引言

虽然我们经常将大部分时间花在训练和测试模型上，但我们这样做的核心原因是希望有一个能够接受新输入并生成期望输出的模型。这通常需要多次尝试训练最优模型，保存该模型，并加载已保存的模型进行推断或预测。

以Fashion MNIST分类为例，我们希望加载一个已训练的模型，展示从未见过的图像，并让它预测正确的分类。为此，我们将在Model类中添加一个新的predict方法：

python">    # Predicts on the samples
    def predict(self, X, *, batch_size=None):

请注意，我们使用可能的batch_size对$X$进行预测。这意味着所有预测，包括仅对一个样本的预测，仍将作为样本列表输入，以NumPy数组的形式，其中第一维是样本列表，第二维是样本数据。例如，如果我们想对一张图像进行预测，仍然需要创建一个NumPy数组，模拟一个包含单个样本的列表——形状为(1, 784)，其中1表示该单个样本，784表示样本中的特征数量（每张图像的像素数）。与evaluate方法类似，我们将计算计划进行的步骤数量：

python">		# Default value if batch size is not being set
        prediction_steps = 1
        # Calculate number of steps
        if batch_size is not None:
            prediction_steps = len(X) // batch_size
            # Dividing rounds down. If there are some remaining
            # data, but not a full batch, this won't include it
            # Add `1` to include this not full batch
            if prediction_steps * batch_size < len(X):
                prediction_steps += 1

然后创建一个列表，我们将在其中填充预测结果：

python">        # Model outputs
        output = []

我们将遍历批次，将样本传递到网络中进行预测，并使用预测结果填充输出：

python">        # Iterate over steps
        for step in range(prediction_steps):
            # If batch size is not set -
            # train using one step and full dataset
            if batch_size is None:
                batch_X = X
            # Otherwise slice a batch
            else:
                batch_X = X[step*batch_size:(step+1)*batch_size]
            # Perform the forward pass
            batch_output = self.forward(batch_X, training=False)
            # Append batch prediction to the list of predictions
            output.append(batch_output)

运行此方法后，输出是一个批次预测的列表。每个预测都是一个NumPy数组，是对输入数据数组中的一批样本进行预测所得的部分结果。任何将使用我们模型推断输出的应用程序或程序，只需传入一个样本列表并获得一个预测列表（两者均以之前提到的NumPy数组形式表示）。

由于我们不专注于训练，在预测中使用批次只是为了确保模型能够适应内存，但我们获得的返回结果也是批次预测的形式。以下是一个简单的示例：

python">import numpy as np

output = []
b = np.array([[1, 2], [3, 4]])
output.append(b)
b = np.array([[5, 6], [7, 8]])
output.append(b)
b = np.array([[9, 10], [11, 12]])
output.append(b)

print(output)

python">>>>
[array([[1, 2],
       [3, 4]]), array([[5, 6],
       [7, 8]]), array([[ 9, 10],
       [11, 12]])]

在这个示例中，我们看到输出的批次大小为2，总共有6个样本。输出是一个数组列表，每个数组包含一批预测结果。而我们希望得到的是一个包含所有预测结果的列表，而不是分批次的结果。为此，我们将使用NumPy的vstack方法：

python">import numpy as np

output = []
b = np.array([[1, 2], [3, 4]])
output.append(b)
b = np.array([[5, 6], [7, 8]])
output.append(b)
b = np.array([[9, 10], [11, 12]])
output.append(b)
output = np.vstack(output)

print(output)

python">>>>
[[ 1  2]
 [ 3  4]
 [ 5  6]
 [ 7  8]
 [ 9 10]
 [11 12]]

它接收一个对象列表，并在可能的情况下将它们堆叠起来，创建一个同质数组。这是当我们传入一个样本列表时，predict方法返回的更理想的形式。使用纯Python，我们可能只是每一步将结果添加到列表中：

python">output = []
b = [[1, 2], [3, 4]]
output += b
b = [[5, 6], [7, 8]]
output += b
b = [[9, 10], [11, 12]]
output += b

print(output)

python">>>>
[[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]]

我们将结果添加到一个列表中，并在最后将它们堆叠起来，而不是在每个批次中将结果附加到NumPy数组中，以避免性能损失。与纯Python不同，NumPy是用C语言编写的，其数据对象在内存中的创建方式有所不同。这意味着没有一种简单的方法可以将数据添加到现有的NumPy数组中，除了合并两个数组并将结果保存为一个新数组。但这会导致性能损失，因为随着预测的进行，结果数组会变得越来越大。

最快且最优化的方式是将NumPy数组附加到一个列表中，当我们收集了所有部分结果后，再一次性将它们垂直堆叠。我们将在返回的输出末尾添加np.vstack：

python">        # Stack and return results
        return np.vstack(output)

整个predict方法：

python">    # Predicts on the samples
    def predict(self, X, *, batch_size=None):
        # Default value if batch size is not being set
        prediction_steps = 1
        # Calculate number of steps
        if batch_size is not None:
            prediction_steps = len(X) // batch_size
            # Dividing rounds down. If there are some remaining
            # data, but not a full batch, this won't include it
            # Add `1` to include this not full batch
            if prediction_steps * batch_size < len(X):
                prediction_steps += 1
        # Model outputs
        output = []
        # Iterate over steps
        for step in range(prediction_steps):
            # If batch size is not set -
            # train using one step and full dataset
            if batch_size is None:
                batch_X = X
            # Otherwise slice a batch
            else:
                batch_X = X[step*batch_size:(step+1)*batch_size]
            # Perform the forward pass
            batch_output = self.forward(batch_X, training=False)
            # Append batch prediction to the list of predictions
            output.append(batch_output)
        # Stack and return results
        return np.vstack(output)

现在我们可以加载模型并测试预测功能：

python"># Create dataset
X, y, X_test, y_test = create_data_mnist('fashion_mnist_images')

# Scale and reshape samples
X_test = (X_test.reshape(X_test.shape[0], -1).astype(np.float32) - 127.5) / 127.5

# Load the model
model = Model.load('fashion_mnist.model')

# Predict on the first 5 samples from validation dataset
# and print the result
confidences = model.predict(X_test[:5])
print(confidences)

python">>>>
[[9.47225571e-01 2.52310792e-06 4.26566275e-03 1.14208065e-04
  5.60502713e-07 1.03709858e-07 4.83857058e-02 9.79777681e-09
  5.65434220e-06 6.24423624e-09]
 [7.76644230e-01 5.56645566e-04 1.82817469e-03 2.07056459e-02
  4.91867031e-05 1.62446213e-07 2.00205415e-01 2.78994799e-10
  1.05146655e-05 1.24752910e-08]
 [9.96223211e-01 3.88239574e-09 4.89091559e-04 1.81238247e-05
  1.49976700e-06 7.25310034e-10 3.26809939e-03 1.81895521e-09
  1.49130344e-08 6.69718003e-10]
 [9.98704791e-01 1.77900521e-08 5.24727257e-05 4.83505391e-06
  1.02738902e-07 5.13466492e-10 1.23780814e-03 9.31118738e-09
  2.84552026e-09 6.17795770e-09]
 [8.52106988e-01 5.32999422e-07 4.70034749e-04 1.28197280e-04
  9.89067530e-07 9.23007946e-08 1.47292748e-01 8.85645761e-08
  1.79957738e-07 2.20160018e-07]]

