Cool, but convo nets are not the right tool though. Neural networks have an implicit smoothness and locality prior (which is what back propagation exploits) which this game does not really posses. Decision trees (e.g. random forests), are able to deal with sharp discontinuities better and would be more appropriate. I would expect less training, and perfect results.
Learning Game of Life with a Convolutional Neural Network
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Re: Learning Game of Life with a Convolutional Neural Network
#12Cool, but convo nets are not the right tool though. Neural networks have an implicit smoothness and locality prior (which is what back propagation exploits) which this game does not really posses. Decision trees (e.g. random forests), are able to deal with sharp discontinuities better and would be more appropriate. I would expect less training, and perfect results.
I agree decision trees are more natural here, but even they are overkill, I think: all that needs to be learned is a function from the 8 neighbors to the center, which means from 8 bits to 2 bits, or in other words, there are just 256 values to be learned.
Literally any reasonable learning algorithm, even nearest neighbor, will learn that fairly quickly. The article had to use millions of samples, which is extremely excessive - a more efficient algorithm should only require thousands.
What might be interesting could be to see whether the neural network learns the underlying rule, that placement does not matter, only the sum matters, and that the crucial value is "3". That would be cool to see.
Re: Learning Game of Life with a Convolutional Neural Network
#13I 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…
Glad to see a critical eye on these sorts of things. I had a question about the choice of loss function. So regression is definitely the wrong choice since our outputs are binary (0 or 1) and not real-valued (0-1).
We could use a softmax classifier as this is meant for multi-class binary classifications. Each class in this case would represent a neighboring pixel, a classification of that class would represent activating that pixel. However, softmax assumes one-label and the probabilities add up to 1. Our problem is a multi-label multi-class binary classification.
We could train 9 of such softmax node groupings for each neighboring pixel but that immediately seems to be a bad idea.
Another awful solution - make each possible pixel configuration (2^9 of these) a class and do a standard soft-max.
I can start to see why the author chose to use regression loss as a sort of hack to get this to work, but I'm trying to think out the best, proper solution.
Any thoughts?
Re: Learning Game of Life with a Convolutional Neural Network
#14Cool, but convo nets are not the right tool though. Neural networks have an implicit smoothness and locality prior (which is what back propagation exploits) which this game does not really posses. Decision trees (e.g. random forests), are able to deal with sharp discontinuities better and would be more appropriate. I would expect less training, and perfect results.
I agree decision trees are more natural here, but even they are overkill, I think: all that needs to be learned is a function from the 8 neighbors to the center, which means from 8 bits to 2 bits, or in other words, there are just 256 values to be learned. Literally any reasonable learning algorithm, even nearest neighbor, will learn that fairly quickly. The article had to use millions of samples, which is extremely…
... there are just 256 values to be learned
This is a very good point and it's the reason why I don't find much value in GAs. There is an inherent conflict between "an algorithm for a specific problem" (which can be optimized to run in a short time - the above problem can be reduced to a lookup in a 256 x 2 bit matrix and thus run in O(1)) and "an algorithm for any problem (in a class)" which, while theoretically capable of finding a solution, is prohibitive in time and/or space.
As far as I can tell, GAs are barely any better than a random walk and thus not useful for any non-trivial problems. I am not yet sure if NNs are in the same category, though I suspect they are.