# Copyright (c) 2021, NVIDIA CORPORATION & AFFILIATES. All rights reserved. # # NVIDIA CORPORATION and its licensors retain all intellectual property # and proprietary rights in and to this software, related documentation # and any modifications thereto. Any use, reproduction, disclosure or # distribution of this software and related documentation without an express # license agreement from NVIDIA CORPORATION is strictly prohibited. """Generator architecture from the paper "Alias-Free Generative Adversarial Networks".""" import numpy as np import scipy.signal import scipy.optimize import torch from torch_utils import misc from torch_utils import persistence from torch_utils.ops import conv2d_gradfix from torch_utils.ops import filtered_lrelu from torch_utils.ops import bias_act #---------------------------------------------------------------------------- @misc.profiled_function def modulated_conv2d( x, # Input tensor: [batch_size, in_channels, in_height, in_width] w, # Weight tensor: [out_channels, in_channels, kernel_height, kernel_width] s, # Style tensor: [batch_size, in_channels] demodulate = True, # Apply weight demodulation? padding = 0, # Padding: int or [padH, padW] input_gain = None, # Optional scale factors for the input channels: [], [in_channels], or [batch_size, in_channels] ): with misc.suppress_tracer_warnings(): # this value will be treated as a constant batch_size = int(x.shape[0]) out_channels, in_channels, kh, kw = w.shape misc.assert_shape(w, [out_channels, in_channels, kh, kw]) # [OIkk] misc.assert_shape(x, [batch_size, in_channels, None, None]) # [NIHW] misc.assert_shape(s, [batch_size, in_channels]) # [NI] # Pre-normalize inputs. if demodulate: w = w * w.square().mean([1,2,3], keepdim=True).rsqrt() s = s * s.square().mean().rsqrt() # Modulate weights. w = w.unsqueeze(0) # [NOIkk] w = w * s.unsqueeze(1).unsqueeze(3).unsqueeze(4) # [NOIkk] # Demodulate weights. if demodulate: dcoefs = (w.square().sum(dim=[2,3,4]) + 1e-8).rsqrt() # [NO] w = w * dcoefs.unsqueeze(2).unsqueeze(3).unsqueeze(4) # [NOIkk] # Apply input scaling. if input_gain is not None: input_gain = input_gain.expand(batch_size, in_channels) # [NI] w = w * input_gain.unsqueeze(1).unsqueeze(3).unsqueeze(4) # [NOIkk] # Execute as one fused op using grouped convolution. x = x.reshape(1, -1, *x.shape[2:]) w = w.reshape(-1, in_channels, kh, kw) x = conv2d_gradfix.conv2d(input=x, weight=w.to(x.dtype), padding=padding, groups=batch_size) x = x.reshape(batch_size, -1, *x.shape[2:]) return x #---------------------------------------------------------------------------- @persistence.persistent_class class FullyConnectedLayer(torch.nn.Module): def __init__(self, in_features, # Number of input features. out_features, # Number of output features. activation = 'linear', # Activation function: 'relu', 'lrelu', etc. bias = True, # Apply additive bias before the activation function? lr_multiplier = 1, # Learning rate multiplier. weight_init = 1, # Initial standard deviation of the weight tensor. bias_init = 0, # Initial value of the additive bias. ): super().__init__() self.in_features = in_features self.out_features = out_features self.activation = activation self.weight = torch.nn.Parameter(torch.randn([out_features, in_features]) * (weight_init / lr_multiplier)) bias_init = np.broadcast_to(np.asarray(bias_init, dtype=np.float32), [out_features]) self.bias = torch.nn.Parameter(torch.from_numpy(bias_init / lr_multiplier)) if bias else None self.weight_gain = lr_multiplier / np.sqrt(in_features) self.bias_gain = lr_multiplier def forward(self, x): w = self.weight.to(x.dtype) * self.weight_gain b = self.bias if b is not