看起来工作正常！经过大量时间训练并找到最佳超参数后，人们常见的问题是如何实际使用模型。需要提醒的是，输出中的每个子数组是一个置信向量，其中包含每个类别的置信度指标。

在这种情况下，我们需要做的第一件事是获取这些置信向量的argmax值。回想一下，我们使用的是softmax分类器，因此这个神经网络尝试拟合的是独热向量（one-hot vectors），其中正确的类别用1表示，其他类别用0表示。在进行推断时，通常很难达到如此完美的结果，但我们通过输出中最高值对应的索引来确定模型的预测类别；这就是我们使用argmax的原因。

虽然我们可以编写代码来实现这一点，但实际上我们已经在所有激活函数类中添加了一个predictions方法来完成这个功能：

python"># Softmax activation
class Activation_Softmax:
	...
    # Calculate predictions for outputs
    def predictions(self, outputs):
        return np.argmax(outputs, axis=1)

我们还在模型中设置了一个属性，用于存储输出层的激活函数，这意味着我们可以通过以下方式通用地获取预测结果：

python"># Load the model
model = Model.load('fashion_mnist.model')

# Predict on the first 5 samples from validation dataset
# and print the result
confidences = model.predict(X_test[:5])
predictions = model.output_layer_activation.predictions(confidences)
print(predictions)

# Print first 5 labels
print(y_test[:5])

python">>>>
[0 0 0 0 0]
[0 0 0 0 0]

在这个例子中，我们的模型预测的全是“类别0”，而我们的测试标签也全是类别0。由于对测试数据进行打乱并不是必须的，因此我们从未对其进行打乱，所以它们的顺序与训练数据一样保持原始顺序。这解释了为什么所有预测结果都是0。

在实际应用中，我们并不关心某个类别的编号，而是想知道它具体是什么。在这个例子中，类别编号直接映射到名称，因此我们在代码中添加以下字典：

python">fashion_mnist_labels = {
    0: 'T-shirt/top',
    1: 'Trouser',
    2: 'Pullover',
    3: 'Dress',
    4: 'Coat',
    5: 'Sandal',
    6: 'Shirt',
    7: 'Sneaker',
    8: 'Bag',
    9: 'Ankle boot'
    }

然后，我们就可以通过执行来获得字符串分类：

python">for prediction in predictions:
    print(fashion_mnist_labels[prediction])

python">>>>
T-shirt/top
T-shirt/top
T-shirt/top
T-shirt/top
T-shirt/top

这很好，但我们仍然需要实际对某些内容进行预测，而不是使用训练数据。在讨论深度学习时，训练步骤通常成为关注的重点；我们希望看到准确率和损失指标表现良好！对于旨在向人们展示如何使用框架的教程来说，专注于训练效果很好，但我们发现的一个更大痛点是如何将模型应用于生产环境，或者只是对从外部获取的新数据进行预测（尤其是外部数据很少会被格式化成与你的训练数据完全匹配的形式）。

目前，我们有一个在服装项目上训练的模型，因此我们需要一些真正的新样本。幸运的是，你很可能是一个拥有衣服的人；如果是这样，你可以从拍摄这些衣服的照片开始。如果不是，可以使用以下示例照片：

你也可以尝试手绘类似这样的样本。一旦你有了希望在生产环境中使用的新图像/样本，就需要以与训练样本相同的方式对它们进行预处理。有些更改相对难以遗忘，比如图像分辨率或颜色通道数；如果我们不做这些处理，程序会报错。

让我们通过加载图像来开始预处理。我们将使用cv2包来读取图像（记得保存tshirt.png和pants.png这两张图片到本地文件）：

python">import cv2

image_data = cv2.imread('tshirt.png', cv2.IMREAD_UNCHANGED)

我们可以查看图像：

python">import matplotlib.pyplot as plt

plt.imshow(cv2.cvtColor(image_data, cv2.COLOR_BGR2RGB))
plt.show()

请注意，我们使用cv2.cvtColor是因为OpenCV默认使用BGR（蓝、绿、红像素值）颜色格式，而matplotlib使用RGB（红、绿、蓝）格式，因此我们需要转换颜色映射来显示图像。

首先，我们将以灰度模式读取这张图像，而不是RGB模式。这与Fashion MNIST图像的处理不同，后者已经是灰度图像，并且我们在使用cv2.imread()时传入了cv2.IMREAD_UNCHANGED参数，告知OpenCV我们的意图是读取灰度且不变的图像。然而，这里我们有一张彩色图像，cv2.IMREAD_UNCHANGED参数不起作用，因为“不变”意味着包含所有颜色；因此，我们将使用cv2.IMREAD_GRAYSCALE来强制在读取图像时进行灰度处理：

python">import cv2
image_data = cv2.imread('tshirt.png', cv2.IMREAD_GRAYSCALE)

然后我们就可以显示它了：

python">import matplotlib.pyplot as plt
plt.imshow(image_data, cmap='gray')
plt.show()

请注意，我们在使用plt.imshow()时，通过将'gray'参数传递给cmap参数来使用灰度颜色映射。结果是一张灰度图像：

接下来，我们将调整图像大小，使其与训练数据相同，为28x28的分辨率：

python">image_data = cv2.resize(image_data, (28, 28))

然后，我们就会显示这张调整过大小的图片：

python">plt.imshow(image_data, cmap='gray')
plt.show()

接下来，我们将对图像进行展平和缩放操作。虽然缩放操作与训练数据相同，但展平操作略有不同；我们这里不是一组图像，而是一张单独的图像。正如之前解释的，单张图像必须作为包含该图像的列表传入。我们通过对图像应用.reshape(1, -1)来展平，其中参数1表示样本数量，-1将图像展平成长度为784的向量。这将生成一个1x784的数组，其中包含我们的一个样本和784个特征（即28x28像素）：

python">image_data = (image_data.reshape(1, -1).astype(np.float32) - 127.5) / 127.5

现在，我们可以加载模型并对图像数据进行预测：

python"># Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)

