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necroforest

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yeah, and as far as I'm aware there isn't even a definition of "civilization" or "intelligence" that doesn't boil down to "sufficiently like me".

LLMs are trained in parallel. The model weights and optimizer state are split over a number (possibly thousands) of accelerators.

The main bottleneck to doing distributed training like this is the communication between nodes.

I used Bayesian analysis for an industry problem where we had a lot of data (~1M samples), but the relationship between the observed data and the latent variables of interest was complicated and non-identifiable. In the non-identifiable setting, point estimates don't converge in the large data limit and quantifying uncetainty becomes critical.

kind of. you can decompose an arbitrary matrix into symmetric and antisymmetric components: R = S + A. Since A = -A^H (anti-symmetric), for any vector x, <x, Ax> = -<x, Ax> => <x, Ax> = 0. So for any matrix where <x, Rx> > 0, you can add an arbitrary anti-symmetric matrix and keep the same induced quadratic form. So people typically enforce symmetry in their definitions because it is the only part that contributes to the quadratic form and is "nicer" to work with (always diagonalizable, positive eigenvalues, etc.)

This should generalize easily to the complex/Hermitian case.

To answer (2): You are token i. In order to see how much of a token j's value v_j you update yourself with, you compare your query q_i with token j's key k_j. This gives you the asymmetry between queries and keys.

This is even more apparent in a cross-attention setting, where one stream of tokens will have only queries associated with it and the other will have only keys/values.