Equation 6 · Part 1 · What Interpretability Actually Costs to Do at Scale
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→Article meaning
The passage around this formula
and the specific variant OpenAI’s interpretability team used to push this to frontier scale, the TopK autoencoder, replaces the soft 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 ] .
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.