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Equation 7 · What Interpretability Actually Costs to Do at Scale

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kk

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the because published topk configurations keep. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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kk

Symbol k

the because published topk configurations keep.

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and the specific variant OpenAI’s interpretability team used to push this to frontier scale, the TopK autoencoder, replaces the soft ℓ1\ell_1 penalty with an explicit constraint: exactly k latents fire, chosen by magnitude, and the rest are hard-zeroed. Gao and colleagues introduced this variant, established scaling laws relating autoencoder size and sparsity to reconstruction error, and — this is the operative fact for a cost accounting — trained a sixteen-million-latent autoencoder on GPT-4’s activations over forty billion tokens [ 1 ] .

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