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Equation 1 · Part 8 · A History of Llama and the Open-Weight AI Movement

subscript

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

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

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 article section

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