rlanday

https://en.wikipedia.org/wiki/Parkinson's_Law > The growth was presented mathematically with the formula x = (2k^m + P)/n, in which k was the number of officials wanting subordinates, m was the hours they spent writing minutes to each other.

(check the original paper for details since this obviously doesn’t explain what n is)

https://transformer-circuits.pub/2021/framework/index.html

> We performed PCA analysis of token embeddings and unembeddings. For models with large d_model, the spectrum quickly decayed, with the embeddings/unembeddings being concentrated in a relatively small fraction of the overall dimensions. To get a sense for whether they occupied the same or different subspaces, we concatenated the normalized embedding and unembedding matrices and applied PCA. This joint PCA process showed a combination of both "mixed" dimensions and dimensions used only by one; the existence of dimensions which are used by only one might be seen as a kind of upper bound on the extent to which they use the same subspace.

So some of the embedding dimensions are used to encode the input tokens and some are used to pick the output tokens (some are used for both), and everything else is only used in intermediate computations. This suggests that you might be able to improve on the standard transformer architecture by increasing (or increasing and then decreasing) the dimension, rather than using the same embedding dimensionality at each layer.

I think his description is basically correct given how the residual streams work. The output of each sublayer is basically added onto the input. See https://transformer-circuits.pub/2021/framework/index.html

> Lastly, his statement that the embedding vector of the final token output needs all the info for the next token is plainly incorrect. The final decoder layer, when predicting the next token, uses all the information from the previous layer's hidden layer, which is the size of the hidden units times the number of tokens so far.

I think the author is correct. Information is only moved between tokens in the attention layers, not in the MLP layers or in the final linear layer before the softmax. You can see how it’s implemented in nanoGPT: https://github.com/karpathy/nanoGPT/blob/f08abb45bd2285627d1...

At training time, probabilities for the next token are computed for each position, so if we feed in a sequence of n tokens, we basically get n training examples, one for each position, but at inference time, we only compute the next token since we’ve already output the preceding ones.