python：神經網絡和深度學習

Question

我目前正在關注 Michael Nielsen 的神經網絡和深度學習介紹指南（鏈接），並被困在第 1 章。

我設置了所有內容並修復了從 python2 -> python3 的較小更改並運行了代碼，但是我在每個時期的價值保持不變。 我認為這意味着無論出於何種原因，權重和偏差都不會更新。

如指南中所述，我遵循它並創建了兩個文件，一個 mnist_loader，它從其他來源加載數據

關於在哪里修復的任何想法？

我目前正在運行最新的 python 3.10.2。

鏈接到 cmd 的圖像

我期望的是本章中給出的每個時代提升的價值

> Epoch 0: 9129 / 10000
> Epoch 1: 9295 / 10000
> Epoch 2: 9348 / 10000
> ...
> Epoch 27: 9528 / 10000
> Epoch 28: 9542 / 10000
> Epoch 29: 9534 / 10000

編輯：添加代碼

"""
mnist_loader
~~~~~~~~~~~~

A library to load the MNIST image data.  For details of the data
structures that are returned, see the doc strings for ``load_data``
and ``load_data_wrapper``.  In practice, ``load_data_wrapper`` is the
function usually called by our neural network code.
"""

# Libraries
# Standard library
import pickle
import gzip

# Third-party libraries
import numpy as np


def load_data():
"""Return the MNIST data as a tuple containing the training data,
the validation data, and the test data.

The ``training_data`` is returned as a tuple with two entries.
The first entry contains the actual training images.  This is a
numpy ndarray with 50,000 entries.  Each entry is, in turn, a
numpy ndarray with 784 values, representing the 28 * 28 = 784
pixels in a single MNIST image.

The second entry in the ``training_data`` tuple is a numpy ndarray
containing 50,000 entries.  Those entries are just the digit
values (0...9) for the corresponding images contained in the first
entry of the tuple.

The ``validation_data`` and ``test_data`` are similar, except
each contains only 10,000 images.

This is a nice data format, but for use in neural networks it's
helpful to modify the format of the ``training_data`` a little.
That's done in the wrapper function ``load_data_wrapper()``, see
below.
"""
    f = gzip.open("C:/Users/Tai/Documents/mnist/neural-networks-and-deep-learning/data/mnist.pkl.gz")
    training_data, validation_data, test_data = pickle.load(f, encoding="latin1")
    print(training_data)
    f.close()
    return (training_data, validation_data, test_data)


def load_data_wrapper():
"""Return a tuple containing ``(training_data, validation_data,
test_data)``. Based on ``load_data``, but the format is more
convenient for use in our implementation of neural networks.

In particular, ``training_data`` is a list containing 50,000
2-tuples ``(x, y)``.  ``x`` is a 784-dimensional numpy.ndarray
containing the input image.  ``y`` is a 10-dimensional
numpy.ndarray representing the unit vector corresponding to the
correct digit for ``x``.

``validation_data`` and ``test_data`` are lists containing 10,000
2-tuples ``(x, y)``.  In each case, ``x`` is a 784-dimensional
numpy.ndarry containing the input image, and ``y`` is the
corresponding classification, i.e., the digit values (integers)
corresponding to ``x``.

Obviously, this means we're using slightly different formats for
the training data and the validation / test data.  These formats
turn out to be the most convenient for use in our neural network
code."""
    tr_d, va_d, te_d = load_data()
    training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
    training_results = [vectorized_result(y) for y in tr_d[1]]
    training_data = list(zip(training_inputs, training_results))
    validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
    validation_data = list(zip(validation_inputs, va_d[1]))
    test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
    test_data = list(zip(test_inputs, te_d[1]))
    return (training_data, validation_data, test_data)


def vectorized_result(j):
"""Return a 10-dimensional unit vector with a 1.0 in the jth
position and zeroes elsewhere.  This is used to convert a digit
(0...9) into a corresponding desired output from the neural
network."""
    e = np.zeros((10, 1))
    e[j] = 1.0
    return e

和網絡的第二個代碼

import numpy as np
import random

"""Network is generating layers of nodes, first layer is the input nodes,
last layer is the output nodes
each layer have random number (gaussian distribution with mean 0 and
standard deviation 1)
applied for weights and bias, first layer has no bias
a network of net = Network([2,3,1]) has 2 input, 3 middle and 1 output 
nodes"""


class Network(object):

    def __init__(self, sizes):
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
        self.weights = [np.random.randn(y, x)
                    for x, y in zip(sizes[:-1], sizes[1:])]

# returns output of the network for node a
    def feedforward(self, a):
        for b, w in zip(self.biases, self.weights):
            a = sigmoid(np.dot(w, a) + b)

# stochastic gradiant descent
# Train the neural network using mini-batch stochastic gradient descent.
# training data: list of tuples (x, y) with input and desired output
# epochs: number of epoch to train for
# mini_batch_size: number of mini-batches to use when sampling
# eta: learning rate
# (optional) test data: evaluation of network after each epoch of
traning, print partial process