到此为止，我们的代码已经完成了加载、预处理和预测：

python">fashion_mnist_labels = {
    0: 'T-shirt/top',
    1: 'Trouser',
    2: 'Pullover',
    3: 'Dress',
    4: 'Coat',
    5: 'Sandal',
    6: 'Shirt',
    7: 'Sneaker',
    8: 'Bag',
    9: 'Ankle boot'
    }

# Read an image
image_data = cv2.imread('tshirt.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Reshape and scale pixel data
image_data = (image_data.reshape(1, -1).astype(np.float32) - 127.5) / 127.5

# Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)

请注意，我们使用predictions[0]是因为我们以列表的形式传入了一张图像，模型返回的是包含单个预测的列表。

只有一个问题……

python">>>>
Ankle boot

有什么问题？让我们将当前预处理的图像与训练数据进行比较：

python">mnist_image = cv2.imread('fashion_mnist_images/train/0/0000.png', cv2.IMREAD_UNCHANGED)
plt.imshow(mnist_image, cmap='gray')
plt.show()

现在，我们将原始图像和示例训练图像与我们的图像进行比较：

我们使用的训练数据是颜色反转的（即背景是黑色而不是白色，等等）。为了在缩放之前反转我们的图像，我们可以直接使用像素数学，而不是使用OpenCV。我们将所有像素值从最大像素值255中减去。例如，值为0的像素将变为$255-0=255$，值为255的像素将变为$255-255=0$。

python">image_data = 255 - image_data

稍作改动后，我们的预测代码就变成了：

python"># Read an image
image_data = cv2.imread('tshirt.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Invert image colors
image_data = 255 - image_data
# Reshape and scale pixel data
image_data = (image_data.reshape(1, -1).astype(np.float32) - 127.5) / 127.5
# Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)

python">>>>
T-shirt/top

现在它可以正常工作了！它现在能正常工作而之前不能的原因在于Dense层的工作方式——它们学习特征（在这种情况下是像素）值及其之间的关联性。这与卷积层形成对比，卷积层被训练来发现和理解图像上的特征（不是作为数据输入节点的特征，而是实际的特征/属性，例如线条和曲线）。

由于像素值差异很大，模型在这种情况下错误地做出了“猜测”。而卷积层可能在这种情况下能够正确预测，因为它可以直接处理图像特征。

试试裤子：

python">image_data = cv2.imread('pants.png', cv2.IMREAD_UNCHANGED)
plt.imshow(cv2.cvtColor(image_data, cv2.COLOR_BGR2RGB))
plt.show()

现在我们进行预处理：

python"># Read an image
image_data = cv2.imread('pants.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Invert image colors
image_data = 255 - image_data

看看我们有什么：

plt.imshow(image_data, cmap=‘gray’)
plt.show()

编写我们的代码：

python"># Label index to label name relation
fashion_mnist_labels = {
    0: 'T-shirt/top',
    1: 'Trouser',
    2: 'Pullover',
    3: 'Dress',
    4: 'Coat',
    5: 'Sandal',
    6: 'Shirt',
    7: 'Sneaker',
    8: 'Bag',
    9: 'Ankle boot'
    }
# Read an image
image_data = cv2.imread('pants.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Invert image colors
image_data = 255 - image_data
# Reshape and scale pixel data
image_data = (image_data.reshape(1, -1).astype(np.float32) -
127.5) / 127.5
# Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)

python">>>>
Trouser

又一次成功！我们现在已经为模型编写了最后一个功能，这也标志着本书中所涵盖主题的完整闭环。

完整代码：

python">import numpy as np
import cv2
import os
import pickle
import copy
import matplotlib.pyplot as plt

# Loads a MNIST dataset
def load_mnist_dataset(dataset, path):
    # Scan all the directories and create a list of labels
    labels = os.listdir(os.path.join(path, dataset))
    # Create lists for samples and labels
    X = []
    y = []
    # For each label folder
    for label in labels:
        # And for each image in given folder
        for file in os.listdir(os.path.join(path, dataset, label)):
            # Read the image
            image = cv2.imread(os.path.join(path, dataset, label, file), cv2.IMREAD_UNCHANGED)
            # And append it and a label to the lists
            X.append(image)
            y.append(label)
    # Convert the data to proper numpy arrays and return
    return np.array(X), np.array(y).astype('uint8')


# MNIST dataset (train + test)
def create_data_mnist(path):
    # Load both sets separately
    X, y = load_mnist_dataset('train', path)
    X_test, y_test = load_mnist_dataset('test', path)
    # And return all the data
    return X, y, X_test, y_test


import numpy as np
import nnfs
from nnfs.datasets import sine_data, spiral_data
import sys

nnfs.init()

# Dense layer
class Layer_Dense:
    # Layer initialization
    def __init__(self, n_inputs, n_neurons,
                 weight_regularizer_l1=0, weight_regularizer_l2=0,
                 bias_regularizer_l1=0, bias_regularizer_l2=0):
        # Initialize weights and biases
        # self.weights = 0.01 * np.random.randn(n_inputs, n_neurons)
        self.weights = 0.1 * np.random.randn(n_inputs, n_neurons)
        self.biases = np.zeros((1, n_neurons))
        # Set regularization strength
        self.weight_regularizer_l1 = weight_regularizer_l1
        self.weight_regularizer_l2 = weight_regularizer_l2
        self.bias_regularizer_l1 = bias_regularizer_l1
        self.bias_regularizer_l2 = bias_regularizer_l2
    
    # Forward pass
    def forward(self, inputs, training):
        # Remember input values
        self.inputs = inputs
        # Calculate output values from inputs, weights and biases
        self.output = np.dot(inputs, self.weights) + self.biases
        
    # Backward pass
    def backward(self, dvalues):
        # Gradients on parameters
        self.dweights = np.dot(self.inputs.T, dvalues)
        self.dbiases = np.sum(dvalues, axis=0, keepdims=True)
        # Gradients on regularization
        # L1 on weights
        if self.weight_regularizer_l1 > 0:
            dL1 = np.ones_like(self.weights)
            dL1[self.weights < 0] = -1
            self.dweights += self.weight_regularizer_l1 * dL1
        # L2 on weights
        if self.weight_regularizer_l2 > 0:
            self.dweights += 2 * self.weight_regularizer_l2 * self.weights
        # L1 on biases
        if self.bias_regularizer_l1 > 0:
            dL1 = np.ones_like(self.biases)
            dL1[self.biases < 0] = -1
            self.dbiases += self.bias_regularizer_l1 * dL1
        # L2 on biases
        if self.bias_regularizer_l2 > 0:
            self.dbiases += 2 * self.bias_regularizer_l2 * self.biases
        # Gradient on values
        self.dinputs = np.dot(dvalues, self.weights.T)
    
