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Equation 10 · Part 5 · Building a Multimodal AI Application That Actually Uses Its Inputs

=

T(w,h)=⌈wP⌉×⌈hP⌉,T(w, h) = \left\lceil \frac{w}{P} \right\rceil \times \left\lceil \frac{h}{P} \right\rceil,
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Image and video inputs are priced by tokenization rules that are public, mechanical, and different enough across vendors that a workload’s cost cannot be estimated from a single provider’s numbers and assumed to generalise. The general form, common to every tiling or patch-based image tokenizer, is T(w,h)=⌈wP⌉×⌈hP⌉T(w, h) = \left\lceil \frac{w}{P} \right\rceil \times \left\lceil \frac{h}{P} \right\rceil. where w and h are the image’s pixel dimensions after any provider-side resize and P is that provider’s patch edge length in pixels. The formula is the same shape everywhere; the constant P , the resize rule applied before it, and the price per resulting token are what an integrator actually has to look up and budget against.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.