← Back to article

Equation 5 · A History of Llama and the Open-Weight AI Movement

What does this equation mean?

EE

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

EE

Symbol E

E is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

where PsharedP_{\mathrm{shared}} is the always-active shared-expert capacity, PexpertP_{\mathrm{expert}} is the parameter count of one routed expert, and k is the number of routed experts activated per token. Total capacity scales with the number of experts E available to the router, roughly PtotalP_{\mathrm{total}} ≈\approx PsharedP_{\mathrm{shared}} + E ⋅\cdot PexpertP_{\mathrm{expert}} , while inference compute scales with PactiveP_{\mathrm{active}} , not PtotalP_{\mathrm{total}} . This is the exact mechanism behind Meta’s headline figures: Maverick’s 400 billion total parameters and 17 billion active parameters are not two different measurements of the same quantity, they are PtotalP_{\mathrm{total}} and PactiveP_{\mathrm{active}} under a router…
Read the full surrounding passage
where PsharedP_{\mathrm{shared}} is the always-active shared-expert capacity, PexpertP_{\mathrm{expert}} is the parameter count of one routed expert, and k is the number of routed experts activated per token. Total capacity scales with the number of experts E available to the router, roughly PtotalP_{\mathrm{total}} ≈\approx PsharedP_{\mathrm{shared}} + E ⋅\cdot PexpertP_{\mathrm{expert}} , while inference compute scales with PactiveP_{\mathrm{active}} , not PtotalP_{\mathrm{total}} . This is the exact mechanism behind Meta’s headline figures: Maverick’s 400 billion total parameters and 17 billion active parameters are not two different measurements of the same quantity, they are PtotalP_{\mathrm{total}} and PactiveP_{\mathrm{active}} under a router with 128 available experts and a small k , and the entire commercial argument for the architecture — a much larger knowledge store served at close to small-model inference cost — depends on that gap holding up under real traffic rather than only in the launch announcement.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to A History of Llama and the Open-Weight AI Movement

Browse the mathematical compendium →