    # Retrieve layer parameters
    def get_parameters(self):
        return self.weights, self.biases
    
    # Set weights and biases in a layer instance
    def set_parameters(self, weights, biases):
        self.weights = weights
        self.biases = biases
    
    
# Dropout
class Layer_Dropout:        
    # Init
    def __init__(self, rate):
        # Store rate, we invert it as for example for dropout
        # of 0.1 we need success rate of 0.9
        self.rate = 1 - rate
        
    # Forward pass
    def forward(self, inputs, training):
        # Save input values
        self.inputs = inputs
        # If not in the training mode - return values
        if not training:
            self.output = inputs.copy()
            return
        # Generate and save scaled mask
        self.binary_mask = np.random.binomial(1, self.rate, size=inputs.shape) / self.rate
        # Apply mask to output values
        self.output = inputs * self.binary_mask
        
    # Backward pass
    def backward(self, dvalues):
        # Gradient on values
        self.dinputs = dvalues * self.binary_mask
        

# Input "layer"
class Layer_Input:
    # Forward pass
    def forward(self, inputs, training):
        self.output = inputs

        
# ReLU activation
class Activation_ReLU:  
    # Forward pass
    def forward(self, inputs, training):
        # Remember input values
        self.inputs = inputs
        # Calculate output values from inputs
        self.output = np.maximum(0, inputs)
        
    # Backward pass
    def backward(self, dvalues):
        # Since we need to modify original variable,
        # let's make a copy of values first
        self.dinputs = dvalues.copy()
        # Zero gradient where input values were negative
        self.dinputs[self.inputs <= 0] = 0
        
    # Calculate predictions for outputs
    def predictions(self, outputs):
        return outputs
        
        
# Softmax activation
class Activation_Softmax:
    # Forward pass
    def forward(self, inputs, training):
        # Remember input values
        self.inputs = inputs
        # Get unnormalized probabilities
        exp_values = np.exp(inputs - np.max(inputs, axis=1, keepdims=True))
        # Normalize them for each sample
        probabilities = exp_values / np.sum(exp_values, axis=1, keepdims=True)
        self.output = probabilities
        
    # Backward pass
    def backward(self, dvalues):
        # Create uninitialized array
        self.dinputs = np.empty_like(dvalues)
        # Enumerate outputs and gradients
        for index, (single_output, single_dvalues) in enumerate(zip(self.output, dvalues)):
            # Flatten output array
            single_output = single_output.reshape(-1, 1)
            # Calculate Jacobian matrix of the output and
            jacobian_matrix = np.diagflat(single_output) - np.dot(single_output, single_output.T)
            # Calculate sample-wise gradient
            # and add it to the array of sample gradients
            self.dinputs[index] = np.dot(jacobian_matrix, single_dvalues)
            
    # Calculate predictions for outputs
    def predictions(self, outputs):
        return np.argmax(outputs, axis=1)
        
      
# Sigmoid activation
class Activation_Sigmoid:
    # Forward pass
    def forward(self, inputs, training):
        # Save input and calculate/save output
        # of the sigmoid function
        self.inputs = inputs
        self.output = 1 / (1 + np.exp(-inputs))
        
    # Backward pass
    def backward(self, dvalues):
        # Derivative - calculates from output of the sigmoid function
        self.dinputs = dvalues * (1 - self.output) * self.output
    
    # Calculate predictions for outputs
    def predictions(self, outputs):
        return (outputs > 0.5) * 1
        
# Linear activation
class Activation_Linear:
    # Forward pass
    def forward(self, inputs, training):
        # Just remember values
        self.inputs = inputs
        self.output = inputs
        
    # Backward pass
    def backward(self, dvalues):
        # derivative is 1, 1 * dvalues = dvalues - the chain rule
        self.dinputs = dvalues.copy()
    
    # Calculate predictions for outputs
    def predictions(self, outputs):
        return outputs
        
        
# SGD optimizer
class Optimizer_SGD:
    # Initialize optimizer - set settings,
    # learning rate of 1. is default for this optimizer
    def __init__(self, learning_rate=1., decay=0., momentum=0.):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.momentum = momentum
        
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay:
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):
        # If we use momentum
        if self.momentum:
            # If layer does not contain momentum arrays, create them
            # filled with zeros
            if not hasattr(layer, 'weight_momentums'):
                layer.weight_momentums = np.zeros_like(layer.weights)
                # If there is no momentum array for weights
                # The array doesn't exist for biases yet either.
                layer.bias_momentums = np.zeros_like(layer.biases)
            # Build weight updates with momentum - take previous
            # updates multiplied by retain factor and update with
            # current gradients
            weight_updates = self.momentum * layer.weight_momentums - self.current_learning_rate * layer.dweights
            layer.weight_momentums = weight_updates
            
            # Build bias updates
            bias_updates = self.momentum * layer.bias_momentums - self.current_learning_rate * layer.dbiases
            layer.bias_momentums = bias_updates
        # Vanilla SGD updates (as before momentum update)
        else:
            weight_updates = -self.current_learning_rate * layer.dweights
            bias_updates = -self.current_learning_rate * layer.dbiases
        # Update weights and biases using either
        # vanilla or momentum updates
        layer.weights += weight_updates
        layer.biases += bias_updates
                
    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1        


# Adagrad optimizer
class Optimizer_Adagrad:
    # Initialize optimizer - set settings
    def __init__(self, learning_rate=1., decay=0., epsilon=1e-7):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.epsilon = epsilon
        
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay:
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):
        # If layer does not contain cache arrays,
        # create them filled with zeros
        if not hasattr(layer, 'weight_cache'):
            layer.weight_cache = np.zeros_like(layer.weights)
            layer.bias_cache = np.zeros_like(layer.biases)
        # Update cache with squared current gradients
        layer.weight_cache += layer.dweights**2
        layer.bias_cache += layer.dbiases**2
        # Vanilla SGD parameter update + normalization
        # with square rooted cache
        layer.weights += -self.current_learning_rate * layer.dweights / (np.sqrt(layer.weight_cache) + self.epsilon)
        layer.biases += -self.current_learning_rate * layer.dbiases / (np.sqrt(layer.bias_cache) + self.epsilon)
    
    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1
            
            
# RMSprop optimizer
class Optimizer_RMSprop:            
    # Initialize optimizer - set settings
    def __init__(self, learning_rate=0.001, decay=0., epsilon=1e-7, rho=0.9):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.epsilon = epsilon
        self.rho = rho
    
