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Equation 7 · How Multimodal Models Actually Handle Video, Audio, and Space

What does this equation mean?

Ntok=HP⋅WP⋅TPt.N_{\mathrm{tok}} = \frac{H}{P} \cdot \frac{W}{P} \cdot \frac{T}{P_t}.

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.

Start withH
Divide byP
This relates toN_tok
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

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.

Read it piece by piece

NtokN_{\mathrm{tok}}

Symbol N_tok

NtN_tok is part of the quantity the equation computes from the expression on the right.

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HH

Symbol H

H occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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PP

Symbol P

the cut into square patches of size.

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WW

Symbol W

the image of height h and width.

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TT

Symbol T

T occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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PtP_t

Symbol P_t

PtP_t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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=

=

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

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fraction

fraction

Divide the expression above the line by the one below it.

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multiplication

multiplication

Multiply the quantities on either side.

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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.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

tokens. Video adds a third factor. If a model attends over T sampled frames, each cut into the same spatial grid, and groups PtP_t consecutive frames per temporal patch, the token count becomes Ntok=HP⋅WP⋅TPtN_{\mathrm{tok}} = \frac{H}{P} \cdot \frac{W}{P} \cdot \frac{T}{P_t}. Every added frame multiplies the spatial cost rather than adding to it. A minute of video at even a modest frame rate is not “a bigger picture” in the way a higher-resolution photograph is; it is a volume, and attention cost over a transformer sequence grows faster than the sequence itself. No system deployed today attends densely over every raw frame of a long clip, because nothing could afford to.

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Sources cited in the article section

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