分类器和 Numpy 数组

Question

from __future__ import print_function

from builtins import range
from builtins import object
import numpy as np
import matplotlib.pyplot as plt
from past.builtins import xrange

class TwoLayerNet(object):
    """
    A two-layer fully-connected neural network. The net has an input dimension of
    D* (correction), a hidden layer dimension of H, and performs classification over C classes.
    We train the network with a softmax loss function and L2 regularization on the
    weight matrices. The network uses a ReLU nonlinearity after the first fully
    connected layer.
    In other words, the network has the following architecture:
    input - fully connected layer - ReLU - fully connected layer - softmax
    The outputs of the second fully-connected layer are the scores for each class.
    """

    def __init__(self, input_size, hidden_size, output_size, std=1e-4):
        """
        Initialize the model. Weights are initialized to small random values and
        biases are initialized to zero. Weights and biases are stored in the
        variable self.params, which is a dictionary with the following keys:
        W1: First layer weights; has shape (D, H)
        b1: First layer biases; has shape (H,)
        W2: Second layer weights; has shape (H, C)
        b2: Second layer biases; has shape (C,)
        Inputs:
        - input_size: The dimension D of the input data.
        - hidden_size: The number of neurons H in the hidden layer.
        - output_size: The number of classes C.
        """
        self.params = {}
        self.params['W1'] = std * np.random.randn(input_size, hidden_size)
        self.params['b1'] = np.zeros(hidden_size)
        self.params['W2'] = std * np.random.randn(hidden_size, output_size)
        self.params['b2'] = np.zeros(output_size)

    def loss(self, X, y=None, reg=0.0):
        """
        Compute the loss and gradients for a two layer fully connected neural
        network.
        Inputs:
        - X: Input data of shape (N, D). Each X[i] is a training sample.
        - y: Vector of training labels. y[i] is the label for X[i], and each y[i] is
          an integer in the range 0 <= y[i] < C. This parameter is optional; if it
          is not passed then we only return scores, and if it is passed then we
          instead return the loss and gradients.
        - reg: Regularization strength.
        Returns:
        If y is None, return a matrix scores of shape (N, C) where scores[i, c] is
        the score for class c on input X[i].
        If y is not None, instead return a tuple of:
        - loss: Loss (data loss and regularization loss) for this batch of training
          samples.
        - grads: Dictionary mapping parameter names to gradients of those parameters
          with respect to the loss function; has the same keys as self.params.
        """
        # Unpack variables from the params dictionary
        W1, b1 = self.params['W1'], self.params['b1']
        W2, b2 = self.params['W2'], self.params['b2']
        N, D = X.shape

        # Compute the forward pass
        scores = None
        #############################################################################
        # TODO: Perform the forward pass, computing the class scores for the input. #
        # Store the result in the scores variable, which should be an array of      #
        # shape (N, C).                                                             #
        #############################################################################
        # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        # perform the forward pass and compute the class scores for the input
        # input - fully connected layer - ReLU - fully connected layer - softmax
        
        # define lamba function for relu
        relu = lambda x: np.maximum(0, x)

        # a1 = X x W1 = (N x D) x (D x H) = N x H
        a1 = relu(X.dot(W1) + b1) # activations of fully connected layer #1

        # store the result in the scores variable, which should be an array of
        # shape (N, C).
        # scores = a1 x W2 = (N x H) x (H x C) = N x C
        scores = a1.dot(W2) + b2 # output of softmax

        # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        # If the targets are not given then jump out, we're done
        if y is None:
            return scores

        # Compute the loss
        loss = None
        #############################################################################
        # TODO: Finish the forward pass, and compute the loss. This should include  #
        # both the data loss and L2 regularization for W1 and W2. Store the result  #
        # in the variable loss, which should be a scalar. Use the Softmax           #
        # classifier loss.                                                          #
        #############################################################################
        # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        # shift values for 'scores' for numeric reasons (over-flow cautious)
        # figure out the max score across all classes
        # scores.shape is N x C
        scores -= scores.max(axis = 1, keepdims = True)

        # probs.shape is N x C
        probs = np.exp(scores)/np.sum(np.exp(scores), axis = 1, keepdims = True)

        loss = -np.log(probs[np.arange(N), y])

        # loss is a single number
        loss = np.sum(loss)   

        # Right now the loss is a sum over all training examples, but we want it
        # to be an average instead so we divide by N.
        loss /= N

        # Add regularization to the loss.
        loss += reg * (np.sum(W1 * W1) + np.sum(W2 * W2))

        # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        # Backward pass: compute gradients
        grads = {}
        #############################################################################
        # TODO: Compute the backward pass, computing the derivatives of the weights #
        # and biases. Store the results in the grads dictionary. For example,       #
        # grads['W1'] should store the gradient on W1, and be a matrix of same size #
        #############################################################################
        # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        # since dL(i)/df(k) = p(k) - 1 (if k = y[i]), where f is a vector of scores for the given example
        # i is the training sample and k is the class
        dscores = probs.reshape(N, -1) # dscores is (N x C)
        dscores[np.arange(N), y] -= 1

        # since scores = a1.dot(W2), we get dW2 by multiplying a1.T and dscores
        # W2 is H x C so dW2 should also match those dimensions
        # a1.T x dscores = (H x N) x (N x C) = H x C
        dW2 = np.dot(a1.T, dscores)

        # Right now the gradient is a sum over all training examples, but we want it
        # to be an average instead so we divide by N.
        dW2 /= N

        # b2 gradient: sum dscores over all N and C
        db2 = dscores.sum(axis = 0)/N

        # since a1 = X.dot(W1), we get dW1 by multiplying X.T and da1
        # W1 is D x H so dW1 should also match those dimensions
        # X.T x da1 = (D x N) x (N x H) = D x H

