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8月6日Pytorch笔记——GAN、WGAN
前言
本文为8月6日Pytorch笔记，分为两个章节：
- GAN；
- WGAN。
一、GAN
1、GAN 原理
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Goal： p ( x ) p(x) p(x)
-How to train?
m i n G , m a x D L ( D , G ) = E x − p r ( x ) [ l o g D ( x ) ] + E z − p z ( z ) [ l o g ( 1 − D ( G ( z ) ) ) ] V ( D , G ) = E x − p r ( x ) [ l o g D ( x ) ] + E x − p g ( x ) [ l o g ( 1 − D ( x ) ] p ( z ) = p ( x g ) min_G, max_D\ L(D, G) = \mathbb{E}_{x-p_r(x)} [logD(x)] + \mathbb{E}_{z-p_z(z)} [log(1 - D(G(z)))]\\ V(D, G) = \mathbb{E}_{x-p_r(x)} [log D(x)] + \mathbb{E}_{x-p_g(x)} [log(1 - D(x)]\\ p(z ) = p(x_g) minG,maxD L(D,G)=Ex−pr(x)[logD(x)]+Ez−pz(z)[log(1−D(G(z)))]V(D,G)=Ex−pr(x)[logD(x)]+Ex−pg(x)[log(1−D(x)]p(z)=p(xg)- 固定
G
G
G，最优的
D
D
D 为：
D G ∗ ( x ) = p d a t a ( x ) p d a t a ( x ) + p g ( x ) D^*_G(x) = \frac{p_{data}(x)}{p_{data}(x) + p_g(x)} DG∗(x)=pdata(x)+pg(x)pdata(x)
- 固定
G
G
G，最优的
D
D
D 为：
-
KL divergence:
D K L ( p ∣ ∣ q ) = ∫ x p ( x ) l o g p ( x ) q ( x ) d x D_{KL}(p||q) = \int_{x} p(x)\ log\frac{p(x)}{q(x)}dx DKL(p∣∣q)=∫xp(x) logq(x)p(x)dx
-
J-S divergence:
D J S ( p ∣ ∣ q ) = 1 2 D K L ( p ∣ ∣ p + q 2 ) + 1 2 D K L ( q ∣ ∣ p + q 2 ) D_{JS}(p||q) = \frac{1}{2}D_{KL}(p||\frac{p+q}{2}) + \frac{1}{2} D_{KL}(q||\frac{p+q}{2} ) DJS(p∣∣q)=21DKL(p∣∣2p+q)+21DKL(q∣∣2p+q)- 找到最优的
D
D
D 后，
G
G
G 如何更新：
D J S ( p r ∣ ∣ p g ) = 1 2 ( l o g 4 + L ( G , D ∗ ) ) L ( G , D ∗ ) = 2 D J S ( p r ∣ ∣ p g ) − 2 l o g 2 D_{JS}(p_r||p_g) = \frac{1}{2} (log\ 4 + L(G, D^*))\\ L(G, D^*) = 2 D_{JS}(p_r||p_g) - 2\ log\ 2 DJS(pr∣∣pg)=21(log 4+L(G,D∗))L(G,D∗)=2DJS(pr∣∣pg)−2 log 2
- 找到最优的
D
D
D 后，
G
G
G 如何更新：
-
只要 θ ≠ 0 \theta \ne 0 θ=0, K L ⇒ ∞ , J S ⇒ l o g 2 KL ⇒ \infty, JS ⇒ log2 KL⇒∞,JS⇒log2
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J-S divergence 的缺陷:
- 当两个分布不重合时， J S ( P G , P d a t a ) = l o g 2 JS(P_G, P_{data}) = log\ 2 JS(PG,Pdata)=log 2；
- 当 θ = 0 \theta = 0 θ=0时， J S ( P G , P d a t a ) = 0 JS(P_G, P_{data}) = 0 JS(PG,Pdata)=0。
代码如下：import torch from torch import nn, optim, autograd import numpy as np import visdom from torch.nn import functional as F from matplotlib import pyplot as plt import random h_dim = 400 batchsz = 512 viz = visdom.Visdom() class Generator(nn.Module): def __init__(self): super(Generator, self).__init__() self.net = nn.Sequential( nn.Linear(2, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, 2), ) def forward(self, z): output = self.net(z) return output class Discriminator(nn.Module): def __init__(self): super(Discriminator, self).__init__() self.net = nn.Sequential( nn.Linear(2, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, 1), nn.Sigmoid() ) def forward(self, x): output = self.net(x) return output.view(-1) def data_generator(): scale = 2. centers = [ (1, 0), (-1, 0), (0, 1), (0, -1), (1. / np.sqrt(2), 1. / np.sqrt(2)), (1. / np.sqrt(2), -1. / np.sqrt(2)), (-1. / np.sqrt(2), 1. / np.sqrt(2)), (-1. / np.sqrt(2), -1. / np.sqrt(2)) ] centers = [(scale * x, scale * y) for x, y in centers] while True: dataset = [] for i in