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay:
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):
        # If layer does not contain cache arrays,
        # create them filled with zeros
        if not hasattr(layer, 'weight_cache'):
            layer.weight_cache = np.zeros_like(layer.weights)
            layer.bias_cache = np.zeros_like(layer.biases)
        # Update cache with squared current gradients
        layer.weight_cache = self.rho * layer.weight_cache + (1 - self.rho) * layer.dweights**2
        layer.bias_cache = self.rho * layer.bias_cache + (1 - self.rho) * layer.dbiases**2
        
        # Vanilla SGD parameter update + normalization
        # with square rooted cache
        layer.weights += -self.current_learning_rate * layer.dweights / (np.sqrt(layer.weight_cache) + self.epsilon)
        layer.biases += -self.current_learning_rate * layer.dbiases / (np.sqrt(layer.bias_cache) + self.epsilon)
    
    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1
            

# Adam optimizer
class Optimizer_Adam:
    # Initialize optimizer - set settings
    def __init__(self, learning_rate=0.001, decay=0., epsilon=1e-7, beta_1=0.9, beta_2=0.999):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.epsilon = epsilon
        self.beta_1 = beta_1
        self.beta_2 = beta_2
    
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay:
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))        

    # Update parameters
    def update_params(self, layer):
        # If layer does not contain cache arrays,
        # create them filled with zeros
        if not hasattr(layer, 'weight_cache'):
            layer.weight_momentums = np.zeros_like(layer.weights)
            layer.weight_cache = np.zeros_like(layer.weights)
            layer.bias_momentums = np.zeros_like(layer.biases)
            layer.bias_cache = np.zeros_like(layer.biases)
        # Update momentum with current gradients
        layer.weight_momentums = self.beta_1 * layer.weight_momentums + (1 - self.beta_1) * layer.dweights
        layer.bias_momentums = self.beta_1 * layer.bias_momentums + (1 - self.beta_1) * layer.dbiases
        # Get corrected momentum
        # self.iteration is 0 at first pass
        # and we need to start with 1 here
        weight_momentums_corrected = layer.weight_momentums / (1 - self.beta_1 ** (self.iterations + 1))
        bias_momentums_corrected = layer.bias_momentums / (1 - self.beta_1 ** (self.iterations + 1))
        # Update cache with squared current gradients
        layer.weight_cache = self.beta_2 * layer.weight_cache + (1 - self.beta_2) * layer.dweights**2
        layer.bias_cache = self.beta_2 * layer.bias_cache + (1 - self.beta_2) * layer.dbiases**2
        # Get corrected cache
        weight_cache_corrected = layer.weight_cache / (1 - self.beta_2 ** (self.iterations + 1))
        bias_cache_corrected = layer.bias_cache / (1 - self.beta_2 ** (self.iterations + 1))
        # Vanilla SGD parameter update + normalization
        # with square rooted cache
        layer.weights += -self.current_learning_rate * weight_momentums_corrected / (np.sqrt(weight_cache_corrected) + self.epsilon)
        layer.biases += -self.current_learning_rate * bias_momentums_corrected / (np.sqrt(bias_cache_corrected) + self.epsilon)
                    
    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1
            
        
# Common loss class
class Loss:
    # Regularization loss calculation
    def regularization_loss(self):        
        # 0 by default
        regularization_loss = 0
        # Calculate regularization loss
        # iterate all trainable layers
        for layer in self.trainable_layers:
            # L1 regularization - weights
            # calculate only when factor greater than 0
            if layer.weight_regularizer_l1 > 0:
                regularization_loss += layer.weight_regularizer_l1 * np.sum(np.abs(layer.weights))
            # L2 regularization - weights
            if layer.weight_regularizer_l2 > 0:
                regularization_loss += layer.weight_regularizer_l2 * np.sum(layer.weights * layer.weights)
            # L1 regularization - biases
            # calculate only when factor greater than 0
            if layer.bias_regularizer_l1 > 0:
                regularization_loss += layer.bias_regularizer_l1 * np.sum(np.abs(layer.biases))
            # L2 regularization - biases
            if layer.bias_regularizer_l2 > 0:
                regularization_loss += layer.bias_regularizer_l2 * np.sum(layer.biases * layer.biases)
        return regularization_loss

    # Set/remember trainable layers
    def remember_trainable_layers(self, trainable_layers):
       self.trainable_layers = trainable_layers

    # Calculates the data and regularization losses
    # given model output and ground truth values
    def calculate(self, output, y, *, include_regularization=False):
        # Calculate sample losses
        sample_losses = self.forward(output, y)
        # Calculate mean loss
        data_loss = np.mean(sample_losses)
        # Add accumulated sum of losses and sample count
        self.accumulated_sum += np.sum(sample_losses)
        self.accumulated_count += len(sample_losses)
        # If just data loss - return it
        if not include_regularization:
            return data_loss
        # Return the data and regularization losses
        return data_loss, self.regularization_loss()   
    
    # Calculates accumulated loss
    def calculate_accumulated(self, *, include_regularization=False):
        # Calculate mean loss
        data_loss = self.accumulated_sum / self.accumulated_count
        # If just data loss - return it
        if not include_regularization:
            return data_loss
        # Return the data and regularization losses
        return data_loss, self.regularization_loss()
    
    # Reset variables for accumulated loss
    def new_pass(self):
        self.accumulated_sum = 0
        self.accumulated_count = 0


# Cross-entropy loss
class Loss_CategoricalCrossentropy(Loss):
    # Forward pass
    def forward(self, y_pred, y_true):
        # Number of samples in a batch
        samples = len(y_pred)
        # Clip data to prevent division by 0
        # Clip both sides to not drag mean towards any value
        y_pred_clipped = np.clip(y_pred, 1e-7, 1 - 1e-7)
        # Probabilities for target values -
        # only if categorical labels
        if len(y_true.shape) == 1:
            correct_confidences = y_pred_clipped[
                range(samples),
                y_true
            ]
        # Mask values - only for one-hot encoded labels
        elif len(y_true.shape) == 2:
            correct_confidences = np.sum(y_pred_clipped * y_true, axis=1)
        # Losses
        negative_log_likelihoods = -np.log(correct_confidences)
        return negative_log_likelihoods
    
    # Backward pass
    def backward(self, dvalues, y_true):
        # Number of samples
        samples = len(dvalues)
        # Number of labels in every sample
        # We'll use the first sample to count them
        labels = len(dvalues[0])
        # If labels are sparse, turn them into one-hot vector
        if len(y_true.shape) == 1:
            y_true = np.eye(labels)[y_true]
        # Calculate gradient
        self.dinputs = -y_true / dvalues
        # Normalize gradient
        self.dinputs = self.dinputs / samples

