Spaces:
Runtime error
Runtime error
File size: 8,490 Bytes
257783b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 |
import torch
from torch.nn import functional as F
import numpy as np
DEFAULT_MIN_BIN_WIDTH = 1e-3
DEFAULT_MIN_BIN_HEIGHT = 1e-3
DEFAULT_MIN_DERIVATIVE = 1e-3
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):
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
}
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
def searchsorted(bin_locations, inputs, eps=1e-6):
bin_locations[..., -1] += eps
return torch.sum(
inputs[..., None] >= bin_locations,
dim=-1
) - 1
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
outputs = torch.zeros_like(inputs)
logabsdet = torch.zeros_like(inputs)
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
outputs[outside_interval_mask] = inputs[outside_interval_mask]
logabsdet[outside_interval_mask] = 0
else:
raise RuntimeError('{} tails are not implemented.'.format(tails))
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
)
return outputs, logabsdet
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')
num_bins = unnormalized_widths.shape[-1]
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')
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]
derivatives = min_derivative + F.softplus(unnormalized_derivatives)
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]
if inverse:
bin_idx = searchsorted(cumheights, inputs)[..., None]
else:
bin_idx = searchsorted(cumwidths, inputs)[..., None]
input_cumwidths = cumwidths.gather(-1, bin_idx)[..., 0]
input_bin_widths = widths.gather(-1, bin_idx)[..., 0]
input_cumheights = cumheights.gather(-1, bin_idx)[..., 0]
delta = heights / widths
input_delta = delta.gather(-1, bin_idx)[..., 0]
input_derivatives = derivatives.gather(-1, bin_idx)[..., 0]
input_derivatives_plus_one = derivatives[..., 1:].gather(-1, bin_idx)[..., 0]
input_heights = heights.gather(-1, bin_idx)[..., 0]
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)
discriminant = b.pow(2) - 4 * a * c
assert (discriminant >= 0).all()
root = (2 * c) / (-b - torch.sqrt(discriminant))
outputs = root * input_bin_widths + input_cumwidths
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)
return outputs, -logabsdet
else:
theta = (inputs - input_cumwidths) / input_bin_widths
theta_one_minus_theta = theta * (1 - theta)
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
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)
return outputs, logabsdet
|