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My understanding is Conway's game of life can be done by simply convolving a 3x3 array of all ones (except a central 0) through every pixel, and then looking at

My understanding is Conway's game of life can be done by simply convolving a 3x3 array of all ones (except a central 0) through every pixel, and then looking at the results of that convolution to see if the pixel is dead or alive, e.g. https://stackoverflow.com/questions/46196346/why-does-my-game-of-life-simulation-slow-down-to-a-crawl-within-seconds-matplot https://stackoverflow.com/questions/46196346/why-does-my-gam... If that's the case, would a nice solution be to model it as a recurrent neural network, e.g. pytorch or jax, with a single convolutional layer, with a single kernel, which you don't backprop to, and then try to minimise to loss with reference to the target image, by backpropagating to the input image? It then becomes highly analogous to Google's deepdream, but instead of optimising the image for the output class, you optimise it to the output image.

PartiallyTyped 6y ago
What you are suggesting is the idea behind StyleTransfer. Given two images, A, B, and a neural network F, you repeatedly modify B using ∂ L(F(A),F(B))/∂B, where L is the loss function, A contains the style and B is the input image.
andersource 6y ago
That's an interesting approach. The problem is that the function to be applied after the convolution is binary, hence not differentiable. You could replace it with a soft variation, my (wild) guess is it would still be difficult to converge: * If the transitions are too sharp it will behave like the stepwise, non-differentiable original * If the transitions are too soft, the optimization will converge to some middle-state compromise that will not behave as desired when binarized But that's just speculation. Also interesting to note that in the very relevant Kaggle competition [0], top solutions don't mention differentiable approaches (as far as I've seen, I admit I haven't looked too deeply). [0] https://www.kaggle.com/c/conways-reverse-game-of-life-2020/discussion?sort=votes https://www.kaggle.com/c/conways-reverse-game-of-life-2020/d...
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PartiallyTyped 6y ago

What you are suggesting is the idea behind StyleTransfer. Given two images, A, B, and a neural network F, you repeatedly modify B using ∂ L(F(A),F(B))/∂B, where L is the loss function, A contains the style and B is the input image.

andersource 6y ago

That's an interesting approach. The problem is that the function to be applied after the convolution is binary, hence not differentiable. You could replace it with a soft variation, my (wild) guess is it would still be difficult to converge: * If the transitions are too sharp it will behave like the stepwise, non-differentiable original * If the transitions are too soft, the optimization will converge to some middle-state compromise that will not behave as desired when binarized But that's just speculation. Also interesting to note that in the very relevant Kaggle competition [0], top solutions don't mention differentiable approaches (as far as I've seen, I admit I haven't looked too deeply). [0] https://www.kaggle.com/c/conways-reverse-game-of-life-2020/discussion?sort=votes https://www.kaggle.com/c/conways-reverse-game-of-life-2020/d...

deleted 6y ago

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