None: b = b.to(x.dtype) if self.bias_gain != 1: b = b * self.bias_gain if self.activation == 'linear' and b is not None: x = torch.addmm(b.unsqueeze(0), x, w.t()) else: x = x.matmul(w.t()) x = bias_act.bias_act(x, b, act=self.activation) return x def extra_repr(self): return f'in_features={self.in_features:d}, out_features={self.out_features:d}, activation={self.activation:s}' #---------------------------------------------------------------------------- @persistence.persistent_class class MappingNetwork(torch.nn.Module): def __init__(self, z_dim, # Input latent (Z) dimensionality. c_dim, # Conditioning label (C) dimensionality, 0 = no labels. w_dim, # Intermediate latent (W) dimensionality. num_ws, # Number of intermediate latents to output. num_layers = 2, # Number of mapping layers. lr_multiplier = 0.01, # Learning rate multiplier for the mapping layers. w_avg_beta = 0.998, # Decay for tracking the moving average of W during training. ): super().__init__() self.z_dim = z_dim self.c_dim = c_dim self.w_dim = w_dim self.num_ws = num_ws self.num_layers = num_layers self.w_avg_beta = w_avg_beta # Construct layers. self.embed = FullyConnectedLayer(self.c_dim, self.w_dim) if self.c_dim > 0 else None features = [self.z_dim + (self.w_dim if self.c_dim > 0 else 0)] + [self.w_dim] * self.num_layers for idx, in_features, out_features in zip(range(num_layers), features[:-1], features[1:]): layer = FullyConnectedLayer(in_features, out_features, activation='lrelu', lr_multiplier=lr_multiplier) setattr(self, f'fc{idx}', layer) self.register_buffer('w_avg', torch.zeros([w_dim])) def forward(self, z, c, truncation_psi=1, truncation_cutoff=None, update_emas=False): misc.assert_shape(z, [None, self.z_dim]) if truncation_cutoff is None: truncation_cutoff = self.num_ws # Embed, normalize, and concatenate inputs. x = z.to(torch.float32) x = x * (x.square().mean(1, keepdim=True) + 1e-8).rsqrt() if self.c_dim > 0: misc.assert_shape(c, [None, self.c_dim]) y = self.embed(c.to(torch.float32)) y = y * (y.square().mean(1, keepdim=True) + 1e-8).rsqrt() x = torch.cat([x, y], dim=1) if x is not None else y # Execute layers. for idx in range(self.num_layers): x = getattr(self, f'fc{idx}')(x) # Update moving average of W. if update_emas: self.w_avg.copy_(x.detach().mean(dim=0).lerp(self.w_avg, self.w_avg_beta)) # Broadcast and apply truncation. x = x.unsqueeze(1).repeat([1, self.num_ws, 1]) if truncation_psi != 1: x[:, :truncation_cutoff] = self.w_avg.lerp(x[:, :truncation_cutoff], truncation_psi) return x def extra_repr(self): return f'z_dim={self.z_dim:d}, c_dim={self.c_dim:d}, w_dim={self.w_dim:d}, num_ws={self.num_ws:d}' #---------------------------------------------------------------------------- @persistence.persistent_class class SynthesisInput(torch.nn.Module): def __init__(self, w_dim, # Intermediate latent (W) dimensionality. channels, # Number of output channels. size, # Output spatial size: int or [width, height]. sampling_rate, # Output sampling rate. bandwidth, # Output bandwidth. ): super().__init__() self.w_dim = w_dim self.channels = channels self.size = np.broadcast_to(np.asarray(size), [2]) self.sampling_rate = sampling_rate self.bandwidth = bandwidth # Draw random frequencies from uniform 2D disc. freqs = torch.randn([self.channels, 2]) radii = freqs.square().sum(dim=1, keepdim=True).sqrt() freqs /= radii * radii.square().exp().pow(0.25) freqs *= bandwidth phases = torch.rand([self.channels]) - 0.5 # Setup parameters and buffers. self.weight = torch.nn.Parameter(torch.randn([self.channels, self.channels])) self.affine = FullyConnectedLayer(w_dim, 4, weight_init=0, bias_init=[1,0,0,0]) self.register_buffer('transform', torch.eye(3, 