        
# Softmax classifier - combined Softmax activation
# and cross-entropy loss for faster backward step
class Activation_Softmax_Loss_CategoricalCrossentropy():  
    # # Creates activation and loss function objects
    # def __init__(self):
    #     self.activation = Activation_Softmax()
    #     self.loss = Loss_CategoricalCrossentropy()
    # # Forward pass
    # def forward(self, inputs, y_true):
    #     # Output layer's activation function
    #     self.activation.forward(inputs)
    #     # Set the output
    #     self.output = self.activation.output
    #     # Calculate and return loss value
    #     return self.loss.calculate(self.output, y_true)
    # Backward pass
    def backward(self, dvalues, y_true):
        # Number of samples
        samples = len(dvalues)     
        # If labels are one-hot encoded,
        # turn them into discrete values
        if len(y_true.shape) == 2:
            y_true = np.argmax(y_true, axis=1)
        # Copy so we can safely modify
        self.dinputs = dvalues.copy()
        # Calculate gradient
        self.dinputs[range(samples), y_true] -= 1
        # Normalize gradient
        self.dinputs = self.dinputs / samples
        

# Binary cross-entropy loss
class Loss_BinaryCrossentropy(Loss): 
    # Forward pass
    def forward(self, y_pred, y_true):
        # Clip data to prevent division by 0
        # Clip both sides to not drag mean towards any value
        y_pred_clipped = np.clip(y_pred, 1e-7, 1 - 1e-7)
        # Calculate sample-wise loss
        sample_losses = -(y_true * np.log(y_pred_clipped) + (1 - y_true) * np.log(1 - y_pred_clipped))
        sample_losses = np.mean(sample_losses, axis=-1)
        # Return losses
        return sample_losses       
    
    # Backward pass
    def backward(self, dvalues, y_true):
        # Number of samples
        samples = len(dvalues)
        # Number of outputs in every sample
        # We'll use the first sample to count them
        outputs = len(dvalues[0])
        # Clip data to prevent division by 0
        # Clip both sides to not drag mean towards any value
        clipped_dvalues = np.clip(dvalues, 1e-7, 1 - 1e-7)
        # Calculate gradient
        self.dinputs = -(y_true / clipped_dvalues - (1 - y_true) / (1 - clipped_dvalues)) / outputs
        # Normalize gradient
        self.dinputs = self.dinputs / samples
        
        
# Mean Squared Error loss
class Loss_MeanSquaredError(Loss): # L2 loss
    # Forward pass
    def forward(self, y_pred, y_true):
        # Calculate loss
        sample_losses = np.mean((y_true - y_pred)**2, axis=-1)
        # Return losses
        return sample_losses
    
    # Backward pass
    def backward(self, dvalues, y_true):
        # Number of samples
        samples = len(dvalues)
        # Number of outputs in every sample
        # We'll use the first sample to count them
        outputs = len(dvalues[0])
        # Gradient on values
        self.dinputs = -2 * (y_true - dvalues) / outputs
        # Normalize gradient
        self.dinputs = self.dinputs / samples
        

# Mean Absolute Error loss
class Loss_MeanAbsoluteError(Loss): # L1 loss
    def forward(self, y_pred, y_true):
        # Calculate loss
        sample_losses = np.mean(np.abs(y_true - y_pred), axis=-1)
        # Return losses
        return sample_losses
    
    # Backward pass
    def backward(self, dvalues, y_true):
        # Number of samples
        samples = len(dvalues)
        # Number of outputs in every sample
        # We'll use the first sample to count them
        outputs = len(dvalues[0])
        # Calculate gradient
        self.dinputs = np.sign(y_true - dvalues) / outputs
        # Normalize gradient
        self.dinputs = self.dinputs / samples
     

# Common accuracy class
class Accuracy:
    # Calculates an accuracy
    # given predictions and ground truth values
    def calculate(self, predictions, y):
        # Get comparison results
        comparisons = self.compare(predictions, y)
        # Calculate an accuracy
        accuracy = np.mean(comparisons)
        # Add accumulated sum of matching values and sample count
        self.accumulated_sum += np.sum(comparisons)
        self.accumulated_count += len(comparisons)
        # Return accuracy
        return accuracy     
    
    # Calculates accumulated accuracy
    def calculate_accumulated(self):
        # Calculate an accuracy
        accuracy = self.accumulated_sum / self.accumulated_count
        # Return the data and regularization losses
        return accuracy
    
    # Reset variables for accumulated accuracy
    def new_pass(self):
        self.accumulated_sum = 0
        self.accumulated_count = 0


# Accuracy calculation for classification model
class Accuracy_Categorical(Accuracy):
    # No initialization is needed
    def init(self, y):
        pass
    # Compares predictions to the ground truth values
    def compare(self, predictions, y):
        if len(y.shape) == 2:
            y = np.argmax(y, axis=1)
        return predictions == y
         
    
# Accuracy calculation for regression model
class Accuracy_Regression(Accuracy):
    def __init__(self):
        # Create precision property
        self.precision = None
    # Calculates precision value
    # based on passed in ground truth
    def init(self, y, reinit=False):
        if self.precision is None or reinit:
            self.precision = np.std(y) / 250
    # Compares predictions to the ground truth values
    def compare(self, predictions, y):
        return np.absolute(predictions - y) < self.precision

        
# Model class
class Model:
    def __init__(self):
        # Create a list of network objects
        self.layers = []
        # Softmax classifier's output object
        self.softmax_classifier_output = None
        
    # Add objects to the model
    def add(self, layer):
        self.layers.append(layer)
    
    # Set loss, optimizer and accuracy
    def set(self, *, loss=None, optimizer=None, accuracy=None):
        if loss is not None:
            self.loss = loss
        if optimizer is not None:
            self.optimizer = optimizer
        if accuracy is not None:
            self.accuracy = accuracy
            
    # Finalize the model
    def finalize(self):
        # Create and set the input layer
        self.input_layer = Layer_Input()
        # Count all the objects
        layer_count = len(self.layers)
        # Initialize a list containing trainable layers:
        self.trainable_layers = []
        # Iterate the objects
        for i in range(layer_count):
            # If it's the first layer,
            # the previous layer object is the input layer
            if i == 0:
                self.layers[i].prev = self.input_layer
                self.layers[i].next = self.layers[i+1]
            # All layers except for the first and the last
            elif i < layer_count - 1:
                self.layers[i].prev = self.layers[i-1]
                self.layers[i].next = self.layers[i+1]
            # The last layer - the next object is the loss
            # Also let's save aside the reference to the last object
            # whose output is the model's output
            else:
                self.layers[i].prev = self.layers[i-1]
                self.layers[i].next = self.loss
                self.output_layer_activation = self.layers[i]
            # If layer contains an attribute called "weights",
            # it's a trainable layer -
            # add it to the list of trainable layers
            # We don't need to check for biases -
            # checking for weights is enough 
            if hasattr(self.layers[i], 'weights'):
            	self.trainable_layers.append(self.layers[i])
            # Update loss object with trainable layers
            # self.loss.remember_trainable_layers(self.trainable_layers)
            if self.loss is not None:
                self.loss.remember_trainable_layers(self.trainable_layers)
        # If output activation is Softmax and
        # loss function is Categorical Cross-Entropy
        # create an object of combined activation
        # and loss function containing
        # faster gradient calculation
        if isinstance(self.layers[-1], Activation_Softmax) and isinstance(self.loss, Loss_CategoricalCrossentropy):
            # Create an object of combined activation
            # and loss functions
            self.softmax_classifier_output = Activation_Softmax_Loss_CategoricalCrossentropy()

