pith. machine review for the scientific record. sign in

arxiv: 2104.13478 · v2 · submitted 2021-04-27 · 💻 cs.LG · cs.AI· cs.CG· cs.CV· stat.ML

Recognition: 2 theorem links

Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Joan Bruna, Michael M. Bronstein, Petar Veli\v{c}kovi\'c, Taco Cohen

Pith reviewed 2026-05-13 02:33 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CGcs.CVstat.ML
keywords geometric deep learningErlangen programsymmetriesequivarianceneural architecturesCNNGNNunification
0
0 comments X

The pith

Geometric principles provide a unified framework for CNNs, RNNs, GNNs, and Transformers while enabling the design of new architectures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to show that the success of deep learning stems from its ability to capture geometric regularities in data rather than learning arbitrary high-dimensional functions. By drawing on ideas from Klein's Erlangen program, it organizes different neural network types around symmetries and structures such as grids, groups, graphs, geodesics, and gauges. This approach supplies both a retrospective explanation for why certain architectures work well and a forward method for building models that respect physical priors. A sympathetic reader would care because it promises to make model design less empirical and more principled, potentially accelerating progress in areas where data has known structure.

Core claim

The authors claim that a geometric unification in the spirit of the Erlangen program furnishes a common mathematical framework for studying successful neural network architectures including CNNs, RNNs, GNNs, and Transformers, while simultaneously offering a constructive procedure to embed prior physical knowledge into neural architectures and to create future ones in a principled manner.

What carries the argument

The geometric structures corresponding to grids, groups, graphs, geodesics, and gauges, which encode symmetries and regularities of data domains to define appropriate neural network operations.

If this is right

  • CNNs on image grids are special cases of group-equivariant networks on the appropriate symmetry group.
  • Graph neural networks arise naturally when the data domain is a graph with its automorphism group.
  • Transformers can be viewed as operating on sets or sequences with permutation or other symmetries.
  • New models for data on manifolds or with gauge symmetries can be derived systematically rather than by trial and error.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying this lens could help identify which tasks are currently under-served by existing architectures due to mismatched geometric assumptions.
  • It suggests that improvements in one domain, such as better group convolutions, might transfer to others through the shared framework.
  • Scientific applications in physics and biology might benefit most, as their data often has explicit geometric structure.
  • Over time, this could shift machine learning from architecture search to geometry-informed design.

Load-bearing premise

The majority of interesting learning tasks possess essential pre-defined regularities that originate from the low-dimensional structure of the physical world and that can be captured by geometric principles.

What would settle it

Demonstrating a task with strong physical structure where no geometric neural network architecture matches or exceeds the performance of a generic black-box model would challenge the claim that geometric unification is broadly useful.

read the original abstract

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 0 minor

Summary. The manuscript is a survey articulating a geometric unification of deep learning architectures (CNNs on grids, GNNs on graphs, Transformers on gauges, etc.) in the spirit of Klein's Erlangen Program. It argues that successful models exploit pre-defined regularities arising from the low-dimensional structure of the physical world, providing both a retrospective common mathematical framework for existing architectures and a constructive procedure for incorporating prior physical knowledge into new designs.

Significance. If the unifying geometric lens holds, the survey offers a significant organizing principle for the field by linking disparate architectures through group theory, differential geometry, and symmetry considerations. It synthesizes established literature without new empirical claims, supplies design heuristics grounded in physical priors, and could guide future architecture development; the absence of free parameters, invented entities, or circular derivations strengthens its value as a reference.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and insightful review, which accurately summarizes the manuscript's goals of providing a geometric unification of deep learning architectures in the spirit of Klein's Erlangen Program. We appreciate the recognition of its value as a reference and organizing principle for the field.

Circularity Check

0 steps flagged

No significant circularity; survey organizes external results

full rationale

The manuscript is a survey that retrospectively organizes CNNs, GNNs, Transformers and related architectures under an Erlangen-style geometric lens drawn from standard group theory and differential geometry. It states its motivating assumption about physical regularities explicitly and offers design heuristics rather than new theorems or fitted predictions. No load-bearing step reduces by construction to a quantity defined inside the paper or to a self-citation chain; all cited results are independent external literature. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that physical-world regularities are low-dimensional and geometrically expressible; no free parameters are fitted, no new entities are postulated, and the axioms invoked are standard results from geometry and group theory.

axioms (2)
  • domain assumption Most tasks of interest come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world.
    Invoked in the abstract and introduction as the motivation for geometric unification.
  • domain assumption Geometric principles (grids, groups, graphs, geodesics, gauges) can be applied throughout a wide spectrum of applications to expose these regularities.
    Core premise of the Erlangen-program-inspired framework stated in the abstract.

