Answers.Body: <p>Recursive artificial networks are a type aligned well with GDL, and it is an increasingly popular one. Using non-orthogonal geometries is natural when using directed graphs as semantic association, data flow, or composition networks.</p>
  
  <p>This more free-form approach enters into <code>industry</code> slowly because most programming languages use orthogonal structures designed around multidimensional arrays and nested loops to iterate through them, made popular in the FORTRAN era. It is common that a student learns to loop through an array before learning to call a function or test and branch. Computer science is, in some ways, entrenched in the orthogonal structure.</p>
  
  <p>To call the two categories Euclidean and non-euclidean is inaccurate. The initial trend in machine learning followed a Cartesian paradigm, one locked into 90° angles in data structures. The free-form graph is non-cartesian but still just as Euclidean, as Euclid worked with angles other than 90° frequently.</p>
  
  <p>Apple and Google are likely candidates for this seepage of recursive networks into industry data centers, for NLP applications. Language associations are free-form even though these structures are serialized for speech and written text.</p>
  
  <p>Cognition is also non-cartesian. Graph based optimization (pre-GDL) has been part of cognitive research since the 1970s, especially in the LISP space at MIT and CMU and the U.S. Naval Research facilities for strategic analysis, <a href="https://projecteuclid.org/download/pdf_1/euclid.aos/1176343791" rel="nofollow noreferrer"><em>Optimal strategies for a class of constrained sequential problems</em></a> by JB Kadane, HA Simon, The Annals of Statistics, 1977. Algorithm 2 is a convergence strategy, but without layers of cells, yet the searching concepts of gradient are already present in the maximal and minimal operations in the search in steps <em>c</em> and <em>f</em>.</p>
  
  <p>The aeronautics and auto industry is a likely candidates for seepage into the embedded computing for automated driving and flight. Most of this is either company confidential or classified.</p>
  
  <p><a href="https://ai.stackexchange.com/questions/7547/is-topological-sophistication-necessary-to-the-furtherance-of-ai/8529#8529">This answer</a> to the question about topological sophistication provides some background why non-euclidean space may be a more natural way to map associations, flow, and composition.</p>
  
  <p>These are some practical applications.</p>
  
  <ul>
  <li><a href="https://papers.nips.cc/paper/5954-convolutional-networks-on-graphs-for-learning-molecular-fingerprints.pdf" rel="nofollow noreferrer"><em>Convolutional networks on graphs for learning molecular fingerprints</em></a> by DK Duvenaud, D Maclaurin, J Iparraguirre, Advances in neural, 2015</li>
  <li><a href="https://link.springer.com/content/pdf/10.1007/JHEP01%282019%29057.pdf" rel="nofollow noreferrer"><em>CD-aware recursive neural networks for jet physics</em></a> by Gilles Louppe, Kyunghyun Cho, Cyril Becot, Kyle Cranmer, 2019</li>
  <li><a href="https://arxiv.org/abs/1905.04497" rel="nofollow noreferrer"><em>Stability Properties of Graph Neural Networks</em></a> by Fernando Gama, Joan Bruna, Alejandro Ribeiro</li>
  <li><a href="https://arxiv.org/abs/1811.11465" rel="nofollow noreferrer"><em>Isospectralization, or how to hear shape, style, and correspondence</em></a> by Luca Cosmo, Mikhail Panine, Arianna Rampini, Maks Ovsjanikov, Michael M. Bronstein, Emanuele Rodolà </li>
  <li><a href="https://arxiv.org/abs/1902.06673" rel="nofollow noreferrer"><em>Fake News Detection on Social Media using Geometric Deep Learning</em></a>, by Federico Monti, Fabrizio Frasca, Davide Eynard, Damon Mannion, Michael M. Bronstein</li>
  </ul>
  
  <p>We've used recursive networks to align complex models with data acquired during laboratory experimentation and hope to publish on that approach as part of another publication. It is effective, since the relationships between features in the real world form squares and cubes only by chance, so it is not very common. Research into materials and energy cannot be confined by Cartesian conceptions, even if the graphs published are on Cartesian coordinate axes, so that others with traditional analytic geometry backgrounds can understand the graphs quickly.</p>
  
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Answers.CreationDate: 2019-05-16T15:26:41.373Z
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Answers.LastEditDate: 2019-05-16T15:39:40.437Z
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Body: <p>I'm interested in the industrial use of GDL (see <a href="https://arxiv.org/abs/1611.08097" rel="noreferrer">https://arxiv.org/abs/1611.08097</a>). Is it used in industry? That is, does any company have access to non-Euclidean data and process it directly instead of converting it to a more standard format?</p>
  
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Comments.CreationDate: 2019-05-06T21:11:29.577Z
Comments.Text: GDL is a relatively new field of study. Apparently, the first graph NN model was introduced in 2005 by Scarselli et al. and only recently GDL models have started to be promising, so I don't think there are a lot of industries that have already adopted it. Maybe the chemical industry.
Comments.UserDisplayName: nbro
Tags: <geometric-deep-learning><applications>
Title: Do you know any examples of geometric deep learning used in industry?
UserDisplayName: Guillermo Mosse
ThreadText: # Do you know any examples of geometric deep learning used in industry?
  
