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Equation 11 · Part 6 · What Alignment Actually Costs

subscript

ρ  =  CRLCpre\rho \;=\; \frac{C_{\mathrm{RL}}}{C_{\mathrm{pre}}}
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

That fraction has moved substantially since 2022. DeepSeek’s R1 model provides the clearest recent public case, because both its pretraining and its reinforcement learning phase were disclosed in enough technical detail for an independent estimate to be built. Epoch AI’s own reconstruction puts DeepSeek-V3’s pretraining at about 5.3 million US dollars, based on 2,048 H800 GPUs run at roughly 2 US dollars per GPU-hour over the reported training schedule, and the initial R1-Zero reinforcement learning phase at about 1 million US dollars, assuming similar hardware utilisation to the pretraining run [ 11 ] . That is roughly seventeen to twenty percent of the pretraining figure — an order of…

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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.

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.