pith-pipeline@v0.9.0 · 5579 in / 1439 out tokens · 61565 ms · 2026-05-13T02:33:20.624266+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • AlexanderDuality (for D=3 linking and invariance) alexander_duality_circle_linking echoes

    Symmetries, Representations, and Invariance... Isomorphisms and Automorphisms... Deformation Stability... Scale Separation

Forward citations

Cited by 29 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The WidthWall: A Strict Expressivity Hierarchy for Hypergraph Neural Networks

    cs.LG 2026-05 unverdicted novelty 8.0

    Hypergraph neural networks obey a strict expressivity hierarchy indexed by hypertree width, creating a Width Wall that no fixed-depth model, hidden dimension, or training procedure can cross for wider patterns.

  2. Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

    cs.LG 2026-05 unverdicted novelty 8.0

    Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.

  3. Gradient-Based Program Synthesis with Neurally Interpreted Languages

    cs.LG 2026-04 unverdicted novelty 8.0

    NLI autonomously discovers a vocabulary of primitive operations and interprets variable-length programs via a neural executor, allowing end-to-end training and gradient-based test-time adaptation that outperforms prio...

  4. The Cartesian Shortcut: Re-evaluate Vision Reasoning in Polar Coordinate Space

    cs.CV 2026-05 unverdicted novelty 7.0

    MLLMs scoring 70-83% on Cartesian visual tasks drop to 31-39% on logically equivalent polar versions, exposing reliance on grid discretization shortcuts instead of topology-invariant reasoning.

  5. TokaMind for Power Grid: Cross-Domain Transfer from Fusion Plasma

    physics.plasm-ph 2026-05 unverdicted novelty 7.0

    TokaMind, pre-trained on MAST tokamak data, transfers to power grid PMU data for severe event classification with F1 0.837, where difficulty depends on grid topology and CSD indicators boost early-warning performance ...

  6. Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity

    stat.ML 2026-05 unverdicted novelty 7.0

    Every fixed finite feedforward neural network definable in an o-minimal structure has finite sample complexity in the agnostic PAC setting.

  7. Operator-Guided Invariance Learning for Continuous Reinforcement Learning

    cs.LG 2026-05 unverdicted novelty 7.0

    VPSD-RL discovers exact and approximate value-preserving Lie-group operators in continuous RL to stabilize learning via transition augmentation and consistency regularization.

  8. Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs

    math.DS 2026-05 unverdicted novelty 7.0

    A field theory of synthetic cognition is cast as a retarded functional differential equation on graphs, with proofs of well-posedness, compact global attractor existence, delay-independent stability under a coupling-s...

  9. Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs

    math.DS 2026-05 unverdicted novelty 7.0

    Establishes well-posedness, compact global attractors, and delay-independent global stability for retarded functional differential equations modeling reentrant value fields as coupled reaction-diffusion systems on fin...

  10. Cardiac Mesh Flow: One-Step Generation of 3D+t Cardiac Four-Chamber Meshes via Flow Matching

    eess.IV 2026-05 unverdicted novelty 7.0

    Cardiac Mesh Flow generates 3D+t four-chamber cardiac meshes with anatomical correspondence and volume conditioning via one-step flow matching on multi-scale deformation fields.

  11. Data-driven discovery of polynomial ODEs with provably bounded solutions

    math.DS 2026-04 unverdicted novelty 7.0

    SILAS jointly optimizes polynomial ODE vector fields and polynomial Lyapunov functions from data to produce models with provably bounded trajectories via compact absorbing sets.

  12. Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems

    cs.LG 2026-04 unverdicted novelty 7.0

    Complex-valued GNNs using phase-equivariant activations achieve global basis invariance for distributed planar control, outperforming real-valued baselines in data efficiency, tracking, and generalization on flocking.

  13. Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

    cs.LG 2026-05 unverdicted novelty 6.0

    HilbNets discretize Hilbert bundle convolutions through Hilbert Cellular Sheaves whose Laplacians converge to the continuous connection Laplacian, enabling consistent learning across samplings.

  14. LINC: Decoupling Local Consequence Scoring from Hidden Matching in Constructive Neural Routing

    cs.LG 2026-05 unverdicted novelty 6.0

    LINC decouples local consequence scoring from hidden matching in constructive neural routing solvers, cutting CVRPTW gaps for PolyNet from 13.83%/38.15% to 7.26%/14.71% on Solomon/Homberger benchmarks.