  (Asked by: username_0 on 2019-05-06)
  
  I'm interested in the industrial use of GDL (see <https://arxiv.org/abs/1611.08097>). Is it used in industry? That is, does any company have access to non-Euclidean data and process it directly instead of converting it to a more standard format?
  
  **Tags:** geometric-deep-learning, applications
  > **Comments:**
  > **username_1**: GDL is a relatively new field of study. Apparently, the first graph NN model was introduced in 2005 by Scarselli et al. and only recently GDL models have started to be promising, so I don't think there are a lot of industries that have already adopted it. Maybe the chemical industry.  
  
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  ## 1 answers
  
  ### Answer by username_2 on 2019-05-16. Score: 1
  
  Recursive artificial networks are a type aligned well with GDL, and it is an increasingly popular one. Using non-orthogonal geometries is natural when using directed graphs as semantic association, data flow, or composition networks.
  
  This more free-form approach enters into `industry` slowly because most programming languages use orthogonal structures designed around multidimensional arrays and nested loops to iterate through them, made popular in the FORTRAN era. It is common that a student learns to loop through an array before learning to call a function or test and branch. Computer science is, in some ways, entrenched in the orthogonal structure.
  
  To call the two categories Euclidean and non-euclidean is inaccurate. The initial trend in machine learning followed a Cartesian paradigm, one locked into 90° angles in data structures. The free-form graph is non-cartesian but still just as Euclidean, as Euclid worked with angles other than 90° frequently.
  
  Apple and Google are likely candidates for this seepage of recursive networks into industry data centers, for NLP applications. Language associations are free-form even though these structures are serialized for speech and written text.
  
  Cognition is also non-cartesian. Graph based optimization (pre-GDL) has been part of cognitive research since the 1970s, especially in the LISP space at MIT and CMU and the U.S. Naval Research facilities for strategic analysis, [*Optimal strategies for a class of constrained sequential problems*](https://projecteuclid.org/download/pdf_1/euclid.aos/1176343791) by JB Kadane, HA Simon, The Annals of Statistics, 1977. Algorithm 2 is a convergence strategy, but without layers of cells, yet the searching concepts of gradient are already present in the maximal and minimal operations in the search in steps *c* and *f*.
  
  The aeronautics and auto industry is a likely candidates for seepage into the embedded computing for automated driving and flight. Most of this is either company confidential or classified.
  
  [This answer](https://ai.stackexchange.com/questions/7547/is-topological-sophistication-necessary-to-the-furtherance-of-ai/8529#8529) to the question about topological sophistication provides some background why non-euclidean space may be a more natural way to map associations, flow, and composition.
  
  These are some practical applications.
  
  * [*Convolutional networks on graphs for learning molecular fingerprints*](https://papers.nips.cc/paper/5954-convolutional-networks-on-graphs-for-learning-molecular-fingerprints.pdf) by DK Duvenaud, D Maclaurin, J Iparraguirre, Advances in neural, 2015
  * [*CD-aware recursive neural networks for jet physics*](https://link.springer.com/content/pdf/10.1007/JHEP01%282019%29057.pdf) by Gilles Louppe, Kyunghyun Cho, Cyril Becot, Kyle Cranmer, 2019
  * [*Stability Properties of Graph Neural Networks*](https://arxiv.org/abs/1905.04497) by Fernando Gama, Joan Bruna, Alejandro Ribeiro
  * [*Isospectralization, or how to hear shape, style, and correspondence*](https://arxiv.org/abs/1811.11465) by Luca Cosmo, Mikhail Panine, Arianna Rampini, Maks Ovsjanikov, Michael M. Bronstein, Emanuele Rodolà
  * [*Fake News Detection on Social Media using Geometric Deep Learning*](https://arxiv.org/abs/1902.06673), by Federico Monti, Fabrizio Frasca, Davide Eynard, Damon Mannion, Michael M. Bronstein
  
  We've used recursive networks to align complex models with data acquired during laboratory experimentation and hope to publish on that approach as part of another publication. It is effective, since the relationships between features in the real world form squares and cubes only by chance, so it is not very common. Research into materials and energy cannot be confined by Cartesian conceptions, even if the graphs published are on Cartesian coordinate axes, so that others with traditional analytic geometry backgrounds can understand the graphs quickly.
  
  
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