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R=fsh⋅nq⋅log⁡2K bits per second.R = \frac{f_s}{h} \cdot n_q \cdot \log_2 K \text{ bits per second.}

Why this formula appears here

The mechanism that does this at scale is a learned neural codec built around residual vector quantization: an encoder compresses the waveform into a sequence of continuous frames, and each frame is then quantized in successive stages, each stage encoding what the previous stage’s codebook missed. SoundStream is the reference architecture, described by its authors as an end-to-end neural audio codec built on a convolutional encoder-decoder pair with a residual vector quantizer, trained jointly and shown to outperform prior codecs at comparable bitrates [ 7 ] . The mechanism gives a concrete, computable token rate. For a signal sampled at fsf_s hertz, encoded with hop length h samples per frame,…

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

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R=fsh⋅nq⋅log⁡2K bits per second.R = \frac{f_s}{h} \cdot n_q \cdot \log_2 K \text{ bits per second.}

Equation 12 · Foundation Models

How Multimodal Models Actually Handle Video, Audio, and Space

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The mechanism that does this at scale is a learned neural codec built around residual vector quantization: an encoder compresses the waveform into a sequence of continuous frames, and each frame is then quantized in successive stages, each stage encoding what the previous stage’s codebook missed. SoundStream is the reference architecture, described by its authors as an end-to-end neural audio codec built on a convolutional encoder-decoder pair with a residual vector quantizer, trained jointly and shown to outperform prior codecs at comparable bitrates [ 7 ] . The mechanism gives a concrete, computable token rate. For a signal sampled at fsf_s hertz, encoded with hop length h samples per frame,…

Meanings in this article

  • RR: the bitrate.
  • hh: the number of samples.
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