← Back to article

Equation 14 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity

What does this equation mean?

NaN_a

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

NaN_a

Symbol N_a

NaN_a 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 →

subscript

subscript

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.

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

The economics are attractive and frequently overstated. Training compute scales with NaN_a , not N , so a sparse model can hold far more knowledge for the same training FLOPs. Patterson and colleagues, computing energy and carbon for several large models including Switch Transformer and GPT-3, found that large but sparsely activated networks can consume less than one tenth the energy of large dense networks without sacrificing accuracy [ 10 ] .

Read the equation in its article →

Sources cited in the surrounding passage

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

Return to Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity

Browse the mathematical compendium →