  15. Temporal Reasoning Is Not the Bottleneck: A Probabilistic Inconsistency Framework for Neuro-Symbolic QA

    cs.AI 2026-05 unverdicted novelty 6.0

    Temporal reasoning is not the core bottleneck for LLMs on time-based QA; the real issue is unstructured text-to-event mapping, addressed by a neuro-symbolic system with PIS that reaches 100% accuracy on benchmarks whe...

  16. Symmetry-Protected Lyapunov Neutral Modes in Equivariant Recurrent Networks

    cs.NE 2026-05 unverdicted novelty 6.0

    Exact equivariance under a Lie group guarantees at least dim(G/H) zero Lyapunov exponents tangent to the group orbit on compact invariant sets with nondegenerate orbit bundles.

  17. Geometric Quantum Physics Informed Neural Network

    quant-ph 2026-05 unverdicted novelty 6.0

    GQPINNs add symmetry awareness to quantum PINNs via equivariant circuits, yielding lower mean absolute error and fewer parameters than standard QPINNs on linear and nonlinear PDE benchmarks.

  18. Leveraging Data Symmetries to Select an Optimal Subset of Training Data under Label Noise

    cs.LG 2026-05 unverdicted novelty 6.0

    Exploiting data symmetries boosts k-NN to select near-optimal low-noise subsets from noisy datasets, approaching Bayes-optimal performance in high dimensions, with learned representations aiding partial symmetry knowledge.

  19. Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems

    cs.LG 2026-05 unverdicted novelty 6.0

    A new scale-aware diagnostic framework shows that unconstrained diffusion generative models exhibit structural freezing and instability instead of smooth physical responses under multiscale perturbations.

  20. Stability Enhanced Gaussian Process Variational Autoencoders

    cs.LG 2026-04 unverdicted novelty 6.0

    SEGP-VAE learns stable low-dimensional LTI systems from video data by deriving GP mean and covariance from LTI equations and using a complete unconstrained parametrization of semi-contracting systems.

  21. Toward a universal foundation model for graph-structured data

    cs.LG 2026-04 unverdicted novelty 6.0

    A pretrained graph model using feature-agnostic structural prompts matches or exceeds supervised baselines and shows strong zero-shot and few-shot transfer on held-out biomedical graphs, with a 21.8% ROC-AUC gain on SagePPI.

  22. LAG-XAI: A Lie-Inspired Affine Geometric Framework for Interpretable Paraphrasing in Transformer Latent Spaces

    cs.CL 2026-04 unverdicted novelty 6.0

    LAG-XAI treats paraphrasing as affine flows in semantic manifolds using Lie-inspired approximations, achieving AUC 0.7713 on paraphrase detection and 95.3% hallucination detection on HaluEval.

  23. Metriplector: From Field Theory to Neural Architecture

    cs.AI 2026-03 unverdicted novelty 6.0

    Metriplector treats neural computation as coupled metriplectic field dynamics whose stress-energy tensor readout achieves competitive results on vision, control, Sudoku, language modeling, and pathfinding with small p...

  24. PhysEDA: Physics-Aware Learning Framework for Efficient EDA With Manhattan Distance Decay

    cs.LG 2026-05 unverdicted novelty 5.0

    PhysEDA folds separable Manhattan-distance exponential decay into linear attention and potential-based rewards, cutting complexity to linear while improving zero-shot transfer and sparse-reward performance on decoupli...

  25. The Role of Node Features in Graph Pooling

    cs.LG 2026-05 unverdicted novelty 5.0

    Pooling improves graph classification only when node features align well with topology, and the authors provide a quantitative measure of this alignment quality.

  26. Coupled Arnol'd cat maps on circulant graphs

    math.DS 2026-05 unverdicted novelty 5.0

    Coupled Arnol'd cat maps on circulant graphs produce entropy independent of connectivity because translational symmetry cancels the expected increase from added links.

  27. Exploring Time Conditioning in Diffusion Generative Models from Disjoint Noisy Data Manifolds

    cs.LG 2026-04 unverdicted novelty 5.0

    Aligning the DDIM forward diffusion process with flow-matching manifold evolution enables high-quality generation without time conditioning, and class-conditional synthesis is possible with an unconditional denoiser b...

  28. Bridging the Dimensionality Gap: A Taxonomy and Survey of 2D Vision Model Adaptation for 3D Analysis

    cs.CV 2026-04 unverdicted novelty 4.0

    The paper offers a taxonomy of 2D-to-3D adaptation strategies divided into data-centric projection, architecture-centric 3D networks, and hybrid methods that combine both.

