZOO OF NEURAL NETWORK ARCHITECTURES
- GNN
- CNN
- DeepSets
- Transformers
- RNN
eRLANGEN pROGRAMME OF Machine Learning
- constructive knowledge
- Geometric Deep Learning
- Perceptions
- First wave of the preceptions
- Group Theory
sUPERVISED ml = fUNCTION aPPROXIMATION
- Input
- Cat image
- Dog image
- blackbox
- output
The curse of dimensionality
- x
- f
- y
The curse of dimensionality
- increasing the dimensions
- the decision boundaries are becoming increasing complex
Computer vision
-
imput image
-
input vector
-
Data argumentations
Computer vision
- Hubel wiesel
- Lecun
Beyond Grids
- graph
- chemical bond within them
- energy U
- Graphics types
- Molecular
- social networks
- messes
- functional networks
- Interaction networks
The curse of dimensionality
- Symmetry Prior
- domain
- Invariant functions: image classification
KaTeX parse error: Can't use function '\)' in math mode at position 4: f(\?)?
Scale separation Prior
f ≈ f \approx f≈
scale separation in Physics
Geometric Deep Learning Blueprint
G ? e q u i v a l e n t G-equivalent G?equivalent
$$
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Learning
- Perceptrons
- CNN
- Group CNN
- LSTM
- DeepSets/ Transformers
- GNNS
Graphs= systems of relations and interections
Social network
- node
- edge
- Node features
Key structural propertities of Graphs
- adjacency atrix
- feature matrix
- Arbitrary ordering of nodes
Invariant Graph Functions
-
Graph Functions
-
node function
-
F ( ) F() F()
-
permutation equivariant
-
local pooling
-
coasen
-
a general blueprint for contructing graph functions
-
multiset
-
local function
-
permutation invarient
A general blueprint for constructing graph function
f ( x i ) = ? ( x i , □ ) f(x_i)=\phi (x_i , □ ) f(xi?)=?(xi?,□)
Weisfeiler- Lehan Test
- graphic descriptors
- necessary but insufficient conditions
- non isomorphic graphs are WL equivalent
Special Cases of GNNs
-
Nodes in the graphics
-
nodes act in their own
-
? ( x i ) \phi (x_i) ?(xi?)
Transformers
? ( x i , □ j = 1 n a ( ) ) \phi (x_i, □_{j=1}^n a()) ?(xi?,□j=1n?a())
Graph substructure network
- ? ( x i , □ j ∈ ) \phi (x_i , □_{j \in }) ?(xi?,□j∈?)
Graph substructure network
- olecule property prediction on ZINC using GSN with k cycles
Grids
-
vIRTUAL DRUG screening
- computational funnel
- synthesizable molecules
- graph NN
- DFT
- QD
- Lab
- QD
- DFT
- graph NN
- synthesizable molecules
- computational funnel
-
New antibiotic discovery
- directed message passing neural network
- large scale predictions
- lead identification
- large scale predictions
- directed message passing neural network
-
drug reposition and combinatorial therapy
- drug drug interaction
- drug protein interaction
- Protein protein interactions
- drug protein interaction
- drug drug interaction
-
food in the packages
- Dark measure of the nutrications
- protein yto protein interaction network
- network based machine learning
- anticancer
- non anticancer
- network based machine learning
- protein yto protein interaction network
- Dark measure of the nutrications
-
hyperfoods
Conclusion
- the knowledge of certain principles easily compensates the lack of knowledge of certain facts
- Claude adrien helvetius
Overlooked
- standard hardware is not friendly for the graphs
- assume the stream of the data
- same operations to multiple data frames
- hardware archetecture
- how the graphics can be updated
- graphword
- Graph work loads
- important to undersatnd
- stike to the input graph
- next reinvent
- District
- models
- to difficution equations
- differentiations
- graph neural networks
- how to discritelize the
- make it user friendly
- super computing
- the computing without causing too much memory
- knowledge knowledge how
- to kn
- assume the stream of the data