range(batchsz): point = np.random.randn(2) * .02 center = random.choice(centers) point[0] += center[0] point[1] += center[1] dataset.append(point) dataset = np.array(dataset, dtype='float32') dataset /= 1.414 # stdev yield dataset # for i in range(100000//25): # for x in range(-2, 3): # for y in range(-2, 3): # point = np.random.randn(2).astype(np.float32) * 0.05 # point[0] += 2 * x # point[1] += 2 * y # dataset.append(point) # # dataset = np.array(dataset) # print('dataset:', dataset.shape) # viz.scatter(dataset, win='dataset', opts=dict(title='dataset', webgl=True)) # # while True: # np.random.shuffle(dataset) # # for i in range(len(dataset)//batchsz): # yield dataset[i*batchsz : (i+1)*batchsz] def generate_image(D, G, xr, epoch): """ Generates and saves a plot of the true distribution, the generator, and the critic. """ N_POINTS = 128 RANGE = 3 plt.clf() points = np.zeros((N_POINTS, N_POINTS, 2), dtype='float32') points[:, :, 0] = np.linspace(-RANGE, RANGE, N_POINTS)[:, None] points[:, :, 1] = np.linspace(-RANGE, RANGE, N_POINTS)[None, :] points = points.reshape((-1, 2)) # (16384, 2) # print('p:', points.shape) # draw contour with torch.no_grad(): points = torch.Tensor(points).cuda() # [16384, 2] disc_map = D(points).cpu().numpy() # [16384] x = y = np.linspace(-RANGE, RANGE, N_POINTS) cs = plt.contour(x, y, disc_map.reshape((len(x), len(y))).transpose()) plt.clabel(cs, inline=1, fontsize=10) # plt.colorbar() # draw samples with torch.no_grad(): z = torch.randn(batchsz, 2).cuda() # [b, 2] samples = G(z).cpu().numpy() # [b, 2] plt.scatter(xr[:, 0], xr[:, 1], c='orange', marker='.') plt.scatter(samples[:, 0], samples[:, 1], c='green', marker='+') viz.matplot(plt, win='contour', opts=dict(title='p(x):%d'%epoch)) def weights_init(m): if isinstance(m, nn.Linear): # m.weight.data.normal_(0.0, 0.02) nn.init.kaiming_normal_(m.weight) m.bias.data.fill_(0) def gradient_penalty(D, xr, xf): """ :param D: :param xr: :param xf: :return: """ LAMBDA = 0.3 # only constrait for Discriminator xf = xf.detach() xr = xr.detach() # [b, 1] => [b, 2] alpha = torch.rand(batchsz, 1).cuda() alpha = alpha.expand_as(xr) interpolates = alpha * xr + ((1 - alpha) * xf) interpolates.requires_grad_() disc_interpolates = D(interpolates) gradients = autograd.grad(outputs=disc_interpolates, inputs=interpolates, grad_outputs=torch.ones_like(disc_interpolates), create_graph=True, retain_graph=True, only_inputs=True)[0] gp = ((gradients.norm(2, dim=1) - 1) ** 2).mean() * LAMBDA return gp def main(): torch.manual_seed(23) np.random.seed(23) G = Generator().cuda() D = Discriminator().cuda() G.apply(weights_init) D.apply(weights_init) optim_G = optim.Adam(G.parameters(), lr=1e-3, betas=(0.5, 0.9)) optim_D = optim.Adam(D.parameters(), lr=1e-3, betas=(0.5, 0.9)) data_iter = data_generator() print('batch:', next(data_iter).shape) viz.line([[0,0]], [0], win='loss', opts=dict(title='loss', legend=['D', 'G'])) for epoch in range(50000): # 1. train discriminator for k steps for _ in range(5): x = next(data_iter) xr = torch.from_numpy(x).cuda() # [b] predr = (D(xr)) # max log(lossr) lossr = - (predr.mean()) # [b, 2] z = torch.randn(batchsz, 2).cuda() # stop gradient on G # [b, 2] xf = G(z).detach() # [b] predf = (D(xf)) # min predf lossf = (predf.mean()) # gradient penalty gp = gradient_penalty(D, xr, xf) loss_D = lossr + lossf + gp optim_D.zero_grad() loss_D.backward() # for p in D.parameters(): # print(p.grad.norm()) optim_D.step() # 2. train Generator z = torch.randn(batchsz, 2).cuda() xf = G(z) predf = (D(xf)) # max predf loss_G = - (predf.mean()) optim_G.zero_grad() loss_G.backward() optim_G.step() if epoch % 100 == 0: viz.line([[loss_D.item(), loss_G.item()]], [epoch], win='loss', update='append') generate_image(D, G, xr, epoch) print(loss_D.item(), loss_G.item()) if __name__ == '__main__': main()- 1
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二、WGAN
2、Wasserstein Distance
W ( P r , P g ) = i n f γ ∈ ∏ ( P r , P g ) E ( x , y ) − γ [ ∣ ∣ x − y ∣ ∣ ] W(\mathbb{P}_r, \mathbb{P}_g) = inf_{\gamma \in \prod (\mathbb{P}_r, \mathbb{P}_g)} \mathbb {E}_{(x, y)-\gamma } [||x - y||] W(Pr,Pg)=infγ∈∏(Pr,Pg)E(x,y)−γ[∣∣x−y∣∣]代码如下：import torch from torch import nn, optim, autograd import numpy as np import visdom from torch.nn import functional as F from matplotlib import pyplot as plt import random h_dim = 400 batchsz = 512 viz = visdom.Visdom() class Generator(nn.Module): def __init__(self): super(Generator, self).__init__() self.net = nn.Sequential( nn.Linear(2, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, 2), ) def forward(self, z): output = self.net(z) return output class Discriminator(nn.Module): def __init__(self): super(Discriminator, self).__init__() self.net = nn.Sequential( nn.Linear(2, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, h_dim), nn.ReLU(True), nn.Linear(h_dim, 1), nn.Sigmoid() ) def forward(self, x): output = self.net(x) return output.view(-1) def data_generator(): scale = 2. centers = [ (1, 0), (-1, 0), (0, 1), (0, -1), (1. / np.sqrt(2), 1. / np.sqrt(2)), (1. / np.sqrt(2), -1. / np.sqrt(2)), (-1. / np.sqrt(2), 1. / np.sqrt(2)), (-1. / np.sqrt(2), -1. / np.sqrt(2)) ] centers = [(scale * x, scale * y) for x, y in centers] while True: dataset = [] for i in range(batchsz): point = np.random.randn(2) * .02 center = random.choice(centers) point[0] += center[0] point[1] += center[1] dataset.append(point) dataset = np.array(dataset, dtype='float32') dataset /= 1.414 # stdev yield dataset # for i in range(100000//25): # for x in range(-2, 3): # for y in range(-2, 3): # point = np.random.randn(2).astype(np.float32) * 0.05 # point[0] += 2 * x # point[1] += 2 * y # dataset.append(point) # # dataset = np.array(dataset) # print('dataset:', dataset.shape) # viz.scatter(dataset, win='dataset', opts=dict(title='dataset', webgl=True)) # # while True: # np.random.shuffle(dataset) # # for i in range(len(dataset)//batchsz): # yield dataset[i*batchsz : (i+1)*batchsz] def generate_image(D, G, xr, epoch): """ Generates and saves a plot of the true distribution, the generator, and the critic. """ N_POINTS = 128 RANGE = 3 plt.clf() points = np.zeros((N_POINTS, N_POINTS, 2), dtype='float32') points[:, :, 0] = np.linspace(-RANGE, RANGE, N_POINTS)[:, None] points[:, :, 1] = np.linspace(-RANGE, RANGE, N_POINTS)[None, :] points = points.reshape((-1, 2)) # (16384, 2) # print('p:', points.shape) # draw contour with torch.no_grad(): points = torch.Tensor(points).cuda() # [16384, 2] disc_map = D(points).cpu().numpy() # [16384] x = y = np.linspace(-RANGE, RANGE, N_POINTS) cs = plt.contour(x, y, disc_map.reshape((len(x), len(y))).transpose()) plt.clabel(cs, inline=1, fontsize=10) # plt.colorbar() # draw samples with torch.no_grad(): z = torch.randn(batchsz, 2).cuda() # [b, 2] samples = G(z).cpu().numpy() # [b, 2] plt.scatter(xr[:, 0], xr[:, 1], c='orange', marker='.') plt.scatter(samples[:, 0], samples[:, 1], c='green', marker='+') viz.matplot(plt, win='contour', opts=dict(title='p(x):%d'%epoch)) def weights_init(m): if isinstance(m, nn.Linear): # m.weight.data.normal_(0.0, 0.02) nn.init.kaiming_normal_(m.weight) m.bias.data.fill_(0) def gradient_penalty(D, xr, xf): """ :param D: :param xr: :param xf: :return: """ LAMBDA = 0.3 # only constrait for Discriminator xf = xf.detach() xr = xr.detach() # [b, 1] => [b, 2] alpha = torch.rand(batchsz, 1).cuda() alpha = alpha.expand_as(xr) interpolates = alpha * xr + ((1 - alpha) * xf) interpolates.requires_grad_() disc_interpolates = D(interpolates) gradients = autograd.grad(outputs=disc_interpolates, inputs=interpolates, grad_outputs=torch.ones_like(disc_interpolates), create_graph=True, retain_graph=True, only_inputs=True)[0] gp = ((gradients.norm(2, dim=1) - 1) ** 2).mean() * LAMBDA return gp def main(): torch.manual_seed(23) np.random.seed(23) G = Generator().cuda() D = Discriminator().cuda() G.apply(weights_init) D.apply(weights_init) optim_G = optim.Adam(G.parameters(), lr=1e-3, betas=(0.5, 0.9)) optim_D = optim.Adam(D.parameters(), lr=1e-3, betas=(0.5, 0.9)) data_iter = data_generator() print('batch:', next(data_iter).shape) viz.line([[0,0]], [0], win='loss', opts=dict(title='loss', legend=['D', 'G'])) for epoch in range(50000): # 1. train discriminator for k steps for _ in range(5): x = next(data_iter) xr = torch.from_numpy(x).cuda() # [b] predr = (D(xr)) # max log(lossr) lossr = - (predr.mean()) # [b, 2] z = torch.randn(batchsz, 2).cuda() # stop gradient on G # [b, 2] xf = G(z).detach() # [b] predf = (D(xf)) # min predf lossf = (predf.mean()) # gradient penalty gp = gradient_penalty(D, xr, xf) loss_D = lossr + lossf + gp optim_D.zero_grad() loss_D.backward() # for p in D.parameters(): # print(p.grad.norm()) optim_D.step() # 2. train Generator z = torch.randn(batchsz, 2).cuda() xf = G(z) predf = (D(xf)) # max predf loss_G = - (predf.mean()) optim_G.zero_grad() loss_G.backward() optim_G.step() if epoch % 100 == 0: viz.line([[loss_D.item(), loss_G.item()]], [epoch], win='loss', update='append') generate_image(D, G, xr, epoch) print(loss_D.item(), loss_G.item()) if __name__ == '__main__': main()- 1
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- 原文地址：https://blog.csdn.net/Ashen_0nee/article/details/126189371
