Knowledge Vault 2/73 - ICLR 2014-2023
Michael Bronstein ICLR 2021 - Invited Talk - Geometric Deep Learning: the Erlangen Programme of ML
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Concept Graph & Resume using Claude 3 Opus | Chat GPT4 | Gemini Adv | Llama 3:

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ICLR 2021] --> B[Geometric deep learning:
unifying framework. 1, 2, 6] A --> C[Symmetry in math
& physics. 3, 4] A --> D[Deep learning: rapid progress,
lacks principles. 5] B --> E[Function estimation problem,
curse of dimensionality. 7, 8] B --> F[CNNs exploit translational
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proteins, misinfo. 21] M --> N[Drug discovery
with GNNs. 22] M --> O[Protein interaction
prediction. 23] M --> P[Food molecules,
cancer prevention. 24] M --> Q[Fake news detection
on social networks. 25] M --> R[3D human shape
reconstruction. 26] A --> S[Research directions: latent graphs,
symbolic regression. 27] A --> T[Challenges: expertise, collaboration,
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1.-The talk was about geometric deep learning, a field pioneered by the speaker Michael Bronstein.

2.-Geometric deep learning aims to provide a unifying mathematical framework for deriving successful neural network architectures based on symmetry and invariance.

3.-Historically, Felix Klein's Erlangen Program approached geometry as the study of symmetries, formalizing it using group theory in the 19th century.

4.-Symmetry has been a fundamental principle in mathematics and physics, as seen in Noether's theorem and the standard model.

5.-Deep learning has advanced rapidly but lacks unifying principles, leading to a "zoo" of architectures and reinvention/rebranding of concepts.

6.-Geometric deep learning serves to provide a common framework and procedure for deriving architectures based on symmetry in a principled way.

7.-Machine learning is essentially a function estimation problem of fitting a function to training data to make predictions on unseen data.

8.-The curse of dimensionality makes naive learning impossible in high dimensions without exploiting additional structure, known as geometric priors.

9.-Convolutional neural networks (CNNs) solve the curse of dimensionality in computer vision by exploiting the translational symmetry of images.

10.-Graphs, molecules, social networks, and manifolds are examples of non-Euclidean data with irregular structure waiting to be analyzed using geometric deep learning.

11.-Key principles of geometric deep learning are 1) invariance/equivariance to symmetry transformations and 2) local scale separation of interactions across scales.

12.-These principles lead to a general design of equivariant layers, invariant pooling, and hierarchical coarsening applicable to grids, graphs, sets, and manifolds.

13.-Gauge equivariance on manifolds leads to intrinsic mesh CNNs used in computer graphics and vision to handle deformable surfaces.

14.-Graph neural networks (GNNs) use local permutation-invariant neighbor aggregation and equivariant message passing to process graph-structured data.

15.-GNNs are theoretically powerful, equivalent to the Weisfeiler-Lehman graph isomorphism test when using injective neighborhood aggregation functions.

16.-Special cases of GNNs include deep sets (for permutation-invariant functions on sets) and transformers (attention-based message passing on fully-connected graphs).

17.-Concepts like positional/structural encoding and graph rewiring/sampling have been introduced to GNNs to improve expressivity and scalability.

18.-Grids are a special case of graphs with a fixed neighborhood structure and order, where convolution emerges naturally from translational symmetry.

19.-Convolution on general manifolds like spheres can be defined based on group convolutions on the symmetry group, e.g. SO(3) rotations.

20.-Gauge equivariance w.r.t. the frame/coordinate changes on manifolds is important to define geometrically intrinsic and stable operators.

21.-Geometric deep learning has been very successful in applications like drug discovery, protein interaction prediction, and fake news detection.

22.-Graph neural networks have achieved state-of-the-art performance in virtual screening of drug molecules, being more accurate and faster than conventional methods.

23.-Protein-protein interaction (PPI) prediction using GNNs has led to the design of new protein binders for difficult cancer-related targets.

24.-Food molecules have been analyzed with GNNs to identify "hyperfoods" rich in anti-cancer compounds, used to design cancer-prevention recipes.

25.-Misinformation detection on social networks has been tackled using graph-based learning to identify fake news based on its spreading patterns.

26.-3D human shape reconstruction from images has progressed from using 3D sensors to now using hybrid 2D CNN + geometric decoder architectures.

27.-Exciting research directions include 1) latent graph learning as a form of algorithmic reasoning and 2) symbolic regression of physical equations using GNNs.

28.-Key challenges in applying geometric deep learning include required domain expertise, collaboration with field experts, and bridging theory and practice.

29.-The speaker has founded several startups commercializing geometric deep learning technology, including Twitter's fake news detection and Ariel AI's 3D avatars.

30.-A "proto-book" on geometric deep learning has been published, aiming to provide a unifying mathematical framework deriving architectures from first principles.

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