#       slows program down considerably
# each epoch random shuffle of training data, partitioning into mini-
batches of specified size
# for each mini_batch single step of gradient descent specified in
#       self.update_mini_batch(mini_batch, eta)
# update weights and biases according to a single iteration of gradient
descent

    def SGD(self, training_data, epochs, mini_batch_size, eta, test_data=None):
        if test_data: n_test = len(test_data)
        n = len(training_data)
        for j in range(epochs):
            random.shuffle(training_data)
            mini_batches = [
                training_data[k:k + mini_batch_size]
                for k in range(0, n, mini_batch_size)]
            for mini_batch in mini_batches:
                self.update_mini_batch(mini_batch, eta)
            if test_data:
                print(
                "Epoch {0}: {1} / {2}".format(
                    j, self.evaluate(test_data), n_test))
            else:
                print(
                "Epoch {0} complete".format(j))

# update network's weights and biases by applying gradient descent using
backpropagation
# to a single mini batch.
# most important line
#   delta_nabla_b, delta_nabla_w = self.backprop(x, y)
# self.backprop ensures the backpropagation of (x, y)

    def update_mini_batch(self, mini_batch, eta):
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        for x, y in mini_batch:
            delta_nabla_b, delta_nabla_w = self.backprop(x, y)
            nabla_b = [nb + dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
            nabla_w = [nw + dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
        self.weights = [w - (eta / len(mini_batch)) * nw
                        for w, nw in zip(self.weights, nabla_w)]
        self.biases = [b - (eta / len(mini_batch)) * nb
                       for b, nb in zip(self.biases, nabla_b)]

    def backprop(self, x, y):
    """Return a tuple ``(nabla_b, nabla_w)`` representing the
    gradient for the cost function C_x.  ``nabla_b`` and
    ``nabla_w`` are layer-by-layer lists of numpy arrays, similar
    to ``self.biases`` and ``self.weights``."""
    nabla_b = [np.zeros(b.shape) for b in self.biases]
    nabla_w = [np.zeros(w.shape) for w in self.weights]
    # feedforward
        activation = x
        activations = [x]  # list to store all the activations, layer by layer
        zs = []  # list to store all the z vectors, layer by layer
        for b, w in zip(self.biases, self.weights):
            z = np.dot(w, activation) + b
            zs.append(z)
            activation = sigmoid(z)
            activations.append(activation)
    # backward pass
        delta = self.cost_derivative(activations[-1], y) * \
                sigmoid_prime(zs[-1])
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
    # Note that the variable l in the loop below is used a little
    # differently to the notation in Chapter 2 of the book.  Here,
    # l = 1 means the last layer of neurons, l = 2 is the
    # second-last layer, and so on.  It's a renumbering of the
    # scheme in the book, used here to take advantage of the fact
    # that Python can use negative indices in lists.
        for l in range(2, self.num_layers):
            z = zs[-l]
            sp = sigmoid_prime(z)
            delta = np.dot(self.weights[-l + 1].transpose(), delta) * sp
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l - 1].transpose())
        return nabla_b, nabla_w

    def evaluate(self, test_data):
    """Return the number of test inputs for which the neural
    network outputs the correct result. Note that the neural
    network's output is assumed to be the index of whichever
    neuron in the final layer has the highest activation."""
    test_results = [(np.argmax(self.feedforward(x)), y)
                    for (x, y) in test_data]
    return sum(int(x == y) for (x, y) in test_results)

    @staticmethod
    def cost_derivative(output_activations, y):
    """Return the vector of partial derivatives \partial C_x /
    \partial a for the output activations."""
    return output_activations - y


# z is a vector, numpy automatically applies sigmoid onto each element of z
def sigmoid(z):
    return 1.0 / (1.0 + np.exp(-z))


# derivative of the sigmoid function
def sigmoid_prime(z):
    return sigmoid(z) * (1 - sigmoid(z))

Answer 1

由於此處的其他評論，我發現了錯誤，我錯過了代碼中的一行

在網絡中：

# returns output of the network for node a
def feedforward(self, a):
    for b, w in zip(self.biases, self.weights):
        a = sigmoid(np.dot(w, a) + b)
    return a

謝謝大家指出！