  29. The Topology of Multimodal Fusion: Why Current Architectures Fail at Creative Cognition

    cs.AI 2026-04 unverdicted novelty 3.0

    Multimodal AI architectures share a geometric prior of modal separability termed contact topology that prevents creative cognition, addressable via a cruciform philosophical-mathematical framework using fiber bundles ...

Reference graph

Works this paper leans on

109 extracted references · 109 canonical work pages · cited by 28 Pith papers · 14 internal anchors

  1. [1]

    and Yahav, E

    Uri Alon and Eran Yahav. On the bottleneck of graph neural networks and its practical implications.arXiv:2006.05205,

    work page arXiv 2006

  2. [2]

    Cormorant: Covariant molecular neural networks.arXiv:1906.04015,

    BrandonAnderson,Truong-SonHy,andRisiKondor. Cormorant: Covariant molecular neural networks.arXiv:1906.04015,

    work page arXiv 1906

  3. [3]

    Layer Normalization

    JimmyLeiBa,JamieRyanKiros,andGeoffreyEHinton. Layernormalization. arXiv:1607.06450,

    work page internal anchor Pith review Pith/arXiv arXiv

  4. [4]

    Neural Machine Translation by Jointly Learning to Align and Translate

    Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate.arXiv:1409.0473,

    work page internal anchor Pith review Pith/arXiv arXiv

  5. [5]

    Discovering transforms: A tutorial on circulant matrices, circular convolution, and the discrete fourier transform.arXiv:1805.05533,

    Bassam Bamieh. Discovering transforms: A tutorial on circulant matrices, circular convolution, and the discrete fourier transform.arXiv:1805.05533,

    work page arXiv

  6. [6]

    Interaction networks for learning about objects, relations and physics.arXiv:1612.00222,

    PeterWBattaglia,RazvanPascanu,MatthewLai,DaniloRezende,andKoray Kavukcuoglu. Interaction networks for learning about objects, relations and physics.arXiv:1612.00222,

    work page arXiv

  7. [7]

    Relational inductive biases, deep learning, and graph networks

    PeterWBattaglia,JessicaBHamrick,VictorBapst,AlvaroSanchez-Gonzalez, ViniciusZambaldi,MateuszMalinowski,AndreaTacchetti,DavidRaposo, Adam Santoro, Ryan Faulkner, et al. Relational inductive biases, deep learning, and graph networks.arXiv:1806.01261,

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [8]

    Directional graph networks

    Dominique Beaini, Saro Passaro, Vincent Létourneau, William L Hamil- ton, Gabriele Corso, and Pietro Liò. Directional graph networks. arXiv:2010.02863,

    work page arXiv 2010

  9. [9]

    Size-invariant graph representations for graph classification extrapolations.arXiv:2103.05045,

    Beatrice Bevilacqua, Yangze Zhou, and Bruno Ribeiro. Size-invariant graph representations for graph classification extrapolations.arXiv:2103.05045,

    work page arXiv

  10. [10]

    Weisfeiler and lehman go topo- logical: Message passing simplicial networks.arXiv:2103.03212,

    Cristian Bodnar, Fabrizio Frasca, Yu Guang Wang, Nina Otter, Guido Mon- túfar, Pietro Liò, and Michael Bronstein. Weisfeiler and lehman go topo- logical: Message passing simplicial networks.arXiv:2103.03212,

    work page arXiv

  11. [11]

    Learning shape correspondence with anisotropic convolutional neural networks

    Davide Boscaini, Jonathan Masci, Emanuele Rodoià, and Michael Bronstein. Learning shape correspondence with anisotropic convolutional neural networks. InNIPS, 2016a. Davide Boscaini, Jonathan Masci, Emanuele Rodolà, Michael M Bronstein, and Daniel Cremers. Anisotropic diffusion descriptors.Computer Graphics Forum, 35(2):431–441, 2016b. Sébastien Bougleux, ...

    work page arXiv

  12. [12]

    Improving graph neural network expressivity via subgraph isomor- phism counting.arXiv:2006.09252,

    Giorgos Bouritsas, Fabrizio Frasca, Stefanos Zafeiriou, and Michael M Bron- stein. Improving graph neural network expressivity via subgraph isomor- phism counting.arXiv:2006.09252,

    work page arXiv 2006

  13. [13]

    Language Models are Few-Shot Learners

    Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Ka- plan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. arXiv:2005.14165,

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  14. [14]

    Combinatorial optimization and reasoning with graph neural networks.arXiv:2102.09544,

    Quentin Cappart, Didier Chételat, Elias Khalil, Andrea Lodi, Christopher Morris, and Petar VeliŁković. Combinatorial optimization and reasoning with graph neural networks.arXiv:2102.09544,

    work page arXiv

  15. [15]

    https://arxiv.org/abs/1806.07366

    Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. Neural ordinary differential equations.arXiv:1806.07366,

    work page arXiv

  16. [16]

    Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation

    Kyunghyun Cho, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bah- danau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation. arXiv:1406.1078,

    work page internal anchor Pith review Pith/arXiv arXiv

  17. [17]

    Spherical cnns

    Taco S Cohen, Mario Geiger, Jonas Köhler, and Max Welling. Spherical cnns. arXiv:1801.10130,

    work page arXiv

  18. [18]

    Recurrent batch normalization.arXiv:1603.09025,

    Tim Cooijmans, Nicolas Ballas, César Laurent, Çağlar Gülçehre, and Aaron Courville. Recurrent batch normalization.arXiv:1603.09025,

    work page arXiv

  19. [19]

    Principal neighbourhood aggregation for graph nets

    Gabriele Corso, Luca Cavalleri, Dominique Beaini, Pietro Liò, and Petar VeliŁković. Principal neighbourhood aggregation for graph nets. arXiv:2004.05718,

    work page arXiv 2004

  20. [20]

    Lagrangian neural networks.arXiv:2003.04630,

    Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel, and Shirley Ho. Lagrangian neural networks.arXiv:2003.04630,

    work page arXiv 2003

  21. [21]

    Learningsymbolic physics with graph networks.arXiv:1909.05862,

    MilesDCranmer,RuiXu,PeterBattaglia,andShirleyHo. Learningsymbolic physics with graph networks.arXiv:1909.05862,

    work page arXiv 1909

  22. [22]

    Xlvin: executed latent value iteration nets

    BIBLIOGRAPHY 135 Andreea Deac, Petar VeliŁković, Ognjen Milinković, Pierre-Luc Bacon, Jian Tang, and Mladen Nikolić. Xlvin: executed latent value iteration nets. arXiv:2010.13146,

    work page arXiv 2010

  23. [23]

    BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

    Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understand- ing. arXiv:1810.04805,

    work page internal anchor Pith review Pith/arXiv arXiv

  24. [24]

    A generalization of transformer networks to graphs.arXiv preprint arXiv:2012.09699, 2020a

    Vijay Prakash Dwivedi and Xavier Bresson. A generalization of transformer networks to graphs.arXiv:2012.09699,

    work page arXiv 2012

  25. [25]

    Spin-weighted spherical CNNs.arXiv:2006.10731,

    Carlos Esteves, Ameesh Makadia, and Kostas Daniilidis. Spin-weighted spherical CNNs.arXiv:2006.10731,

    work page arXiv 2006

  26. [26]

    Hierarchical inter-message passing for learning on molecular graphs.arXiv:2006.12179,

    Matthias Fey, Jan-Gin Yuen, and Frank Weichert. Hierarchical inter-message passing for learning on molecular graphs.arXiv:2006.12179,

    work page arXiv 2006

  27. [27]

    Neural shuffle-exchange networks–sequence processing in o (n log n) time.arXiv:1907.07897,

    K¯arlis Freivalds, Em¯ıls Ozolin,š, and Agris ’ostaks. Neural shuffle-exchange networks–sequence processing in o (n log n) time.arXiv:1907.07897,

    work page arXiv 1907

  28. [28]

    Johannes Gasteiger, Janek Groß, and Stephan Gün- nemann

    Fabian B Fuchs, Daniel E Worrall, Volker Fischer, and Max Welling. SE(3)-transformers: 3D roto-translation equivariant attention networks. arXiv:2006.10503,

    work page arXiv 2006

  29. [29]

    Learninggraphrepresentations with embedding propagation.arXiv:1710.03059,

    AlbertoGarcía-DuránandMathiasNiepert. Learninggraphrepresentations with embedding propagation.arXiv:1710.03059,

    work page arXiv

  30. [30]

    Texture synthesis usingconvolutionalneuralnetworks

    Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Texture synthesis usingconvolutionalneuralnetworks. arXivpreprintarXiv:1505.07376 ,2015. ThomasGaudelet,BenDay,ArianRJamasb,JyothishSoman,CristianRegep, Gertrude Liu, Jeremy BR Hayter, Richard Vickers, Charles Roberts, Jian Tang, et al. Utilising graph machine learning within drug discovery and develop...

    work page arXiv 2015

  31. [31]

    Neural message passing for quantum chemistry

    Justin Gilmer, Samuel S Schoenholz, Patrick F Riley, Oriol Vinyals, and George E Dahl. Neural message passing for quantum chemistry. arXiv:1704.01212,

    work page arXiv

  32. [32]

