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193 changes: 193 additions & 0 deletions
193
models/synthesizer/models/sublayer/common/transforms.py
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Original file line number | Diff line number | Diff line change |
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import torch | ||
from torch.nn import functional as F | ||
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import numpy as np | ||
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DEFAULT_MIN_BIN_WIDTH = 1e-3 | ||
DEFAULT_MIN_BIN_HEIGHT = 1e-3 | ||
DEFAULT_MIN_DERIVATIVE = 1e-3 | ||
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def piecewise_rational_quadratic_transform(inputs, | ||
unnormalized_widths, | ||
unnormalized_heights, | ||
unnormalized_derivatives, | ||
inverse=False, | ||
tails=None, | ||
tail_bound=1., | ||
min_bin_width=DEFAULT_MIN_BIN_WIDTH, | ||
min_bin_height=DEFAULT_MIN_BIN_HEIGHT, | ||
min_derivative=DEFAULT_MIN_DERIVATIVE): | ||
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if tails is None: | ||
spline_fn = rational_quadratic_spline | ||
spline_kwargs = {} | ||
else: | ||
spline_fn = unconstrained_rational_quadratic_spline | ||
spline_kwargs = { | ||
'tails': tails, | ||
'tail_bound': tail_bound | ||
} | ||
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outputs, logabsdet = spline_fn( | ||
inputs=inputs, | ||
unnormalized_widths=unnormalized_widths, | ||
unnormalized_heights=unnormalized_heights, | ||
unnormalized_derivatives=unnormalized_derivatives, | ||
inverse=inverse, | ||
min_bin_width=min_bin_width, | ||
min_bin_height=min_bin_height, | ||
min_derivative=min_derivative, | ||
**spline_kwargs | ||
) | ||
return outputs, logabsdet | ||
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def searchsorted(bin_locations, inputs, eps=1e-6): | ||
bin_locations[..., -1] += eps | ||
return torch.sum( | ||
inputs[..., None] >= bin_locations, | ||
dim=-1 | ||
) - 1 | ||
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def unconstrained_rational_quadratic_spline(inputs, | ||
unnormalized_widths, | ||
unnormalized_heights, | ||
unnormalized_derivatives, | ||
inverse=False, | ||
tails='linear', | ||
tail_bound=1., | ||
min_bin_width=DEFAULT_MIN_BIN_WIDTH, | ||
min_bin_height=DEFAULT_MIN_BIN_HEIGHT, | ||
min_derivative=DEFAULT_MIN_DERIVATIVE): | ||
inside_interval_mask = (inputs >= -tail_bound) & (inputs <= tail_bound) | ||
outside_interval_mask = ~inside_interval_mask | ||
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outputs = torch.zeros_like(inputs) | ||
logabsdet = torch.zeros_like(inputs) | ||
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if tails == 'linear': | ||
unnormalized_derivatives = F.pad(unnormalized_derivatives, pad=(1, 1)) | ||
constant = np.log(np.exp(1 - min_derivative) - 1) | ||
unnormalized_derivatives[..., 0] = constant | ||
unnormalized_derivatives[..., -1] = constant | ||
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outputs[outside_interval_mask] = inputs[outside_interval_mask] | ||
logabsdet[outside_interval_mask] = 0 | ||
else: | ||
raise RuntimeError('{} tails are not implemented.'.format(tails)) | ||
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outputs[inside_interval_mask], logabsdet[inside_interval_mask] = rational_quadratic_spline( | ||
inputs=inputs[inside_interval_mask], | ||
unnormalized_widths=unnormalized_widths[inside_interval_mask, :], | ||
unnormalized_heights=unnormalized_heights[inside_interval_mask, :], | ||
unnormalized_derivatives=unnormalized_derivatives[inside_interval_mask, :], | ||
inverse=inverse, | ||
left=-tail_bound, right=tail_bound, bottom=-tail_bound, top=tail_bound, | ||
min_bin_width=min_bin_width, | ||
min_bin_height=min_bin_height, | ||
min_derivative=min_derivative | ||
) | ||
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return outputs, logabsdet | ||
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def rational_quadratic_spline(inputs, | ||
unnormalized_widths, | ||
unnormalized_heights, | ||
unnormalized_derivatives, | ||
inverse=False, | ||
left=0., right=1., bottom=0., top=1., | ||
min_bin_width=DEFAULT_MIN_BIN_WIDTH, | ||
min_bin_height=DEFAULT_MIN_BIN_HEIGHT, | ||
min_derivative=DEFAULT_MIN_DERIVATIVE): | ||
if torch.min(inputs) < left or torch.max(inputs) > right: | ||
raise ValueError('Input to a transform is not within its domain') | ||
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num_bins = unnormalized_widths.shape[-1] | ||
