We look in the final layer of the residual stream and find a linear 2D subspace where activations have a structure remarkably similar to that of our predicted fractal. We do this by performing standard linear regression from the residual stream activations (64 dimensional vectors) to the belief distributions (3 dimensional vectors) which associated with them in the MSP.
Naive technical question, but can I ask for a more detailed description of how you go from the activations in the residual stream to the map you have here? Or like, can someone point me in the direction of the resources I'd need to undestand? I know that the activations in any given layer of an NN can be interpreted as a vector in a space the same number of dimensions as there are neurons in that layer, but I don't know how you map that onto a 2D space, esp. in a way that maps belief states onto this kind of three-pole system you've got with the triangles here.
Naive technical question, but can I ask for a more detailed description of how you go from the activations in the residual stream to the map you have here? Or like, can someone point me in the direction of the resources I'd need to undestand? I know that the activations in any given layer of an NN can be interpreted as a vector in a space the same number of dimensions as there are neurons in that layer, but I don't know how you map that onto a 2D space, esp. in a way that maps belief states onto this kind of three-pole system you've got with the triangles here.