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Equation 12 · Part 8 · How Multimodal Models Actually Handle Video, Audio, and Space

multiplication

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

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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Learn the underlying idea

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

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Sources cited in the surrounding passage

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