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if min_bin_width * num_bins > 1.0: | ||
raise ValueError('Minimal bin width too large for the number of bins') | ||
if min_bin_height * num_bins > 1.0: | ||
raise ValueError('Minimal bin height too large for the number of bins') | ||
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widths = F.softmax(unnormalized_widths, dim=-1) | ||
widths = min_bin_width + (1 - min_bin_width * num_bins) * widths | ||
cumwidths = torch.cumsum(widths, dim=-1) | ||
cumwidths = F.pad(cumwidths, pad=(1, 0), mode='constant', value=0.0) | ||
cumwidths = (right - left) * cumwidths + left | ||
cumwidths[..., 0] = left | ||
cumwidths[..., -1] = right | ||
widths = cumwidths[..., 1:] - cumwidths[..., :-1] | ||
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derivatives = min_derivative + F.softplus(unnormalized_derivatives) | ||
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heights = F.softmax(unnormalized_heights, dim=-1) | ||
heights = min_bin_height + (1 - min_bin_height * num_bins) * heights | ||
cumheights = torch.cumsum(heights, dim=-1) | ||
cumheights = F.pad(cumheights, pad=(1, 0), mode='constant', value=0.0) | ||
cumheights = (top - bottom) * cumheights + bottom | ||
cumheights[..., 0] = bottom | ||
cumheights[..., -1] = top | ||
heights = cumheights[..., 1:] - cumheights[..., :-1] | ||
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if inverse: | ||
bin_idx = searchsorted(cumheights, inputs)[..., None] | ||
else: | ||
bin_idx = searchsorted(cumwidths, inputs)[..., None] | ||
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input_cumwidths = cumwidths.gather(-1, bin_idx)[..., 0] | ||
input_bin_widths = widths.gather(-1, bin_idx)[..., 0] | ||
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input_cumheights = cumheights.gather(-1, bin_idx)[..., 0] | ||
delta = heights / widths | ||
input_delta = delta.gather(-1, bin_idx)[..., 0] | ||
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input_derivatives = derivatives.gather(-1, bin_idx)[..., 0] | ||
input_derivatives_plus_one = derivatives[..., 1:].gather(-1, bin_idx)[..., 0] | ||
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input_heights = heights.gather(-1, bin_idx)[..., 0] | ||
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if inverse: | ||
a = (((inputs - input_cumheights) * (input_derivatives | ||
+ input_derivatives_plus_one | ||
- 2 * input_delta) | ||
+ input_heights * (input_delta - input_derivatives))) | ||
b = (input_heights * input_derivatives | ||
- (inputs - input_cumheights) * (input_derivatives | ||
+ input_derivatives_plus_one | ||
- 2 * input_delta)) | ||
c = - input_delta * (inputs - input_cumheights) | ||
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discriminant = b.pow(2) - 4 * a * c | ||
assert (discriminant >= 0).all() | ||
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root = (2 * c) / (-b - torch.sqrt(discriminant)) | ||
outputs = root * input_bin_widths + input_cumwidths | ||
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theta_one_minus_theta = root * (1 - root) | ||
denominator = input_delta + ((input_derivatives + input_derivatives_plus_one - 2 * input_delta) | ||
* theta_one_minus_theta) | ||
derivative_numerator = input_delta.pow(2) * (input_derivatives_plus_one * root.pow(2) | ||
+ 2 * input_delta * theta_one_minus_theta | ||
+ input_derivatives * (1 - root).pow(2)) | ||
logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator) | ||
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return outputs, -logabsdet | ||
else: | ||
theta = (inputs - input_cumwidths) / input_bin_widths | ||
theta_one_minus_theta = theta * (1 - theta) | ||
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numerator = input_heights * (input_delta * theta.pow(2) | ||
+ input_derivatives * theta_one_minus_theta) | ||
denominator = input_delta + ((input_derivatives + input_derivatives_plus_one - 2 * input_delta) | ||
* theta_one_minus_theta) | ||
outputs = input_cumheights + numerator / denominator | ||
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derivative_numerator = input_delta.pow(2) * (input_derivatives_plus_one * theta.pow(2) | ||
+ 2 * input_delta * theta_one_minus_theta | ||
+ input_derivatives * (1 - theta).pow(2)) | ||
logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator) | ||
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return outputs, logabsdet |
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