Connectional physics

[Philip Thrift]

Connectional physics

Some have written on how the connectional (neural network) approach will not rival the traditional equational ( https://inews.co.uk/news/science/this-is-the-equation-stephen-hawking-wanted-on-his-tombstone-323699 ) approach, but then why should nature necessarily be expressed in simple language.

 

https://arxiv.org/abs/1802.08313 :

Deep Learning and AdS/CFT

https://arxiv.org/abs/1801.03918 :

Black Holes as Brains: Neural Networks with Area Law Entropy

https://its.unc.edu/files/2018/10/DRUTDeepLearningQM.pdf (slides):

Deep learning quantum matter: Machine-learning approaches to the quantum many-body problem  

https://www.researchgate.net/publication/ :319272134_Quantum_fields_as_deep_learning

Quantum fields as deep learning

https://arxiv.org/abs/1910.03637 :

Machine learning quantum field theory with local probes

https://arxiv.org/abs/1811.06533 :

Learning to Predict the Cosmological Structure Formation

https://arxiv.org/abs/1902.05965 :

From Dark Matter to Galaxies with Convolutional Networks

https://arxiv.org/abs/1706.02390 :

CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks

Wave physics as an analog recurrent neural network :

https://advances.sciencemag.org/content/5/12/eaay6946 :

cf. https://en.wikipedia.org/wiki/Machine_learning_in_physics

@philipthrift

[Brent Meeker]

It seems to me that our brains and those of other animals developed at NN and via evolution and experience learned from examples (i.e. natural selection).  Humans diverged from this by developing language and symbolic representations, which led to reasoning via imagination and modeling.  But this is layered on top of the NN, which is still what you need to recognize faces and ride a bicycle.

Brent

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[Philip Thrift]

These references have nothing to do really with biological brains.

Modeling the human brain is not their purpose at all. Their purpose is tho see where the connectional paradigm (aka artificial neural networks - within the practice of computer science machine learning) can lead to in doing physics.

@philipthrift

[Russell Standish]

On Sat, Feb 08, 2020 at 06:44:16AM -0800, Philip Thrift wrote:
>
> Connectional physics
>
> Some have written on how the connectional (neural network) approach will not
> rival the traditional equational ( https://inews.co.uk/news/science/
> this-is-the-equation-stephen-hawking-wanted-on-his-tombstone-323699 ) approach,
> but then why should nature necessarily be expressed in simple language.

Both equations and connectionist models rely on finding and expoiting
patterns in nature. Why these patterns exist is really Wigner's hoary
old question of the "unreasonable effectiveness of mathematics". To
which, I would answer because of the Solomonoff-Levin theorem,
sometimes called the Occams Razor theorem.

The equation approach is remarkably effective for some situations (eg
celestial mechanics), and before we had decent computers, we focussed on
domains where these models were effective. Now we find that some
models (think weather models, for example), where the computational
cost of the equation approach exceeds the computational cost of
throwing a neural network at it, allowing considerable speedup of
computing the model using a connectionist shortcut. I think it is
interesting from a having another tool in the toolbox, but probably
not interesting philosophically.



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[Philip Thrift]

On the "unreasonable effectiveness of mathematics" I approach this - as you know -  ala Hartry Field:

https://as.nyu.edu/content/nyu-as/as/faculty/hartry-field.html

https://en.wikipedia.org/wiki/Hartry_Field

Field holds that the existence of sets may be denied, in opposition to Quine–Putnam indispensability argument of Quine and Putnam.

I have my own version:

https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/

On the simplicity of equations, if is hard to see how this equation is pretty:

https://www.symmetrymagazine.org/sites/default/files/images/standard/sml.png

(The equation for the Standard Model - can you count how many symbols/glyphs are there?)

On the connectional vs. equational paradigm in physics: I think the connectional could profoundly change what is both practically and philosophically viewed as a model of physics, and that the equational is left behind in a past era of platonism.

@philipthrift

[Lawrence Crowell]

The tessellation of an AdS spacetime is a tensor network https://arxiv.org/abs/1106.1082 . In a pure AdS_n with no Lanczos junctions this tessellation has an unbroken discrete symmetry. With broken symmetry, say junction etc, this network is in some sense adapted so there are distinct causal wedges.

LC