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Equation 26 · Part 6 · What Interpretability Actually Costs to Do at Scale

subscript

CSAE≈2dnTC_{\mathrm{SAE}} \approx 2dnT
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.

The passage around this formula

The compute ledger has a plausible, if unproven, path downward. CSAEC_{\mathrm{SAE}} ≈\approx 2dnT is a cost that infrastructure and algorithmic improvements — sparser encoders, better initialization that reaches convergence at lower n , transcoders that replace rather than merely observe a component — can attack directly, the same way serving-side engineering rather than raw parameter growth has driven most within-generation price reduction for inference elsewhere in this field. TopK autoencoders were themselves exactly this kind of improvement over the softer, less efficient sparsity penalties they replaced [ 1 ] . There is no comparable engineering lever visible yet for the labor ledger.…

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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.

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Sources cited in the surrounding passage

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