← All parts of this equation

Equation 11 · Part 4 · What Alignment Actually Costs

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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…

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.