Even a simple regression will do that
it won't AFAIK, without some extra hand coded logic
Transformer neural net learns to run Conway's Game of Life just from examples
21–30 of 36 posts
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#22Rip John Conway, died of Covid.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#23To be honest an unsurprising result. But I think the paper fails to answer the most important question. It alleges that this isn't a statistical model: "it is not a statistical model that predicts the most likely next state based on all the examples it has been trained on. We observe that it learns to use its attention mechanism to compute 3x3 convolutions — 3x3 convolutions are a common way to implement the Game of…
The diagonal-looking attention matrix shown in the post is mathematically equivalent to 3 by 3 convolution . The model learns how to do that via its attention mechanism - it's not obvious that it would be able to do that via attention. (This can be shown by comparing that attention matrix to a "manually computed Neighbour Attention matrix", which is known to be equivalent to 3 by 3 conv.)
Yes, I also quoted that part from the article. This does not address that the attention Matrix does not represent all learned parameters. Even supposing that the form of the attention matrix guarantees the correct functioning of the algorithm why was that not used as the metric to decide convergence?
"We detected that the model had converged by looking for 1024 training batches with perfect predictions, and that it could perfectly run 100 Life games for 100 steps." This would be superfluous (and even a pretty bizarre methodology) if the shape of the attention matrix was proof that the Network performed the actual game of life algorithm.
Just to be clear, I am not saying that the NN isn't converging to performing some computation that would also be seen in other algorithms. I am saying that the paper does not investigate whether the resulting NN actually performs the game of life algorithm. The convolution part is certainly evidence, but I think it would have been worthwhile to look at the actual resulting Net and figure out if the trained weights together actually formed an algorithm. This is also the only way to determine the truth of the initial claim, that this isn't just a statistical model, but rather an actual algorithm.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#24Earlier quoted context omitted.
The diagonal-looking attention matrix shown in the post is mathematically equivalent to 3 by 3 convolution . The model learns how to do that via its attention mechanism - it's not obvious that it would be able to do that via attention. (This can be shown by comparing that attention matrix to a "manually computed Neighbour Attention matrix", which is known to be equivalent to 3 by 3 conv.)
Yes, I also quoted that part from the article. This does not address that the attention Matrix does not represent all learned parameters. Even supposing that the form of the attention matrix guarantees the correct functioning of the algorithm why was that not used as the metric to decide convergence? "We detected that the model had converged by looking for 1024 training batches with perfect predictions, and that it c…
> the paper does not investigate whether the resulting NN actually performs the game of life algorithm
How could it not be computing the game of life algorithm? Given that it gets 100% accuracy over multiple steps on a bunch random game boards it's never seen before.
And then based on the structure of the net, and by examining the attention layers and finding that it's doing 3 by 3 average pooling, we can see that the attention layer produces a set of tokens, where each token contains the information of the number of neighbours it had, and its previous state. This then goes through a classifier layer, which decides it's next state, given that information.
Further evidence for that: it was possible to use linear probes to confirm that the tokens that had been through the attention layer contained the information about the number of neighbours and the previous state.
From all of this, it's clear that the model is running the Game of Life properly.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#25Earlier quoted context omitted.
Yes, I also quoted that part from the article. This does not address that the attention Matrix does not represent all learned parameters. Even supposing that the form of the attention matrix guarantees the correct functioning of the algorithm why was that not used as the metric to decide convergence? "We detected that the model had converged by looking for 1024 training batches with perfect predictions, and that it c…
> the paper does not investigate whether the resulting NN actually performs the game of life algorithm How could it not be computing the game of life algorithm? Given that it gets 100% accuracy over multiple steps on a bunch random game boards it's never seen before. And then based on the structure of the net, and by examining the attention layers and finding that it's doing 3 by 3 average pooling, we can see that th…
Do you not understand the difference between empirical evidence and mathematical proof? Surely every person talking about NN research should be aware of that distinction.
> How could it not be computing the game of life algorithm? Given that it gets 100% accuracy over multiple steps on a bunch random game boards it's never seen before.
This is such an insane statement.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#26I don't get the point. A simple CNN with stride =1 should be able to solve it perfectly and generalize it to any size.
It wasn't obvious that a transformer could do this, and learn to produce conv via attention
But it is, as long as the positional embedding are sufficient, i.e. use relative positional embeddings here.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#27I would like to point out a much more exciting modelling process, whereby neural networks extract the underlying boolean logic from simulation outputs: https://google-research.github.io/self-organising-systems/di... I firmly believe that differentiable logic CA is the winner, in particular because it extracts the logic directly, and thus leads to generalize-able programs as opposed to staying stuck in matrix multipli…
This is one of those papers that are so good I would like to keep it secret.
I shared it with a friend and he thought its wasn't that useful.
That made me happy since I knew my secret maybe safe.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#28To be honest an unsurprising result. But I think the paper fails to answer the most important question. It alleges that this isn't a statistical model: "it is not a statistical model that predicts the most likely next state based on all the examples it has been trained on. We observe that it learns to use its attention mechanism to compute 3x3 convolutions — 3x3 convolutions are a common way to implement the Game of…
The diagonal-looking attention matrix shown in the post is mathematically equivalent to 3 by 3 convolution . The model learns how to do that via its attention mechanism - it's not obvious that it would be able to do that via attention. (This can be shown by comparing that attention matrix to a "manually computed Neighbour Attention matrix", which is known to be equivalent to 3 by 3 conv.)
It would be more convincing if they did an exhaustive enumeration and verified that for every possible 3x3 Life the learned NN was correct. How do I know looking at a speckled screenshot that it is exactly correct and there's not a little floating point error somewhere or something like that which results in 1 edge-case being slightly off? If the only testing is '100 Life games for 100 steps', that isn't water-tight. (While if you do exhaustive enumeration, well, it has to be correct, because the NN is deterministic and fixed and there's no way for it to go wrong then.)
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#29I was hoping for an explanation of, or some insight from, the loss curve. Training makes very little progress for a long time, then suddenly converges. In my (brief) experience with NN training, I typically see more rapid progress at the beginning, then a plateau of diminishing returns, not an S-curve like this.
Re: Transformer neural net learns to run Conway's Game of Life just from examples
#30I would like to point out a much more exciting modelling process, whereby neural networks extract the underlying boolean logic from simulation outputs: https://google-research.github.io/self-organising-systems/di... I firmly believe that differentiable logic CA is the winner, in particular because it extracts the logic directly, and thus leads to generalize-able programs as opposed to staying stuck in matrix multipli…
This is one of those papers that are so good I would like to keep it secret. I shared it with a friend and he thought its wasn't that useful. That made me happy since I knew my secret maybe safe.
I think it's interesting, but I don't see how it's useful. Can you describe what you think is useful about it?