3)) # User-specified inverse transform wrt. resulting image. self.register_buffer('freqs', freqs) self.register_buffer('phases', phases) def forward(self, w): # Introduce batch dimension. transforms = self.transform.unsqueeze(0) # [batch, row, col] freqs = self.freqs.unsqueeze(0) # [batch, channel, xy] phases = self.phases.unsqueeze(0) # [batch, channel] # Apply learned transformation. t = self.affine(w) # t = (r_c, r_s, t_x, t_y) t = t / t[:, :2].norm(dim=1, keepdim=True) # t' = (r'_c, r'_s, t'_x, t'_y) m_r = torch.eye(3, device=w.device).unsqueeze(0).repeat([w.shape[0], 1, 1]) # Inverse rotation wrt. resulting image. m_r[:, 0, 0] = t[:, 0] # r'_c m_r[:, 0, 1] = -t[:, 1] # r'_s m_r[:, 1, 0] = t[:, 1] # r'_s m_r[:, 1, 1] = t[:, 0] # r'_c m_t = torch.eye(3, device=w.device).unsqueeze(0).repeat([w.shape[0], 1, 1]) # Inverse translation wrt. resulting image. m_t[:, 0, 2] = -t[:, 2] # t'_x m_t[:, 1, 2] = -t[:, 3] # t'_y transforms = m_r @ m_t @ transforms # First rotate resulting image, then translate, and finally apply user-specified transform. # Transform frequencies. phases = phases + (freqs @ transforms[:, :2, 2:]).squeeze(2) freqs = freqs @ transforms[:, :2, :2] # Dampen out-of-band frequencies that may occur due to the user-specified transform. amplitudes = (1 - (freqs.norm(dim=2) - self.bandwidth) / (self.sampling_rate / 2 - self.bandwidth)).clamp(0, 1) # Construct sampling grid. theta = torch.eye(2, 3, device=w.device) theta[0, 0] = 0.5 * self.size[0] / self.sampling_rate theta[1, 1] = 0.5 * self.size[1] / self.sampling_rate grids = torch.nn.functional.affine_grid(theta.unsqueeze(0), [1, 1, self.size[1], self.size[0]], align_corners=False) # Compute Fourier features. x = (grids.unsqueeze(3) @ freqs.permute(0, 2, 1).unsqueeze(1).unsqueeze(2)).squeeze(3) # [batch, height, width, channel] x = x + phases.unsqueeze(1).unsqueeze(2) x = torch.sin(x * (np.pi * 2)) x = x * amplitudes.unsqueeze(1).unsqueeze(2) # Apply trainable mapping. weight = self.weight / np.sqrt(self.channels) x = x @ weight.t() # Ensure correct shape. x = x.permute(0, 3, 1, 2) # [batch, channel, height, width] misc.assert_shape(x, [w.shape[0], self.channels, int(self.size[1]), int(self.size[0])]) return x def extra_repr(self): return '\n'.join([ f'w_dim={self.w_dim:d}, channels={self.channels:d}, size={list(self.size)},', f'sampling_rate={self.sampling_rate:g}, bandwidth={self.bandwidth:g}']) #---------------------------------------------------------------------------- @persistence.persistent_class class SynthesisLayer(torch.nn.Module): def __init__(self, w_dim, # Intermediate latent (W) dimensionality. is_torgb, # Is this the final ToRGB layer? is_critically_sampled, # Does this layer use critical sampling? use_fp16, # Does this layer use FP16? # Input & output specifications. in_channels, # Number of input channels. out_channels, # Number of output channels. in_size, # Input spatial size: int or [width, height]. out_size, # Output spatial size: int or [width, height]. in_sampling_rate, # Input sampling rate (s). out_sampling_rate, # Output sampling rate (s). in_cutoff, # Input cutoff frequency (f_c). out_cutoff, # Output cutoff frequency (f_c). in_half_width, # Input transition band half-width (f_h). out_half_width, # Output Transition band half-width (f_h). # Hyperparameters. conv_kernel = 3, # Convolution kernel size. Ignored for final the ToRGB layer. filter_size = 6, # Low-pass filter size relative to the lower resolution when up/downsampling. lrelu_upsampling = 2, # Relative sampling rate for leaky ReLU. Ignored for final the ToRGB layer. use_radial_filters = False, # Use radially symmetric downsampling filter? Ignored for critically sampled layers. conv_clamp = 256, # Clamp the output to [-X, +X], None = disable clamping. magnitude_ema_beta = 0.999, # Decay rate for the moving average of input magnitudes. ): super().