Learning Game of Life with a Convolutional Neural Network

#1

Post by DanielRapp » Wed, Sep 30, 2015, 2:16 PM UTC

Learning Game of Life with a Convolutional Neural Network
danielrapp.github.io

Re: Learning Game of Life with a Convolutional Neural Network

#2

Post by shaggyfrog » Wed, Sep 30, 2015, 3:42 PM UTC

This is the perfect place to quote one of the hacker koans:

In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6.

"What are you doing?", asked Minsky.

"I am training a randomly wired neural net to play Tic-Tac-Toe" Sussman replied.

"Why is the net wired randomly?", asked Minsky.

"I do not want it to have any preconceptions of how to play", Sussman said.

Minsky then shut his eyes.

"Why do you close your eyes?", Sussman asked his teacher.

"So that the room will be empty."

At that moment, Sussman was enlightened.

Re: Learning Game of Life with a Convolutional Neural Network

#3

Post by hughes » Wed, Sep 30, 2015, 4:03 PM UTC

I guess it works for a few specific cases you mentioned, but the example animation at the end diverges after twelve steps[1]

[1] http://imgur.com/a/gcUCH

Re: Learning Game of Life with a Convolutional Neural Network

#4

Post by mark_l_watson » Wed, Sep 30, 2015, 4:06 PM UTC

Neat example! I had not run across convnet.js before, so thanks. Karpathy was I believe one of Hinton's students. I looked over my archived courses last night and saved all of Hinton's videos and viewgraphs from his coursera class in 2012. Really good stuff, and it is a real shame that COursera does not continually re-run that course on auto-pilot (I am sure that Hinton and his students are too busy to participate in the forums but the videos, auto-generated homework, and the quizes would stand on their own without TA intervention.)

Convolutional networks, deep learning, and machine learning in general are arguably the most disruptive technologies in our lifetimes. BTW, pardon the shameless plug, but I just started a new blog this morning to host ML resources and my own experiments: http://blog.cognition.tech/?view=classic

Re: Learning Game of Life with a Convolutional Neural Network

#5

Post by karpathy » Wed, Sep 30, 2015, 4:13 PM UTC

hughes wrote: post #3

I guess it works for a few specific cases you mentioned, but the example animation at the end diverges after twelve steps[1] [1] http://imgur.com/a/gcUCH

It does seem like it wasn't trained in the most optimal fashion.

- The conv layer has only 20 relu units, I'm not sure if that suffices to memorize the rules. The net might be "underfitting" the rule set, and therefore making mistakes in rare pixel arrangements.

- More worryingly it's also strange that the author uses a fully connected layer right after the conv layer (this is implicitly added in ConvNetJS when you specify a loss layer). This means that the output neurons are a function of the entire preceding CONV layer activations everywhere, while the game of life rules are local. The way to do this would be to instead use a 1x1 CONV layer with 2 neurons on top of the first 3x3 CONV layer, and interpret it as computing the class scores at every spatial position. However, in this case you'd want to apply the loss on every spatial position, and this "fully-convolutional" loss use case is not supported out of the box in ConvNetJS, but could be written.

- However, with a fully-convolutional loss zero-padding of 1 used around the borders might cause trouble. Normally this is okay with images, but here this might cause trouble because the neurons all share parameters spatially (and hence compute the same function) and don't "know" if they are at the border on in the middle of the image. I'm not sure how how this game of life handles boundary conditions, but if borders obey different dynamics then you'd want to distinguish the border pixels with a special "border" feature vector at the input. E.g. each pixel is a 3-vector, with a 1-hot encoding for (border, positive pixel, negative pixel).

- And it's also strange that the author uses "regression" loss for some that is a binary classification problem.

So, nice attempt but several funny choices, and clear why it didn't fully work :)

Re: Learning Game of Life with a Convolutional Neural Network

#6

Post by boothead » Wed, Sep 30, 2015, 4:33 PM UTC

Convolution is a comonad. http://kukuruku.co/hub/haskell/cellular-automata-using-comon...

I love it when there's a nugget of rigor behind things like this that can be pulled out and applied elsewhere!