        # first get da1 using scores = a1.dot(W2)
        # a1 is N x H so da1 should also match those dimensions
        # dscores x W2.T = (N x C) x (C x H) = N x H
        da1 = dscores.dot(W2.T)
        da1[a1 == 0] = 0 # set gradient of units that did not activate to 0
        dW1 = X.T.dot(da1)

        # Right now the gradient is a sum over all training examples, but we want it
        # to be an average instead so we divide by N.
        dW1 /= N        

        # b1 gradient: sum da1 over all N and H
        db1 = da1.sum(axis = 0)/N        

        # Add regularization loss to the gradient
        dW1 += 2 * reg * W1     
        dW2 += 2 * reg * W2     

        grads = {'W1': dW1, 'b1': db1, 'W2': dW2, 'b2': db2}

        # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        return loss, grads

    def train(self, X, y, X_val, y_val,
              learning_rate=1e-3, learning_rate_decay=0.95,
              reg=5e-6, num_iters=100,
              batch_size=200, verbose=False):
        """
        Train this neural network using stochastic gradient descent.
        Inputs:
        - X: A numpy array of shape (N, D) giving training data.
        - y: A numpy array f shape (N,) giving training labels; y[i] = c means that
          X[i] has label c, where 0 <= c < C.
        - X_val: A numpy array of shape (N_val, D) giving validation data.
        - y_val: A numpy array of shape (N_val,) giving validation labels.
        - learning_rate: Scalar giving learning rate for optimization.
        - learning_rate_decay: Scalar giving factor used to decay the learning rate
          after each epoch.
        - reg: Scalar giving regularization strength.
        - num_iters: Number of steps to take when optimizing.
        - batch_size: Number of training examples to use per step.
        - verbose: boolean; if true print progress during optimization.
        """
        num_train = X.shape[0]
        iterations_per_epoch = max(num_train / batch_size, 1)

        # Use SGD to optimize the parameters in self.model
        loss_history = []
        train_acc_history = []
        val_acc_history = []

        for it in range(num_iters):
            X_batch = None
            y_batch = None

            #########################################################################
            # TODO: Create a random minibatch of training data and labels, storing  #
            # them in X_batch and y_batch respectively.                             #
            #########################################################################
            # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

            # generate random indices
            indices = np.random.choice(num_train, batch_size)
            X_batch, y_batch = X[indices], y[indices]

            # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

            # Compute loss and gradients using the current minibatch
            loss, grads = self.loss(X_batch, y=y_batch, reg=reg)
            loss_history.append(loss)

            #########################################################################
            # TODO: Use the gradients in the grads dictionary to update the         #
            # parameters of the network (stored in the dictionary self.params)      #
            # using stochastic gradient descent. You'll need to use the gradients   #
            # stored in the grads dictionary defined above.                         #
            #########################################################################
            # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

            self.params['W1'] -= learning_rate * grads['W1']
            self.params['W2'] -= learning_rate * grads['W2']
            self.params['b1'] -= learning_rate * grads['b1']
            self.params['b2'] -= learning_rate * grads['b2']

            # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

            if verbose and it % 100 == 0:
                print('iteration %d / %d: loss %f' % (it, num_iters, loss))

            # Every epoch, check train and val accuracy and decay learning rate.
            if it % iterations_per_epoch == 0:
                # Check accuracy
                train_acc = (self.predict(X_batch) == y_batch).mean()
                val_acc = (self.predict(X_val) == y_val).mean()
                train_acc_history.append(train_acc)
                val_acc_history.append(val_acc)

                # Decay learning rate
                learning_rate *= learning_rate_decay

        return {
          'loss_history': loss_history,
          'train_acc_history': train_acc_history,
          'val_acc_history': val_acc_history,
        }

    def predict(self, X):
        """
        Use the trained weights of this two-layer network to predict labels for
        data points. For each data point we predict scores for each of the C
        classes, and assign each data point to the class with the highest score.
        Inputs:
        - X: A numpy array of shape (N, D) giving N D-dimensional data points to
          classify.
        Returns:
        - y_pred: A numpy array of shape (N,) giving predicted labels for each of
          the elements of X. For all i, y_pred[i] = c means that X[i] is predicted
          to have class c, where 0 <= c < C.
        """
        y_pred = None

        ###########################################################################
        # TODO: Implement this function; it should be VERY simple!                #
        ###########################################################################
        # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
        
        # define lamba function for relu
        relu = lambda x: np.maximum(0, x)
        
        # activations of fully connected layer #1
        a1 = relu(X.dot(self.params['W1']) + self.params['b1']) 

        # output of softmax
        # scores = a1 x W2 = (N x H) x (H x C) = N x C
        scores = a1.dot(self.params['W2']) + self.params['b2']
        y_pred = np.argmax(scores, axis = 1)

        # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

        return y_pred

我关于上面代码的问题是

loss = -np.log(probs[np.arange(N), y])

我从代码中了解到Probs是N C，y是1 C。首先是y的形状1*C？上面的代码一定是正确的，因为我是从github上的可靠来源获取的。但是当我尝试时非常相似我的电脑出现问题我收到以下错误是我电脑中的代码。 请解释我上面提到的损失中发生了什么，我有尺寸问题。 在此处输入图像描述

我在上面提到了我尝试过的与该问题非常相关的内容。 在这里输入图片描述我也把它放在这里。

Answer 1

因为你的数组a的大小是 (2, 2)

print(a.shape)

(2, 2)

这意味着索引是0和1 ，但在数组y中有一个2 ，您尝试在其中切片索引为 2 的 2*2 数组，它超出了它的范围。

只需更改您的y = np.array([[0, 1]])或y = np.array([[0, 0]])或y = np.array([[1, 1]]) ，但不指数的通过范围。