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Equation 1 · Part 7 · A History of Llama and the Open-Weight AI Movement

addition

Pactive≈Pshared+k⋅Pexpert,P_{\mathrm{active}} \approx P_{\mathrm{shared}} + k \cdot P_{\mathrm{expert}},
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

For a mixture-of-experts layer routing each token to one shared expert plus a fixed number of routed experts, the active parameter count per token is approximately Pactive≈Pshared+k⋅PexpertP_{\mathrm{active}} \approx P_{\mathrm{shared}} + k \cdot P_{\mathrm{expert}}. 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…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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