← All parts of this equation

Equation 10 · Part 7 · Building a Multimodal AI Application That Actually Uses Its Inputs

multiplication

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

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

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.

Read this part in the article →

Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

Open the illustrated multiplication: combining factors guide →

Sources cited in the article section

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