Reverse engineering a neural network's clever solution to binary addition (2023)
1–10 of 19 posts
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#2>As I mentioned, before, I had imagined the network learning some fancy combination of logic gates to perform the whole addition process digitally, similarly to how a binary adder operates. This trick is yet another example of neural networks finding unexpected ways to solve problems.
My intuition is that this solution allows for some form of gradient approach to a solution, which is why it's unintuitive. We think about solutions as all or nothing and look for complete solutions.
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#3Original submission: https://news.ycombinator.com/item?id=34399142
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#4This seems interesting, but I got stuck fairly early on when I read "all 32,385 possible input combinations". There are two 8 bit numbers, 16 totally independent bits. That's 65_536 combinations. 32_285 is close to half that, but not quite. Looking at it in binary it's 01111110_10000001, i.e. two 8 bit words that are the inverse of each other. How was this number arrived at, and why?
Looking later there's also a strange DAC that gives the lowest resistance to the least significant bit, thus making it the biggest contributor to the output. Very confusing.
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#5This seems interesting, but I got stuck fairly early on when I read "all 32,385 possible input combinations". There are two 8 bit numbers, 16 totally independent bits. That's 65_536 combinations. 32_285 is close to half that, but not quite. Looking at it in binary it's 01111110_10000001, i.e. two 8 bit words that are the inverse of each other. How was this number arrived at, and why? Looking later there's also a stra…
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Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#6This seems interesting, but I got stuck fairly early on when I read "all 32,385 possible input combinations". There are two 8 bit numbers, 16 totally independent bits. That's 65_536 combinations. 32_285 is close to half that, but not quite. Looking at it in binary it's 01111110_10000001, i.e. two 8 bit words that are the inverse of each other. How was this number arrived at, and why? Looking later there's also a stra…
Is that the number of adds that don’t overflow an 8-bit result?
On that hunch, I just checked and I get 32896.
Edit: if I exclude either input being zero, I get 32385.
You also get the same number when including input zeros but excluding results above 253. But I’d bet on the author’s reason being filtering of input zeros. Maybe the NN does something bad with zeros, maybe can’t learn them for some reason.
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#7This seems interesting, but I got stuck fairly early on when I read "all 32,385 possible input combinations". There are two 8 bit numbers, 16 totally independent bits. That's 65_536 combinations. 32_285 is close to half that, but not quite. Looking at it in binary it's 01111110_10000001, i.e. two 8 bit words that are the inverse of each other. How was this number arrived at, and why? Looking later there's also a stra…
Interesting puzzle. 32385 is 255 pick 2. My guess would be, to hopefully make interpretation easier, they always had the larger number on one side. So (1,2) but not (2,1). And also 0 wasn’t included. So perhaps their generation loop looks like [[(i,j) for j (i-1 -> 1) for i (256 -> 1)]
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#8>As I mentioned, before, I had imagined the network learning some fancy combination of logic gates to perform the whole addition process digitally, similarly to how a binary adder operates. This trick is yet another example of neural networks finding unexpected ways to solve problems. My intuition is that this solution allows for some form of gradient approach to a solution, which is why it's unintuitive. We think ab…
The more interesting question is is it even possible to learn the logic gates solution through gradient descent?
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#9This seems interesting, but I got stuck fairly early on when I read "all 32,385 possible input combinations". There are two 8 bit numbers, 16 totally independent bits. That's 65_536 combinations. 32_285 is close to half that, but not quite. Looking at it in binary it's 01111110_10000001, i.e. two 8 bit words that are the inverse of each other. How was this number arrived at, and why? Looking later there's also a stra…
You are potentially conflating combinations with permutations.
Re: Reverse engineering a neural network's clever solution to binary addition (2023)
#10> While playing around with this setup, I tried re-training the network with the activation function for the first layer replaced with sin(x) and it ends up working pretty much the same way.
There is some evidence that the activation functions and weights can be arbitrarily selected assuming you have a way to evolve the topology of the network.