Mise en œuvre concise de la régression Softmax

Implémentation à l'aide de PyTorch facilite la tâche par rapport à une implémentation from scratch

import torch
import torchvision
from torch.utils import data
from torchvision import transforms
from torch import nn
#from IPython import display
from d2l import torch as d2l
import plotly.io as pio
pio.renderers.default = 'notebook'
from matplotlib import pyplot as plt
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

def accuracy(y_hat, y):  #@save
    """Calcul du nombre prédictions bien classées"""
    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
        y_hat = y_hat.argmax(axis=1)
    cmp = y_hat.type(y.dtype) == y
    return float(cmp.type(y.dtype).sum())


def evaluate_accuracy(net, data_iter):  #@save
    """Compute the accuracy for a model on a dataset."""
    if isinstance(net, torch.nn.Module):
        net.eval()  # Set the model to evaluation mode
    metric = Accumulator(2)  # No. of correct predictions, no. of predictions

    with torch.no_grad():
        for X, y in data_iter:
            metric.add(accuracy(net(X), y), y.numel())
    return metric[0] / metric[1]




class Accumulator:  #@save
    """For accumulating sums over `n` variables."""
    def __init__(self, n):
        self.data = [0.0] * n

    def add(self, *args):
        self.data = [a + float(b) for a, b in zip(self.data, args)]

    def reset(self):
        self.data = [0.0] * len(self.data)

    def __getitem__(self, idx):
        return self.data[idx]



def train_epoch_ch3(net, train_iter, loss, updater):  #@save
    """Boucle d'apprentissage"""
    # Set the model to training mode
    if isinstance(net, torch.nn.Module):
        net.train()
    # Sum of training loss, sum of training accuracy, no. of examples
    metric = Accumulator(3)
    for X, y in train_iter:
        # Compute gradients and update parameters
        y_hat = net(X)
        l = loss(y_hat, y)
        if isinstance(updater, torch.optim.Optimizer):
            # Using PyTorch in-built optimizer & loss criterion
            updater.zero_grad()
            l.sum().backward()
            updater.step()
        else:
            # Using custom built optimizer & loss criterion
            l.sum().backward()
            updater(X.shape[0])
        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    # Return training loss and training accuracy
    return metric[0] / metric[2], metric[1] / metric[2]


class Animator:  #@save
    """For plotting data in animation."""
    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,
                 ylim=None, xscale='linear', yscale='linear',
                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,
                 figsize=(3.5, 2.5)):
        # Incrementally plot multiple lines
        if legend is None:
            legend = []
        d2l.use_svg_display()
        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)
        if nrows * ncols == 1:
            self.axes = [self.axes, ]
        # Use a lambda function to capture arguments
        self.config_axes = lambda: d2l.set_axes(
            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
        self.X, self.Y, self.fmts = None, None, fmts

    def add(self, x, y):
        # Add multiple data points into the figure
        if not hasattr(y, "__len__"):
            y = [y]
        n = len(y)
        if not hasattr(x, "__len__"):
            x = [x] * n
        if not self.X:
            self.X = [[] for _ in range(n)]
        if not self.Y:
            self.Y = [[] for _ in range(n)]
        for i, (a, b) in enumerate(zip(x, y)):
            if a is not None and b is not None:
                self.X[i].append(a)
                self.Y[i].append(b)
        self.axes[0].cla()
        for x, y, fmt in zip(self.X, self.Y, self.fmts):
            self.axes[0].plot(x, y, fmt)
        self.config_axes()
        display.display(self.fig)
        display.clear_output(wait=True)


def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  #@save
    """Train a model"""
    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],
                        legend=['train loss', 'train acc', 'test acc'])
    for epoch in range(num_epochs):
        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
        test_acc = evaluate_accuracy(net, test_iter)
        animator.add(epoch + 1, train_metrics + (test_acc,))
    train_loss, train_acc = train_metrics
    assert train_loss < 0.5, train_loss
    assert train_acc <= 1 and train_acc > 0.7, train_acc
    assert test_acc <= 1 and test_acc > 0.7, test_acc




def predict_ch3(net, test_iter, n=50):  #@save
    """Predict labels"""
    for X, y in test_iter:
        break
    trues = d2l.get_fashion_mnist_labels(y)
    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))
    titles = [true +'\n' + pred for true, pred in zip(trues, preds)]
    d2l.show_images(
        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])

Découvertes du jeu de données

# `ToTensor` va convertir les images du format de stockage PIL au type float 32-bit
trans = transforms.ToTensor()
mnist_train = torchvision.datasets.FashionMNIST(
    root="../data", train=True, transform=trans, download=True)
mnist_test = torchvision.datasets.FashionMNIST(
    root="../data", train=False, transform=trans, download=True)

def get_fashion_mnist_labels(labels):  #@save
    """Return text labels for the Fashion-MNIST dataset."""
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]

def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  #@save
    """Plot a list of images."""
    figsize = (num_cols * scale, num_rows * scale)
    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
    axes = axes.flatten()
    for i, (ax, img) in enumerate(zip(axes, imgs)):
        if torch.is_tensor(img):
            # Tensor Image
            ax.imshow(img.numpy())
        else:
            # PIL Image
            ax.imshow(img)
        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        if titles:
            ax.set_title(titles[i])
    return axes

myiter = iter(data.DataLoader(mnist_train, batch_size=18))
X, y = next(myiter)
d2l.show_images(X.reshape(18, 28, 28), 3, 6, titles=get_fashion_mnist_labels(y));

Initialisation des paramètres du modèle, perte et algorithme d'optimisation

La couche de sortie de la régression softmax est une couche entièrement connectée. Par conséquent, pour mettre en œuvre notre modèle, il nous suffit d'ajouter une couche entièrement connectée avec $10$ sorties à notre séquence de couches. Ici encore, la déclaration en séquence n'est pas vraiment nécessaire, mais autant en prendre l'habitude puisqu'il sera omniprésent lors de la mise en œuvre de modèles de deep learning. Encore une fois, nous initialisons les poids au hasard avec une moyenne de $0$ et un écart type de $0.01$.

# PyTorch does not implicitly reshape the inputs. Thus we define the flatten
# layer to reshape the inputs before the linear layer in our network
net = nn.Sequential(nn.Flatten(), nn.Linear(784, 10))
def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01)

net.apply(init_weights)

loss = nn.CrossEntropyLoss()

trainer = torch.optim.SGD(net.parameters(), lr=0.01)

Apprentissage

#num_epochs = 10
#train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

Mise en œuvre concise des perceptrons multicouches

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.ReLU(),
                    nn.Linear(256, 128),
                    nn.ReLU(),
                    nn.Linear(128, 10))

def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01)

net.apply(init_weights);

batch_size, lr, num_epochs = 64, 0.01, 50
loss = nn.CrossEntropyLoss()
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
#train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

Sans la fonction train_ch3

metric_tr = Accumulator(3)

for epoch in range(num_epochs):
    for X, y in train_iter:
        y_hat = net(X)
        l = loss(y_hat ,y)
        trainer.zero_grad()
        l.backward()
        trainer.step()
        metric_tr.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    #l = loss(net(features), labels)accuracy(y_hat, y)
    print("train loss : " + str(metric_tr[0] / metric_tr[2]) + "  train accuracy :" + str(metric_tr[1] / metric_tr[2]))

net.eval()  # Set the model to evaluation mode
metric = Accumulator(2)  # No. of correct predictions, no. of predictions
with torch.no_grad():
    for X, y in test_iter:
        metric.add(accuracy(net(X), y), y.numel())
    
print("test accuracy :" + str(metric[0] / metric[1]))