Re: Learning Game of Life with a Convolutional Neural Network

#7

Post by JabavuAdams » Wed, Sep 30, 2015, 4:49 PM UTC

mark_l_watson wrote: post #4

Neat example! I had not run across convnet.js before, so thanks. Karpathy was I believe one of Hinton's students. I looked over my archived courses last night and saved all of Hinton's videos and viewgraphs from his coursera class in 2012. Really good stuff, and it is a real shame that COursera does not continually re-run that course on auto-pilot (I am sure that Hinton and his students are too busy to participate in…

That course was fantastic. Work prevented me from doing the assignments, but I've also archived the materials.

Re: Learning Game of Life with a Convolutional Neural Network

#8

Post by JabavuAdams » Wed, Sep 30, 2015, 4:51 PM UTC

karpathy wrote: post #5

hughes wrote: post #3

I guess it works for a few specific cases you mentioned, but the example animation at the end diverges after twelve steps[1] [1] http://imgur.com/a/gcUCH

It does seem like it wasn't trained in the most optimal fashion. - The conv layer has only 20 relu units, I'm not sure if that suffices to memorize the rules. The net might be "underfitting" the rule set, and therefore making mistakes in rare pixel arrangements. - More worryingly it's also strange that the author uses a fully connected layer right after the conv layer (this is implicitly added in ConvNetJS when you s…

Comments like this, and Hinton's Coursera course remind me that there's a whole "Black Art" to training these systems.

Do you think a similar approach could be used to learn to generalize Navier-Stokes by looking at fluid flows?

Re: Learning Game of Life with a Convolutional Neural Network

#9

Post by dave_sullivan » Wed, Sep 30, 2015, 5:29 PM UTC

JabavuAdams wrote: post #8

karpathy wrote: post #5

Earlier quoted context omitted.

It does seem like it wasn't trained in the most optimal fashion. - The conv layer has only 20 relu units, I'm not sure if that suffices to memorize the rules. The net might be "underfitting" the rule set, and therefore making mistakes in rare pixel arrangements. - More worryingly it's also strange that the author uses a fully connected layer right after the conv layer (this is implicitly added in ConvNetJS when you s…

Comments like this, and Hinton's Coursera course remind me that there's a whole "Black Art" to training these systems. Do you think a similar approach could be used to learn to generalize Navier-Stokes by looking at fluid flows?

It's not any more of a black art than programming is. There's no magic to it, you just have to know what you're doing. Also, you should use some kind of scheme (like bayesian optimization) to optimize the hyperparameters of many experimental models. That's the best way to make sure you're getting the best results (but of course takes a while, so you do have to be selective about which parameters you optimize or what combinations you allow).

And I'll also aknowledge that "programming" is a vastly more mature field than "deep learning" or even "machine learning". So it's fair to argue that there's much we don't know, but there's more and more we do.

Re: Learning Game of Life with a Convolutional Neural Network

#10

Post by claar » Wed, Sep 30, 2015, 5:35 PM UTC

shaggyfrog wrote: post #2

This is the perfect place to quote one of the hacker koans: In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6. "What are you doing?", asked Minsky. "I am training a randomly wired neural net to play Tic-Tac-Toe" Sussman replied. "Why is the net wired randomly?", asked Minsky. "I do not want it to have any preconceptions of how to play", Sussman said. Minsky then shut his ey…

If you don't understand this (like me), see https://en.wikipedia.org/wiki/Hacker_koan#Uncarved_block for an explanation.

According to that link, it's based on a true story:

  So Sussman began working on a program. Not long after,
  this odd-looking bald guy came over. Sussman figured the
  guy was going to boot him out, but instead the man sat
  down, asking, "Hey, what are you doing?" Sussman talked
  over his program with the man, Marvin Minsky. At one point
  in the discussion, Sussman told Minsky that he was using a
  certain randomizing technique in his program because he
  didn't want the machine to have any preconceived notions.

  Minsky said, "Well, it has them, it's just that you don't
  know what they are." It was the most profound thing Gerry
  Sussman had ever heard. And Minsky continued, telling him
  that the world is built a certain way, and the most
  important thing we can do with the world is avoid
  randomness, and figure out ways by which things can be
  planned. Wisdom like this has its effect on
  seventeen-year-old freshmen, and from then on Sussman was
  hooked.