    Generative Adversarial Networks

    Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde- Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks.arXiv:1406.2661,

    work page internal anchor Pith review arXiv

  33. [33]

    arXiv preprint arXiv:1308.0850 (2013) 4, 5

    Alex Graves. Generating sequences with recurrent neural networks. arXiv:1308.0850,

    work page arXiv

  34. [34]

    Neural Turing Machines

    Alex Graves, Greg Wayne, and Ivo Danihelka. Neural turing machines. arXiv:1410.5401,

    work page internal anchor Pith review arXiv

  35. [35]

    Grill, F

    Jean-Bastien Grill, Florian Strub, Florent Altché, Corentin Tallec, Pierre H Richemond,ElenaBuchatskaya,CarlDoersch,BernardoAvilaPires,Zhao- han Daniel Guo, Mohammad Gheshlaghi Azar, et al. Bootstrap your own latent: A new approach to self-supervised learning.arXiv:2006.07733,

    work page arXiv 2006

  36. [36]

    Network medicine framework for identifying drug repurposing opportunities for COVID-19.arXiv:2004.07229,

    Deisy Morselli Gysi, Ítalo Do Valle, Marinka Zitnik, Asher Ameli, Xiao Gan, Onur Varol, Helia Sanchez, Rebecca Marlene Baron, Dina Ghiassian, Joseph Loscalzo, et al. Network medicine framework for identifying drug repurposing opportunities for COVID-19.arXiv:2004.07229,

    work page arXiv 2004

  37. [37]

    Identity matters in deep learning

    Moritz Hardt and Tengyu Ma. Identity matters in deep learning. arXiv:1611.04231,

    work page arXiv

  38. [38]

    Vain: Attentional multi-agent predictive modeling

    Yedid Hoshen. Vain: Attentional multi-agent predictive modeling. arXiv:1706.06122,

    work page arXiv

  39. [39]

    LieTransformer: Equivariant self- attention for Lie groups.arXiv:2012.10885,

    Michael Hutchinson, Charline Le Lan, Sheheryar Zaidi, Emilien Dupont, Yee Whye Teh, and Hyunjik Kim. LieTransformer: Equivariant self- attention for Lie groups.arXiv:2012.10885,

    work page arXiv 2012

  40. [40]

    Sarah Itani and Dorina Thanou

    URLhttps: //doi.org/10.5281/zenodo.2526396. Sarah Itani and Dorina Thanou. Combining anatomical and functional net- worksforneuropathologyidentification: Acasestudyonautismspectrum disorder. Medical Image Analysis, 69:101986,

    work page doi:10.5281/zenodo.2526396

  41. [41]

    Łukasz Kaiser, Aidan N

    Šukasz Kaiser and Ilya Sutskever. Neural GPUs learn algorithms. arXiv:1511.08228,

    work page arXiv

  42. [42]

    Neural machine translation in linear time.arXiv:1610.10099,

    Nal Kalchbrenner, Lasse Espeholt, Karen Simonyan, Aaron van den Oord, Alex Graves, and Koray Kavukcuoglu. Neural machine translation in linear time.arXiv:1610.10099,

    work page arXiv

  43. [43]

    Dif- ferentiable graph module (DGM) graph convolutional networks

    Anees Kazi, Luca Cosmo, Nassir Navab, and Michael Bronstein. Dif- ferentiable graph module (DGM) graph convolutional networks. arXiv:2002.04999,

    work page arXiv 2002

  44. [44]

    Interpretable stability bounds for spectral graph filters.arXiv:2102.09587,

    Henry Kenlay, Dorina Thanou, and Xiaowen Dong. Interpretable stability bounds for spectral graph filters.arXiv:2102.09587,

    work page arXiv

  45. [45]

    Adam: A Method for Stochastic Optimization

    DiederikPKingmaandJimmyBa. Adam: Amethodforstochasticoptimiza- tion. arXiv:1412.6980,

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Auto-Encoding Variational Bayes

    Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv:1312.6114,

    work page internal anchor Pith review Pith/arXiv arXiv

  47. [47]

    Semi-Supervised Classification with Graph Convolutional Networks

    ThomasNKipfandMaxWelling. Semi-supervisedclassificationwithgraph convolutional networks.arXiv:1609.02907, 2016a. Thomas N Kipf and Max Welling. Variational graph auto-encoders. arXiv:1611.07308, 2016b. BIBLIOGRAPHY 141 Dmitry B Kireev. Chemnet: a novel neural network based method for graph/property mapping.J. Chemical Information and Computer Sciences, 35(...

    work page internal anchor Pith review Pith/arXiv arXiv

  48. [48]

