Equation 17 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity
What does this equation mean?
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 equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol N_a
is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
What sparse routing breaks: = N . Best when training compute is the binding constraint and memory is not.
Sources cited in the article section
- [4] Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer ↗
- [5] Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity ↗
- [10] Carbon Emissions and Large Neural Network Training ↗
- [9] AI and Memory Wall ↗
These citations give research context. Read each source to check which claims it supports.
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