    # Train the model
    # def train(self, X, y, *, epochs=1, print_every=1, validation_data=None):
    def train(self, X, y, *, epochs=1, batch_size=None, print_every=1, validation_data=None):
        # Initialize accuracy object
        self.accuracy.init(y)
        # Default value if batch size is not being set
        train_steps = 1
        # If there is validation data passed,
        # set default number of steps for validation as well
        if validation_data is not None:
            validation_steps = 1
            # For better readability
            X_val, y_val = validation_data
        # Calculate number of steps
        if batch_size is not None:
            train_steps = len(X) // batch_size
            # Dividing rounds down. If there are some remaining
            # data, but not a full batch, this won't include it
            # Add `1` to include this not full batch
            if train_steps * batch_size < len(X):
                train_steps += 1
            if validation_data is not None:
                validation_steps = len(X_val) // batch_size
                # Dividing rounds down. If there are some remaining
                # data, but nor full batch, this won't include it
                # Add `1` to include this not full batch
                if validation_steps * batch_size < len(X_val):
                    validation_steps += 1
        # Main training loop
        for epoch in range(1, epochs+1):
            # Print epoch number
            print(f'epoch: {epoch}')
            # Reset accumulated values in loss and accuracy objects
            self.loss.new_pass()
            self.accuracy.new_pass()
            # Iterate over steps
            for step in range(train_steps):
                # If batch size is not set -
                # train using one step and full dataset
                if batch_size is None:
                    batch_X = X
                    batch_y = y
                # Otherwise slice a batch
                else:
                    batch_X = X[step*batch_size:(step+1)*batch_size]
                    batch_y = y[step*batch_size:(step+1)*batch_size]
                # Perform the forward pass
                output = self.forward(batch_X, training=True)
                # Calculate loss
                data_loss, regularization_loss = self.loss.calculate(output, batch_y, include_regularization=True)
                loss = data_loss + regularization_loss
                # Get predictions and calculate an accuracy
                predictions = self.output_layer_activation.predictions(output)
                accuracy = self.accuracy.calculate(predictions, batch_y)
                # Perform backward pass
                self.backward(output, batch_y)
                # Optimize (update parameters)
                self.optimizer.pre_update_params()
                for layer in self.trainable_layers:
                    self.optimizer.update_params(layer)
                self.optimizer.post_update_params()
                # Print a summary
                if not step % print_every or step == train_steps - 1:
                    print(f'step: {step}, ' +
                          f'acc: {accuracy:.3f}, ' +
                          f'loss: {loss:.3f} (' +
                          f'data_loss: {data_loss:.3f}, ' +
                          f'reg_loss: {regularization_loss:.3f}), ' +
                          f'lr: {self.optimizer.current_learning_rate}')
            # Get and print epoch loss and accuracy
            epoch_data_loss, epoch_regularization_loss = self.loss.calculate_accumulated(include_regularization=True)
            epoch_loss = epoch_data_loss + epoch_regularization_loss
            epoch_accuracy = self.accuracy.calculate_accumulated()
            print(f'training, ' +
                  f'acc: {epoch_accuracy:.3f}, ' +
                  f'loss: {epoch_loss:.3f} (' +
                  f'data_loss: {epoch_data_loss:.3f}, ' +
                  f'reg_loss: {epoch_regularization_loss:.3f}), ' +
                  f'lr: {self.optimizer.current_learning_rate}')
            # If there is the validation data
            if validation_data is not None:
                # Evaluate the model:
                self.evaluate(*validation_data, batch_size=batch_size)

    # Performs forward pass
    def forward(self, X, training):
        # Call forward method on the input layer
        # this will set the output property that
        # the first layer in "prev" object is expecting
        self.input_layer.forward(X, training)
        # Call forward method of every object in a chain
        # Pass output of the previous object as a parameter
        for layer in self.layers:
            layer.forward(layer.prev.output, training)
        # "layer" is now the last object from the list,
        # return its output
        return layer.output

    # Performs backward pass
    def backward(self, output, y):
        # If softmax classifier
        if self.softmax_classifier_output is not None:
            # First call backward method
            # on the combined activation/loss
            # this will set dinputs property
            self.softmax_classifier_output.backward(output, y)
            # Since we'll not call backward method of the last layer
            # which is Softmax activation
            # as we used combined activation/loss
            # object, let's set dinputs in this object
            self.layers[-1].dinputs = self.softmax_classifier_output.dinputs
            # Call backward method going through
            # all the objects but last
            # in reversed order passing dinputs as a parameter
            for layer in reversed(self.layers[:-1]):
                layer.backward(layer.next.dinputs)
            return
        # First call backward method on the loss
        # this will set dinputs property that the last
        # layer will try to access shortly
        self.loss.backward(output, y)
        # Call backward method going through all the objects
        # in reversed order passing dinputs as a parameter
        for layer in reversed(self.layers):
            layer.backward(layer.next.dinputs) 
    
    # Evaluates the model using passed in dataset
    def evaluate(self, X_val, y_val, *, batch_size=None):
        # Default value if batch size is not being set
        validation_steps = 1
        # Calculate number of steps
        if batch_size is not None:
            validation_steps = len(X_val) // batch_size
            # Dividing rounds down. If there are some remaining
            # data, but not a full batch, this won't include it
            # Add `1` to include this not full batch
            if validation_steps * batch_size < len(X_val):
                validation_steps += 1
        # Reset accumulated values in loss
        # and accuracy objects
        self.loss.new_pass()
        self.accuracy.new_pass()
        # Iterate over steps
        for step in range(validation_steps):
            # If batch size is not set -
            # train using one step and full dataset
            if batch_size is None:
                batch_X = X_val
                batch_y = y_val
            # Otherwise slice a batch
            else:
                batch_X = X_val[step*batch_size:(step+1)*batch_size]
                batch_y = y_val[step*batch_size:(step+1)*batch_size]
            # Perform the forward pass
            output = self.forward(batch_X, training=False)
            # Calculate the loss
            self.loss.calculate(output, batch_y)
            # Get predictions and calculate an accuracy
            predictions = self.output_layer_activation.predictions(output)
            self.accuracy.calculate(predictions, batch_y)
        # Get and print validation loss and accuracy
        validation_loss = self.loss.calculate_accumulated()
        validation_accuracy = self.accuracy.calculate_accumulated()
        # Print a summary
        print(f'validation, ' +
              f'acc: {validation_accuracy:.3f}, ' +
              f'loss: {validation_loss:.3f}')
      
