Equation 3 · The Real Economics of Shipping a Model to a Device
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.
the one-time training cost. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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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 this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Here is the one-time training cost, Q is the number of queries served over the deployment’s life, and and are the marginal cost per query of serving each model, wherever that serving happens. The break-even query volume is
Sources cited in the article section
- [1] Alpaca: A Strong, Replicable Instruction-Following Model ↗
- [2] Sky-T1: Train your own O1 preview model within $450 ↗
- [5] DeepSeek-V3 Technical Report ↗
- [11] OpenAI's Sam Altman says giant A.I. models are over—but going small won't appease regulators ↗
- [3] Trends in the Dollar Training Cost of Machine Learning Systems ↗
These citations give research context. Read each source to check which claims it supports.
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