Thursday, March 29, 2018

Machine Learning for Physics?!?

Today was the last day of a nice workshop here at the Arnold Sommerfeld Center organised by Thomas Grimm and Sven Krippendorf on the use of Big Data and Machine Learning in string theory. While the former (at this workshop mainly in the form of developments following Kreuzer/Skarke and taking it further for F-theory constructions, orbifolds and the like) appears to be quite advanced as of today, the latter is still in its very early days. At best.

I got the impression that for many physicists that have not yet spent too much time with this, deep learning and in particular deep neural networks are expected to be some kind of silver bullet that can answer all kinds of questions that humans have not been able to answer despite some effort. I think this hope is at best premature and looking at the (admittedly impressive) examples where it works (playing Go, classifying images, speech recognition, event filtering at LHC) these seem to be more like those problems where humans have at least a rough idea how to solve them (if it is not something that humans do everyday like understanding text) and also roughly how one would code it but that are too messy or vague to be treated by a traditional program.

So, during some of the less entertaining talks I sat down and thought about problems where I would expect neural networks to perform badly. And then, if this approach fails even in simpler cases that are fully under control one should maybe curb the expectations for the more complex cases that one would love to have the answer for. In the case of the workshop that would be guessing some topological (discrete) data (that depends very discontinuously on the model parameters). Here a simple problem would be a 2-torus wrapped by two 1-branes. And the computer is supposed to compute the number of matter generations arising from open strings at the intersections, i.e. given two branes (in terms of their slope w.r.t. the cycles of the torus) how often do they intersect? Of course these numbers depend sensitively on the slope (as a real number) as for rational slopes [latex]p/q[/latex] and [latex]m/n[/latex] the intersection number is the absolute value of [latex]pn-qm[/latex]. My guess would be that this is almost impossible to get right for a neural network, let alone the much more complicated variants of this simple problem.

Related but with the possibility for nicer pictures is the following: Can a neural network learn the shape of the Mandelbrot set? Let me remind those of you who cannot remember the 80ies anymore, for a complex number c you recursively apply the function
[latex]f_c(z)= z^2 +c[/latex]
starting from 0 and ask if this stays bounded (a quick check shows that once you are outside [latex]|z| < 2[/latex] you cannot avoid running to infinity). You color the point c in the complex plane according to the number of times you have to apply f_c to 0 to leave this circle. I decided to do this for complex numbers x+iy in the rectangle -0.74
I have written a small mathematica program to compute this image. Built into mathematica is also a neural network: You can feed training data to the function Predict[], for me these were 1,000,000 points in this rectangle and the number of steps it takes to leave the 2-ball. Then mathematica thinks for about 24 hours and spits out a predictor function. Then you can plot this as well:


There is some similarity but clearly it has no idea about the fractal nature of the Mandelbrot set. If you really believe in magic powers of neural networks, you might even hope that once it learned the function for this rectangle one could extrapolate to outside this rectangle. Well, at least in this case, this hope is not justified: The neural network thinks the correct continuation looks like this:
Ehm. No.

All this of course with the caveat that I am no expert on neural networks and I did not attempt anything to tune the result. I only took the neural network function built into mathematica. Maybe, with a bit of coding and TensorFlow one can do much better. But on the other hand, this is a simple two dimensional problem. At least for traditional approaches this should be much simpler than the other much higher dimensional problems the physicists are really interested in.

82 comments:

شركة المثالية said...
This comment has been removed by a blog administrator.
Roman Pylypchuk said...

https://aboveintelligent.com/what-do-deep-neural-networks-understand-of-fractals-2ae354911601