__init__() self.w_dim = w_dim self.is_torgb = is_torgb self.is_critically_sampled = is_critically_sampled self.use_fp16 = use_fp16 self.in_channels = in_channels self.out_channels = out_channels self.in_size = np.broadcast_to(np.asarray(in_size), [2]) self.out_size = np.broadcast_to(np.asarray(out_size), [2]) self.in_sampling_rate = in_sampling_rate self.out_sampling_rate = out_sampling_rate self.tmp_sampling_rate = max(in_sampling_rate, out_sampling_rate) * (1 if is_torgb else lrelu_upsampling) self.in_cutoff = in_cutoff self.out_cutoff = out_cutoff self.in_half_width = in_half_width self.out_half_width = out_half_width self.conv_kernel = 1 if is_torgb else conv_kernel self.conv_clamp = conv_clamp self.magnitude_ema_beta = magnitude_ema_beta # Setup parameters and buffers. self.affine = FullyConnectedLayer(self.w_dim, self.in_channels, bias_init=1) self.weight = torch.nn.Parameter(torch.randn([self.out_channels, self.in_channels, self.conv_kernel, self.conv_kernel])) self.bias = torch.nn.Parameter(torch.zeros([self.out_channels])) self.register_buffer('magnitude_ema', torch.ones([])) # Design upsampling filter. self.up_factor = int(np.rint(self.tmp_sampling_rate / self.in_sampling_rate)) assert self.in_sampling_rate * self.up_factor == self.tmp_sampling_rate self.up_taps = filter_size * self.up_factor if self.up_factor > 1 and not self.is_torgb else 1 self.register_buffer('up_filter', self.design_lowpass_filter( numtaps=self.up_taps, cutoff=self.in_cutoff, width=self.in_half_width*2, fs=self.tmp_sampling_rate)) # Design downsampling filter. self.down_factor = int(np.rint(self.tmp_sampling_rate / self.out_sampling_rate)) assert self.out_sampling_rate * self.down_factor == self.tmp_sampling_rate self.down_taps = filter_size * self.down_factor if self.down_factor > 1 and not self.is_torgb else 1 self.down_radial = use_radial_filters and not self.is_critically_sampled self.register_buffer('down_filter', self.design_lowpass_filter( numtaps=self.down_taps, cutoff=self.out_cutoff, width=self.out_half_width*2, fs=self.tmp_sampling_rate, radial=self.down_radial)) # Compute padding. pad_total = (self.out_size - 1) * self.down_factor + 1 # Desired output size before downsampling. pad_total -= (self.in_size + self.conv_kernel - 1) * self.up_factor # Input size after upsampling. pad_total += self.up_taps + self.down_taps - 2 # Size reduction caused by the filters. pad_lo = (pad_total + self.up_factor) // 2 # Shift sample locations according to the symmetric interpretation (Appendix C.3). pad_hi = pad_total - pad_lo self.padding = [int(pad_lo[0]), int(pad_hi[0]), int(pad_lo[1]), int(pad_hi[1])] def forward(self, x, w, noise_mode='random', force_fp32=False, update_emas=False): assert noise_mode in ['random', 'const', 'none'] # unused misc.assert_shape(x, [None, self.in_channels, int(self.in_size[1]), int(self.in_size[0])]) misc.assert_shape(w, [x.shape[0], self.w_dim]) # Track input magnitude. if update_emas: with torch.autograd.profiler.record_function('update_magnitude_ema'): magnitude_cur = x.detach().to(torch.float32).square().mean() self.magnitude_ema.copy_(magnitude_cur.lerp(self.magnitude_ema, self.magnitude_ema_beta)) input_gain = self.magnitude_ema.rsqrt() # Execute affine layer. styles = self.affine(w) if self.is_torgb: weight_gain = 1 / np.sqrt(self.in_channels * (self.conv_kernel ** 2)) styles = styles * weight_gain # Execute modulated conv2d. dtype = torch.float16 if (self.use_fp16 and not force_fp32 and x.device.type == 'cuda') else torch.float32 x = modulated_conv2d(x=x.to(dtype), w=self.weight, s=styles, padding=self.conv_kernel-1, demodulate=(not self.is_torgb), input_gain=input_gain) # Execute bias, filtered leaky ReLU, and clamping. gain = 1 if self.is_torgb else np.sqrt(2) slope = 1 if self.is_torgb else 0.2 x = filtered_lrelu.filtered_lrelu(x=x, fu=self.up_filter, fd=self.down_filter, b=self.bias.to(x.dtype), up=self.up_factor, down=self.down_factor, padding=self.padding, gain=gain, slope=slope, clamp=self.conv_clamp) # Ensure correct shape and dtype. misc.assert_shape(x, [None, self.out_channels, int(self.out_size[1]), int(self.out_size[0])]) assert x.dtype == dtype return x @staticmethod def design_lowpass_filter(numtaps, cutoff, width, fs, radial=False): assert numtaps >= 1 # Identity filter. if numtaps == 1: return None # Separable Kaiser low-pass filter. if not radial: f = scipy.signal.firwin(numtaps=numtaps, cutoff=cutoff, width=width, fs=fs) return torch.as_tensor(f, dtype=torch.float32) # Radially symmetric jinc-based filter. x = (np.arange(numtaps) - (numtaps - 1) / 2) / fs r = np.hypot(*np.meshgrid(x, x)) f = scipy.special.j1(2 * cutoff * (np.pi * r)) / (np.pi * r) beta = scipy.signal.kaiser_beta(scipy.signal.kaiser_atten(numtaps, width / (fs / 2))) w = np.kaiser(numtaps, beta) f *= np.outer(w, w) f /= np.sum(f) return torch.as_tensor(f, dtype=torch.float32) def extra_repr(self): return '\n'.join([ f'w_dim={self.w_dim:d}, is_torgb={self.is_torgb},', f'is_critically_sampled={self.is_critically_sampled}, use_fp16={self.use_fp16},', f'in_sampling_rate={self.in_sampling_rate:g}, out_sampling_rate={self.out_sampling_rate:g},', f'in_cutoff={self.in_cutoff:g}, out_cutoff={self.out_cutoff:g},', f'in_half_width={self.in_half_width:g}, out_half_width={self.out_half_width:g},', f'in_size={list(self.in_size)}, out_size={list(self.out_size)},', f'in_channels={self.in_channels:d}, out_channels={self.out_channels:d}']) #---------------------------------------------------------------------------- @persistence.persistent_class class SynthesisNetwork(torch.nn.Module): def __init__(self, w_dim, # Intermediate latent (W) dimensionality. img_resolution, # Output image resolution. img_channels, # Number of color channels. channel_base = 32768, # Overall multiplier for the number of channels. channel_max = 512, # Maximum number of channels in any layer. num_layers = 14, # Total number of layers, excluding Fourier features and ToRGB. num_critical = 2, # Number of critically sampled layers at the end. first_cutoff = 2, # Cutoff frequency of the first layer (f_{c,0}). first_stopband = 2**2.1, # Minimum stopband of the first layer (f_{t,0}). last_stopband_rel = 2**0.3, # Minimum stopband of the last layer, expressed relative to the cutoff. margin_size = 10, # Number of additional pixels outside the image. output_scale = 0.25, # Scale factor for the output image. num_fp16_res = 4, # Use FP16 for the N highest resolutions. **layer_kwargs, # Arguments for SynthesisLayer. ): super().__init__() self.w_dim = w_dim self.num_ws = num_layers + 2 self.img_resolution = img_resolution self.img_channels = img_channels self.num_layers = num_layers self.num_critical = num_critical self.margin_size = margin_size self.output_scale = output_scale self.num_fp16_res = num_fp16_res # Geometric progression of layer cutoffs and min. stopbands. last_cutoff = self.img_resolution / 2 # f_{c,N} last_stopband = last_cutoff * last_stopband_rel # f_{t,N} exponents = np.minimum(np.arange(self.num_layers + 1) / (self.num_layers - self.num_critical), 1) cutoffs = first_cutoff * (last_cutoff / first_cutoff) ** exponents # f_c[i] stopbands = first_stopband * (last_stopband / first_stopband) ** exponents # f_t[i] # Compute remaining layer parameters. sampling_rates = np.exp2(np.ceil(np.log2(np.minimum(stopbands * 2, self.img_resolution)))) # s[i] half_widths = np.maximum(stopbands, sampling_rates / 2) - cutoffs # f_h[i] sizes = sampling_rates + self.margin_size * 2 sizes[-2:] = self.img_resolution channels = np.rint(np.minimum((channel_base / 2) / cutoffs, channel_max)) channels[-1] = self.img_channels # Construct layers. self.input = SynthesisInput( w_dim=self.w_dim, channels=int(channels[0]), size=int(sizes[0]), sampling_rate=sampling_rates[0], bandwidth=cutoffs[0]) self.layer_names = [] for idx in range(self.num_layers + 1): prev = max(idx - 1, 0) is_torgb = (idx == self.num_layers) is_critically_sampled = (idx >= self.num_layers - self.num_critical) use_fp16 = (sampling_rates[idx] * (2 ** self.num_fp16_res) > self.img_resolution) layer = SynthesisLayer( w_dim=self.w_dim, is_torgb=is_torgb, is_critically_sampled=is_critically_sampled, use_fp16=use_fp16, in_channels=int(channels[prev]), out_channels= int(channels[idx]), in_size=int(sizes[prev]), out_size=int(sizes[idx]), in_sampling_rate=int(sampling_rates[prev]), out_sampling_rate=int(sampling_rates[idx]), in_cutoff=cutoffs[prev], out_cutoff=cutoffs[idx], in_half_width=half_widths[prev], out_half_width=half_widths[idx], **layer_kwargs) name = f'L{idx}_{layer.out_size[0]}_{layer.out_channels}' setattr(self, name, layer) self.layer_names.append(name) def forward(self, ws, **layer_kwargs): misc.assert_shape(ws, [None, self.num_ws, self.w_dim]) ws = ws.to(torch.float32).unbind(dim=1) # Execute layers. x = self.input(ws[0]) for name, w in zip(self.layer_names, ws[1:]): x = getattr(self, name)(x, w, **layer_kwargs) if self.output_scale != 1: x = x * self.output_scale # Ensure correct shape and dtype. misc.assert_shape(x, [None, self.img_channels, self.img_resolution, self.img_resolution]) x = x.to(torch.float32) return x def extra_repr(self): return '\n'.join([ f'w_dim={self.w_dim:d}, num_ws={self.num_ws:d},', f'img_resolution={self.img_resolution:d}, img_channels={self.img_channels:d},', f'num_layers={self.num_layers:d}, num_critical={self.num_critical:d},', f'margin_size={self.margin_size:d}, num_fp16_res={self.num_fp16_res:d}']) #---------------------------------------------------------------------------- @persistence.persistent_class class Generator(torch.nn.Module): def __init__(self, z_dim, # Input latent (Z) dimensionality. c_dim, # Conditioning label (C) dimensionality. w_dim, # Intermediate latent (W) dimensionality. img_resolution, # Output resolution. img_channels, # Number of output color channels. mapping_kwargs = {}, # Arguments for MappingNetwork. **synthesis_kwargs, # Arguments for SynthesisNetwork. ): super().__init__() self.z_dim = z_dim self.c_dim = c_dim self.w_dim = w_dim self.img_resolution = img_resolution self.img_channels = img_channels self.synthesis = SynthesisNetwork(w_dim=w_dim, img_resolution=img_resolution, img_channels=img_channels, **synthesis_kwargs) self.num_ws = self.synthesis.num_ws self.mapping = MappingNetwork(z_dim=z_dim, c_dim=c_dim, w_dim=w_dim, num_ws=self.num_ws, **mapping_kwargs) def forward(self, z, c, truncation_psi=1, truncation_cutoff=None, update_emas=False, **synthesis_kwargs): ws = self.mapping(z, c, truncation_psi=truncation_psi, truncation_cutoff=truncation_cutoff, update_emas=update_emas) img = self.synthesis(ws, update_emas=update_emas, **synthesis_kwargs) return img #----------------------------------------------------------------------------