← Back to article

Equation 4 · Where Multimodal Frontier Models Actually Differ, Beyond the Marketing

What does this equation mean?

τaudio≈32\tau_{\text{audio}} \approx 32

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 gives an approximation: it relates the quantities while allowing an approximation. 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

τaudio\tau_{\text{audio}}

Symbol tau_audio

tauau_audio is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

≈

≈

Approximately equal to; the equality is not exact.

Understand this part →

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.

Understand this part →

How to interpret it

Its accuracy depends on the assumptions and range of use described in the article.

What the article says around this equation

where, at default resolution, the sampling rate f is one frame per second, each frame costs τframe\tau_{\text{frame}} ≈\approx 258 tokens, and the audio track costs τaudio\tau_{\text{audio}} ≈\approx 32 tokens per second — giving cvideoc_{\text{video}} ≈\approx 290 tokens per second, close to the approximately 300 tokens per second Google documents directly for default-resolution video [ 5 ] . The formula is unremarkable arithmetic, but what it exposes is the real assumption underneath the “native” claim: a single request is billed, and therefore presumably processed, as one combined audio-visual stream, not as a picture track with a separately bolted-on transcript.

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to Where Multimodal Frontier Models Actually Differ, Beyond the Marketing

See this formula across 1 published context →

Browse the mathematical compendium →