Michael Bronstein ICLR 2021 - Invited Talk - Geometric Deep Learning: the Erlangen Programme of ML

**Concept Graph & Resume using Claude 3 Opus | Chat GPT4 | Gemini Adv | Llama 3:**

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A[Michael Bronstein

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

symmetry. 9] B --> G[Non-Euclidean data awaits

geometric analysis. 10] B --> H[Key principles: invariance,

equivariance, locality. 11] H --> I[Equivariant layers, pooling,

coarsening. 12] I --> J[Gauge equivariant

mesh CNNs. 13] I --> K[Graph neural networks

GNNs. 14, 15, 16, 17] I --> L[Convolution on grids,

manifolds. 18, 19, 20] A --> M[Successful applications: drugs,

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,

theory-practice gap. 28] A --> U[Startups commercializing

geometric DL. 29] A --> V['Proto-book' on geometric

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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

symmetry. 9] B --> G[Non-Euclidean data awaits

geometric analysis. 10] B --> H[Key principles: invariance,

equivariance, locality. 11] H --> I[Equivariant layers, pooling,

coarsening. 12] I --> J[Gauge equivariant

mesh CNNs. 13] I --> K[Graph neural networks

GNNs. 14, 15, 16, 17] I --> L[Convolution on grids,

manifolds. 18, 19, 20] A --> M[Successful applications: drugs,

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,

theory-practice gap. 28] A --> U[Startups commercializing

geometric DL. 29] A --> V['Proto-book' on geometric

deep learning. 30] class A,B,D,E,F,G dl; class C,H,I,J,K,L,M,N,O,P,Q,R,S gdl; class T,U,V misc;

**Resume: **

**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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