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Equation 12 · Part 1 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity

Symbol N_a

Na=NN_a = N
NaN_a

What this part means

NaN_a is part of the quantity the equation computes from the expression on the right.

Its job in the formula

NaN_a is part of the quantity the equation computes from the expression on the right.

The passage around this formula

Mixture-of-experts breaks the identity NaN_a = N . Shazeer and colleagues introduced the sparsely-gated MoE layer, in which a learned gate selects a small subset of expert sub-networks per example, allowing parameter counts far beyond what could be densely activated at the same compute [ 4 ] . Fedus, Zoph, and Shazeer simplified it decisively: the Switch layer routes each token to exactly one expert rather than the top- k , which reduced routing computation and communication cost while preserving quality, and they scaled the approach to trillion-parameter models [ 5 ] .

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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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Sources cited in the surrounding passage

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