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Equation 1 · Part 4 · Comparing the Main Approaches to AI Inference Economics

Symbol N_active

CdenseCMoE≈NdenseNactive\frac{C_{\mathrm{dense}}}{C_{\mathrm{MoE}}} \approx \frac{N_{\mathrm{dense}}}{N_{\mathrm{active}}}
NactiveN_{\mathrm{active}}

What this part means

NaN_active occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

NaN_active occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

…actually touched [ 13 , 11 ] , the ratio of dense to MoE compute at equal activated size is approximately CdenseCMoE≈NdenseNactive\frac{C_{\mathrm{dense}}}{C_{\mathrm{MoE}}} \approx \frac{N_{\mathrm{dense}}}{N_{\mathrm{active}}}. for a dense model with NdenseN_{\mathrm{dense}} parameters compared against an MoE model activating NactiveN_{\mathrm{active}} of its NtotalN_{\mathrm{total}} parameters per token. What this ratio hides is exactly what a compute-only comparison always hides: memory. Serving an MoE model requires holding all NtotalN_{\mathrm{total}} parameters resident — on one device or, more often, sharded across several with…

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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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