Anonymous said...
This comment has been removed by a blog administrator.
شركة رواد الحرمين said...
This comment has been removed by a blog administrator.
Priyanka said...
This comment has been removed by a blog administrator.
Priyanka said...
This comment has been removed by a blog administrator.
CloudLearn ERP said...
This comment has been removed by a blog administrator.
sherlie said...
This comment has been removed by a blog administrator.
harshni said...
This comment has been removed by a blog administrator.
harshni said...
This comment has been removed by a blog administrator.
harshni said...
This comment has been removed by a blog administrator.
lavanya said...
This comment has been removed by a blog administrator.
sathya said...
This comment has been removed by a blog administrator.
anand said...
This comment has been removed by a blog administrator.
surya said...
This comment has been removed by a blog administrator.
ramesh said...
This comment has been removed by a blog administrator.
aravind said...
This comment has been removed by a blog administrator.
Rashika said...
This comment has been removed by a blog administrator.
dhinesh said...
This comment has been removed by a blog administrator.
swaroop said...
This comment has been removed by a blog administrator.
devi said...
This comment has been removed by a blog administrator.
Cyber Security said...
This comment has been removed by a blog administrator.
Cyber Security said...
This comment has been removed by a blog administrator.
Revathi said...
This comment has been removed by a blog administrator.
vivekvedha said...
This comment has been removed by a blog administrator.
sushmi said...
This comment has been removed by a blog administrator.
prabhu said...
This comment has been removed by a blog administrator.
Sages Marketing said...
This comment has been removed by a blog administrator.
Cyber Security said...
This comment has been removed by a blog administrator.
Priyanka said...
This comment has been removed by a blog administrator.
Cyber Security said...
This comment has been removed by a blog administrator.
angeleena said...
This comment has been removed by a blog administrator.
Tamio enmu said...
This comment has been removed by a blog administrator.
Data Science said...
This comment has been removed by a blog administrator.
Training for IT and Software Courses said...
This comment has been removed by a blog administrator.
Best Training Institute said...
This comment has been removed by a blog administrator.
Realtime Experts said...
This comment has been removed by a blog administrator.
Ashleel Londa said...
This comment has been removed by a blog administrator.
Ashleel Londa said...
This comment has been removed by a blog administrator.
Web tech mantra said...
This comment has been removed by a blog administrator.
IamLinkfeeder said...
This comment has been removed by a blog administrator.
IamLinkfeeder said...
This comment has been removed by a blog administrator.
Data Analytics Courses in Bangalore said...
This comment has been removed by a blog administrator.
Info World said...
This comment has been removed by a blog administrator.
kumarfield29 said...
This comment has been removed by a blog administrator.
Musa Rishu said...
This comment has been removed by a blog administrator.
Anonymous said...
This comment has been removed by a blog administrator.
Anonymous said...
This comment has been removed by a blog administrator.
Amazon my tv said...
This comment has been removed by a blog administrator.
Ramesh Sampangi said...
This comment has been removed by a blog administrator.
Anonymous said...
This comment has been removed by a blog administrator.
princika said...
This comment has been removed by a blog administrator.
Judy A. Walters said...
This comment has been removed by a blog administrator.
Digital Brolly said...
This comment has been removed by a blog administrator.
mstwotoes.com said...
This comment has been removed by a blog administrator.
ravi said...
This comment has been removed by a blog administrator.
Leyla Doyle said...
This comment has been removed by a blog administrator.
digitalkrik23 said...
This comment has been removed by a blog administrator.
ravi said...
This comment has been removed by a blog administrator.
Brand2grand said...
This comment has been removed by a blog administrator.
Unknown said...
This comment has been removed by a blog administrator.
Optoma India said...
This comment has been removed by a blog administrator.
Optoma India said...
This comment has been removed by a blog administrator.
Unknown said...
This comment has been removed by a blog administrator.
honeywebsolutions said...
This comment has been removed by a blog administrator.
Devi said...
This comment has been removed by a blog administrator.
Priyankajain said...
This comment has been removed by a blog administrator.
sabresalih said...
This comment has been removed by a blog administrator.
Diligent Security Services Inc said...
This comment has been removed by a blog administrator.
Truck and Trailer said...
This comment has been removed by a blog administrator.
Sell House said...
This comment has been removed by a blog administrator.
What is Website said...
This comment has been removed by a blog administrator.
chocky said...
This comment has been removed by a blog administrator.
Data Science said...
This comment has been removed by a blog administrator.
Venkatesh said...
This comment has been removed by a blog administrator.
Michelle Roy said...
This comment has been removed by a blog administrator.
lily jake said...
This comment has been removed by a blog administrator.
chocky said...
This comment has been removed by a blog administrator.
Tutorials said...
This comment has been removed by a blog administrator.
Benefits of Himalayan Salt said...
This comment has been removed by a blog administrator.
sabresalih said...
This comment has been removed by a blog administrator.
Anonymous said...
This comment has been removed by a blog administrator.