Equation 9 · Part 1 · What Interpretability Actually Costs to Do at Scale
Symbol k
What this part means
the because published topk configurations keep.
Its job in the formula
k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol k→Article meaning
Where the article explains it
Because published TopK configurations keep k in the tens to low hundreds while n runs into the millions, n k and the encoding term dominates almost entirely: 2dnT .
The passage around this formula
Work out what that architecture actually spends compute on per token, because the two halves of it behave differently. The encoding step needs a score for every one of the n candidate latents before it can select the top k , so it is an unavoidably dense matrix multiply: roughly 2dn floating-point operations. The decoding step only touches the k latents that survived, so it is sparse: roughly 2dk operations. Summed and multiplied across T training tokens, a first-order compute model for training the dictionary is
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Sources cited in the article section
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