    Albert Gu and Tri Dao

    Johannes Klicpera, Janek Groß, and Stephan Günnemann. Directional mes- sage passing for molecular graphs.arXiv:2003.03123,

    work page arXiv 2003

  49. [49]

    Energyflownetworks: deep sets for particle jets.Journal of High Energy Physics, 2019(1):121,

    PatrickTKomiske,EricMMetodiev,andJesseThaler. Energyflownetworks: deep sets for particle jets.Journal of High Energy Physics, 2019(1):121,

    work page 2019

  50. [50]

    Neural random- access machines.arXiv:1511.06392,

    Karol Kurach, Marcin Andrychowicz, and Ilya Sutskever. Neural random- access machines.arXiv:1511.06392,

    work page arXiv

  51. [51]

    Gated graph sequence neural networks.arXiv:1511.05493,

    Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural networks.arXiv:1511.05493,

    work page arXiv

  52. [52]

    Neural arithmetic units

    Andreas Madsen and Alexander Rosenberg Johansen. Neural arithmetic units. arXiv:2001.05016,

    work page arXiv 2001

  53. [53]

    3d facial matching by spiral convolutional metric learning and a biometric fusion-net of demographic properties

    Soha Sadat Mahdi, Nele Nauwelaers, Philip Joris, Giorgos Bouritsas, Shun- wang Gong, Sergiy Bokhnyak, Susan Walsh, Mark Shriver, Michael Bronstein, and Peter Claes. 3d facial matching by spiral convolutional metric learning and a biometric fusion-net of demographic properties. arXiv:2009.04746,

    work page arXiv 2009

  54. [54]

    Learn- ing representations of missing data for predicting patient outcomes

    BIBLIOGRAPHY 143 Brandon Malone, Alberto Garcia-Duran, and Mathias Niepert. Learn- ing representations of missing data for predicting patient outcomes. arXiv:1811.04752,

    work page arXiv

  55. [55]

    Invariant and equivariant graph networks.arXiv:1812.09902,

    HaggaiMaron,HeliBen-Hamu,NadavShamir,andYaronLipman. Invariant and equivariant graph networks.arXiv:1812.09902,

    work page arXiv

  56. [56]

    Prov- ably powerful graph networks.arXiv:1905.11136,

    HaggaiMaron,HeliBen-Hamu,HadarServiansky,andYaronLipman. Prov- ably powerful graph networks.arXiv:1905.11136,

    work page arXiv 1905

  57. [57]

    Scatteringnetworksonthesphereforscalableandrotationallyequivariant spherical cnns.arXiv:2102.02828,

    Jason D McEwen, Christopher GR Wallis, and Augustine N Mavor-Parker. Scatteringnetworksonthesphereforscalableandrotationallyequivariant spherical cnns.arXiv:2102.02828,

    work page arXiv

  58. [58]

    Learning with invariances in random features and kernel models.arXiv:2102.13219,

    Song Mei, Theodor Misiakiewicz, and Andrea Montanari. Learning with invariances in random features and kernel models.arXiv:2102.13219,

    work page arXiv

  59. [59]

    Representation learning via invariant causal mechanisms

    JovanaMitrovic, BrianMcWilliams, JacobWalker, Lars Buesing, andCharles Blundell. Representation learning via invariant causal mechanisms. arXiv:2010.07922,

    work page arXiv 2010

  60. [60]

    Fakenewsdetectiononsocialmediausinggeometric deep learning.arXiv:1902.06673,

    Federico Monti, Fabrizio Frasca, Davide Eynard, Damon Mannion, and MichaelMBronstein. Fakenewsdetectiononsocialmediausinggeometric deep learning.arXiv:1902.06673,

    work page arXiv 1902

  61. [61]

    Loopy belief propagation for approximate inference: An empirical study.arXiv:1301.6725,

    BIBLIOGRAPHY 145 Kevin Murphy, Yair Weiss, and Michael I Jordan. Loopy belief propagation for approximate inference: An empirical study.arXiv:1301.6725,

    work page arXiv

  62. [62]

    Janossy pooling: Learning deep permutation-invariant functions for variable-size inputs.arXiv:1811.01900,

    Ryan L Murphy, Balasubramaniam Srinivasan, Vinayak Rao, and Bruno Ribeiro. Janossy pooling: Learning deep permutation-invariant functions for variable-size inputs.arXiv:1811.01900,

    work page arXiv

  63. [63]

    Fourier-based and rational graph filters for spectral pro- cessing

    Giuseppe Patanè. Fourier-based and rational graph filters for spectral pro- cessing. arXiv:2011.04055,

    work page arXiv 2011

  64. [64]

