meaning of the values for hyperprior

[AlbertoPresta]

Hi,
sorry if I bother you again, but I have a question related to these variables (I am talking about the hyperprior model);

SCALES_MIN = 0.11
SCALES_MAX = 256
SCALES_LEVELS = 64

How do you use these variable in the update() function?

Alberto

[YodaEmbedding]

"Scale" refers to the "width" or "standard deviation" of the normal probability distribution.

CompressAI/compressai/models/google.py

Lines 196 to 203 in 216af74

	# From Balle's tensorflow compression examples
	SCALES_MIN = 0.11
	SCALES_MAX = 256
	SCALES_LEVELS = 64
	def get_scale_table(min=SCALES_MIN, max=SCALES_MAX, levels=SCALES_LEVELS):
	return torch.exp(torch.linspace(math.log(min), math.log(max), levels))

get_scale_table() is used to create 64 standard deviations ranging from σ = 0.11 to σ = 256. The standard deviations are listed as follows:

[0.11, 0.12, 0.14, 0.16, 0.18, 0.20, 0.23, 0.26, 0.29, 0.33, 0.38, 0.43, 0.48, 0.54, 0.62, 0.70, 0.79, 0.89, 1.01, 1.14, 1.29, 1.46, 1.65, 1.86, 2.11, 2.38, 2.70, 3.05, 3.45, 3.90, 4.41, 4.99, 5.64, 6.38, 7.22, 8.16, 9.23, 10.44, 11.81, 13.35, 15.10, 17.08, 19.32, 21.85, 24.71, 27.94, 31.60, 35.74, 40.42, 45.71, 51.70, 58.47, 66.13, 74.79, 84.58, 95.65, 108.18, 122.35, 138.37, 156.48, 176.98, 200.15, 226.36, 256.00]

The following then uses each standard deviation to define a Gaussian distribution (i.e. _standardized_cumulative):

CompressAI/compressai/entropy_models/entropy_models.py

Lines 625 to 640 in 216af74

	def update(self):
	multiplier = -self._standardized_quantile(self.tail_mass / 2)
	pmf_center = torch.ceil(self.scale_table * multiplier).int()
	pmf_length = 2 * pmf_center + 1
	max_length = torch.max(pmf_length).item()
	device = pmf_center.device
	samples = torch.abs(
	torch.arange(max_length, device=device).int() - pmf_center[:, None]
	)
	samples_scale = self.scale_table.unsqueeze(1)
	samples = samples.float()
	samples_scale = samples_scale.float()
	upper = self._standardized_cumulative((0.5 - samples) / samples_scale)
	lower = self._standardized_cumulative((-0.5 - samples) / samples_scale)
	pmf = upper - lower

[AlbertoPresta]

ok thanks! maybe is a stupid question, but in the end the quantized_cdf is referred to what? to the guassian latent space? I do not get the reasons why yiu computed the cdf on the domain extracted from the scales. In the end should we have a standard deviation for each dimension of the latent space?

[AlbertoPresta]

And how it is used then the quantized_cdf in the compress method? it should represent the distribution of the latent space, but I do not get the meaning of the variables indexes also.

[YodaEmbedding]

• For all EntropyModels: The symbols are the actual tensor values that we want to encode. The indexes represent the CDFs used to encode various symbols.
• For EntropyBottleneck: _quantized_cdf is a table of non-parametric distributions that depend on the matrixes and biases. The CDFs generated by update() thus change after a training epoch. In the CompressAI implementation, the indexes are [0, 0, ..., 1, 1, ..., 2, 2, ..., 191, 191] since an entire channel is encoded using only a single corresponding CDF.
• For GaussianConditional: _quantized_cdf is a table of various pregenerated Gaussian CDFs whose standard deviations range over [0.11, 256.00]. The indexes allow us to choose which Gaussian CDF we are talking about. Thus, there is a one-to-one mapping between indexes and standard deviations. In fact, we compute the indexes directly using the model-predicted scales when we call the build_indexes function.