Jacobian matrix
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Most misleading part clarified: The “J-space” is not a separate, hidden space. It is an alternative *coordinate system* for intermediate layer activations. Using a Jacobian between the last layer right before unembedding and the intermediate layer, you can “move” rows of the unembedding matrix (corresponding to distinct tokens) into the space that the intermediate activations live in. So each unembedding row/vector has a corresponding vector in the intermediate activation space this way. They us
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Most misleading part clarified: The “J-space” is not a separate, hidden space. It is an alternative *coordinate system* for intermediate layer activations. Using a Jacobian between the last layer right before unembedding and the intermediate layer, you can “move” rows of the unembedding matrix (corresponding to distinct tokens) into the space that the intermediate activations live in. So each unembedding row/vector has a corresponding vector in the intermediate activation space this way. They us
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