I suspect you use the word “opaque” in a different way than Eliezer Yudkowsky here. At least I fail to see from your summary, how this would contradict my interpretation of Eliezer’s statement (and your title and introduction seems to imply that it is a contradiction).
Consider the hypothetical example, where GPT-3 states (incorrectly) that Geneva is the capital of Switzerland. Can we look at the weights of GPT-3 and see if it was just playing dumb or if it genuinely thinks that Geneva is the capital of Switzerland? If the weights/”matrices”/”giant wall of floating point numbers” are opaque (in the sense of Eliezer according to my guess), then we would look at it and shrug our shoulders. I fail to see from your summary, how the effective theories would help in this example. (Disclaimer: In this specific example or similar examples, I would not be surprised if it was actually possible to figure out if it was playing dumb or what caused GPT-3 to play dumb. Also I do not expect GPT-3 to actually believe that Geneva is the capital of Switzerland).
My guess of your meaning of “opaque” would be something like “we have no idea why deep learning works at all” or “we have no mathematical theory for the training of neural nets”, which your summary disproves.
Solution:
Then one can check that the produced file is identical:
edit: How I found the solution: I found some of the other comments helpful, especially from gjm (although I did not read all). In particular, interpreting the data as a sequence of 64-bit floating point numbers saved me a lot of time. Also gjm’s mention of the pattern a, -a, b, c, -c, d was an inspiration. If you look at the first couple of numbers, you can see that they are sometimes half of an earlier number. Playing around further with the numbers I eventually found the patterns
a[i] * a[i+1] + 1.0
anda[i] - a[i+1]
. It remained to figure out when thea[i]/2
rule applies and when thea[i] * a[i+1] + 1.0
rule applies. Here it was a hint that the numbers do not grow too large in size. After trying out several rules that form bounds ona[i]
anda[i+1]
, I eventually found the right one.