    Learning mesh-based simulation with graph networks.arXiv preprint arXiv:2010.03409, 2020

    Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W Battaglia. Learning mesh-based simulation with graph networks. arXiv:2010.03409,

    work page arXiv 2010

  65. [65]

    Qu and L

    H Qu and L Gouskos. Particlenet: jet tagging via particle clouds. arXiv:1902.08570,

    work page arXiv 1902

  66. [66]

    Implicit regularization in deep learning may not be explainable by norms.arXiv:2005.06398,

    Noam Razin and Nadav Cohen. Implicit regularization in deep learning may not be explainable by norms.arXiv:2005.06398,

    work page arXiv 2005

  67. [67]

    Neural programmer-interpreters

    Scott Reed and Nando De Freitas. Neural programmer-interpreters. arXiv:1511.06279,

    work page arXiv

  68. [68]

    Girshick, and Jian Sun

    Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r- cnn: Towards real-time object detection with region proposal networks. arXiv:1506.01497,

    work page arXiv

  69. [69]

    Temporal pointwise convolutional networks for length of stay prediction in the intensive care unit

    Emma Rocheteau, Pietro Liò, and Stephanie Hyland. Temporal pointwise convolutional networks for length of stay prediction in the intensive care unit. arXiv:2007.09483,

    work page arXiv 2007

  70. [70]

    arXiv:2101.03940,

    Emma Rocheteau, Catherine Tong, Petar VeliŁković, Nicholas Lane, and PietroLiò.Predictingpatientoutcomeswithgraphrepresentationlearning. arXiv:2101.03940,

    work page arXiv

  71. [71]

    Temporal graph networks for deep learning on dynamic graphs,

    Frank Rosenblatt. The perceptron: a probabilistic model for information storageandorganizationinthebrain. PsychologicalReview,65(6):386,1958. 148 BRONSTEIN, BRUNA, COHEN & VELIČKOVIfl EmanueleRossi,BenChamberlain,FabrizioFrasca,DavideEynard,Federico Monti,andMichaelBronstein. Temporalgraphnetworksfordeeplearning on dynamic graphs.arXiv:2006.10637,

    work page arXiv 1958

  72. [72]

    Weight normalization: A sim- ple reparameterization to accelerate training of deep neural networks

    Tim Salimans and Diederik P Kingma. Weight normalization: A sim- ple reparameterization to accelerate training of deep neural networks. arXiv:1602.07868,

    work page arXiv

  73. [73]

    Hamiltonian graph networks with ODE integrators.arXiv:1909.12790,

    Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, and Peter Battaglia. Hamiltonian graph networks with ODE integrators.arXiv:1909.12790,

    work page arXiv 1909

  74. [74]

    Relational recurrent neural networks.arXiv:1806.01822,

    Adam Santoro, Ryan Faulkner, David Raposo, Jack Rae, Mike Chrzanowski, Theophane Weber, Daan Wierstra, Oriol Vinyals, Razvan Pascanu, and Timothy Lillicrap. Relational recurrent neural networks.arXiv:1806.01822,

    work page arXiv

  75. [75]

    How does batch normalization help optimization?arXiv:1805.11604,

    Shibani Santurkar, Dimitris Tsipras, Andrew Ilyas, and Aleksander Madry. How does batch normalization help optimization?arXiv:1805.11604,

    work page arXiv

  76. [76]

    Random features strengthen graph neural networks.arXiv:2002.03155,

    Ryoma Sato, Makoto Yamada, and Hisashi Kashima. Random features strengthen graph neural networks.arXiv:2002.03155,

    work page arXiv 2002

  77. [77]

    E(n) equivari- ant graph neural networks.arXiv:2102.09844,

    BIBLIOGRAPHY 149 Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. E(n) equivari- ant graph neural networks.arXiv:2102.09844,

    work page arXiv

  78. [78]

    Proximal Policy Optimization Algorithms

    John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms.arXiv:1707.06347,

    work page internal anchor Pith review Pith/arXiv arXiv

  79. [79]

    Implicit regularization in relu networks with the square loss.arXiv:2012.05156,

    Ohad Shamir and Gal Vardi. Implicit regularization in relu networks with the square loss.arXiv:2012.05156,

    work page arXiv 2012

  80. [80]

    Very Deep Convolutional Networks for Large-Scale Image Recognition

    KarenSimonyanandAndrewZisserman. Verydeepconvolutionalnetworks for large-scale image recognition.arXiv:1409.1556,

    work page internal anchor Pith review Pith/arXiv arXiv

Showing first 80 references.