3 ms·

When human labor is not cost effective

• famouswaffles 3y ago
  https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mechanistic-interpretability-analysis-of-grokking https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mec... It's right there in the paper/article "The algorithm learned to do modular addition can be fully reverse engineered. The algorithm is roughly: Map inputs x , y → cos ( w x ) , cos ( w y ) , sin ( w x ) , sin ( w y ) with a Discrete Fourier Transform, for some frequency w Multiply and rearrange to get cos ( w ( x + y ) ) = cos ( w x ) cos ( w y ) − sin ( w x ) sin ( w y ) and sin ( w ( x + y ) ) = cos ( w x ) sin ( w y ) + sin ( w x ) cos ( w y ) By choosing a frequency w = 2 π n k we get period dividing n, so this is a function of x + y ( mod n ) Map to the output logits z with cos ( w ( x + y ) ) cos ( w z ) + sin ( w ( x + y ) ) sin ( w z ) = cos ( w ( x + y − z ) ) - this has the highest logit at z ≡ x + y ( mod n ) , so softmax gives the right answer. To emphasise, this algorithm was purely learned by gradient descent! I did not predict or understand this algorithm in advance and did nothing to encourage the model to learn this way of doing modular addition. I only discovered it by reverse engineering the weights" Yes it learned the algorithm. You're wrong. It's okay to be wrong but insisting you're right after clear evidence of the former is very strange. I'm not being arrogant. You're being obtuse.
  • famouswaffles 3y ago
    ah shit sorry. Only just saw i replied to the wrong comment and can't delete anymore.