    # Retrieves and returns parameters of trainable layers
    def get_parameters(self):
        # Create a list for parameters
        parameters = []
        # Iterable trainable layers and get their parameters
        for layer in self.trainable_layers:
            parameters.append(layer.get_parameters())
        # Return a list
        return parameters
            
    # Updates the model with new parameters
    def set_parameters(self, parameters):
        # Iterate over the parameters and layers
        # and update each layers with each set of the parameters
        for parameter_set, layer in zip(parameters, self.trainable_layers):
            layer.set_parameters(*parameter_set)

    # Saves the parameters to a file
    def save_parameters(self, path):
        # Open a file in the binary-write mode
        # and save parameters to it
        with open(path, 'wb') as f:
            pickle.dump(self.get_parameters(), f)

    # Loads the weights and updates a model instance with them
    def load_parameters(self, path):
        # Open file in the binary-read mode,
        # load weights and update trainable layers
        with open(path, 'rb') as f:
            self.set_parameters(pickle.load(f))
    
    # Saves the model
    def save(self, path):
        # Make a deep copy of current model instance
        model = copy.deepcopy(self)
        # Reset accumulated values in loss and accuracy objects
        model.loss.new_pass()
        model.accuracy.new_pass()
        # Remove data from input layer
        # and gradients from the loss object
        model.input_layer.__dict__.pop('output', None)
        model.loss.__dict__.pop('dinputs', None)
        # For each layer remove inputs, output and dinputs properties
        for layer in model.layers:
            for property in ['inputs', 'output', 'dinputs', 'dweights', 'dbiases']:
                layer.__dict__.pop(property, None)
        # Open a file in the binary-write mode and save the model
        with open(path, 'wb') as f:
            pickle.dump(model, f)

    # Loads and returns a model
    @staticmethod
    def load(path):
        # Open file in the binary-read mode, load a model
        with open(path, 'rb') as f:
            model = pickle.load(f)
        # Return a model
        return model

    # Predicts on the samples
    def predict(self, X, *, batch_size=None):
        # Default value if batch size is not being set
        prediction_steps = 1
        # Calculate number of steps
        if batch_size is not None:
            prediction_steps = len(X) // batch_size
            # Dividing rounds down. If there are some remaining
            # data, but not a full batch, this won't include it
            # Add `1` to include this not full batch
            if prediction_steps * batch_size < len(X):
                prediction_steps += 1
        # Model outputs
        output = []
        # Iterate over steps
        for step in range(prediction_steps):
            # If batch size is not set -
            # train using one step and full dataset
            if batch_size is None:
                batch_X = X
            # Otherwise slice a batch
            else:
                batch_X = X[step*batch_size:(step+1)*batch_size]
            # Perform the forward pass
            batch_output = self.forward(batch_X, training=False)
            # Append batch prediction to the list of predictions
            output.append(batch_output)
        # Stack and return results
        return np.vstack(output)
    
# Create dataset
X, y, X_test, y_test = create_data_mnist('fashion_mnist_images')

# Scale and reshape samples
X_test = (X_test.reshape(X_test.shape[0], -1).astype(np.float32) - 127.5) / 127.5

# Load the model
model = Model.load('fashion_mnist.model')

# Predict on the first 5 samples from validation dataset
# and print the result
confidences = model.predict(X_test[:5])
predictions = model.output_layer_activation.predictions(confidences)
print(predictions)

# Print first 5 labels
print(y_test[:5])

#############################################
## tshirt
fashion_mnist_labels = {
    0: 'T-shirt/top',
    1: 'Trouser',
    2: 'Pullover',
    3: 'Dress',
    4: 'Coat',
    5: 'Sandal',
    6: 'Shirt',
    7: 'Sneaker',
    8: 'Bag',
    9: 'Ankle boot'
    }
for prediction in predictions:
    print(fashion_mnist_labels[prediction])
# Read an image
image_data = cv2.imread('tshirt.png', cv2.IMREAD_UNCHANGED)
plt.imshow(cv2.cvtColor(image_data, cv2.COLOR_BGR2RGB))
plt.show()
# Read an image
image_data = cv2.imread('tshirt.png', cv2.IMREAD_GRAYSCALE)
plt.imshow(image_data, cmap='gray')
plt.show()
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
plt.imshow(image_data, cmap='gray')
plt.show()
# Reshape and scale pixel data
image_data = (image_data.reshape(1, -1).astype(np.float32) - 127.5) / 127.5
# Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)
mnist_image = cv2.imread('fashion_mnist_images/train/0/0000.png', cv2.IMREAD_UNCHANGED)
plt.imshow(mnist_image, cmap='gray')
plt.show()
# Read an image
image_data = cv2.imread('tshirt.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Invert image colors
image_data = 255 - image_data
# Reshape and scale pixel data
image_data = (image_data.reshape(1, -1).astype(np.float32) - 127.5) / 127.5
# Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)

#############################################
## pants
image_data = cv2.imread('pants.png', cv2.IMREAD_UNCHANGED)
plt.imshow(cv2.cvtColor(image_data, cv2.COLOR_BGR2RGB))
plt.show()
# Read an image
image_data = cv2.imread('pants.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Invert image colors
image_data = 255 - image_data
plt.imshow(image_data, cmap='gray')
plt.show()
# Label index to label name relation
fashion_mnist_labels = {
    0: 'T-shirt/top',
    1: 'Trouser',
    2: 'Pullover',
    3: 'Dress',
    4: 'Coat',
    5: 'Sandal',
    6: 'Shirt',
    7: 'Sneaker',
    8: 'Bag',
    9: 'Ankle boot'
    }
# Read an image
image_data = cv2.imread('pants.png', cv2.IMREAD_GRAYSCALE)
# Resize to the same size as Fashion MNIST images
image_data = cv2.resize(image_data, (28, 28))
# Invert image colors
image_data = 255 - image_data
# Reshape and scale pixel data
image_data = (image_data.reshape(1, -1).astype(np.float32) -
127.5) / 127.5
# Load the model
model = Model.load('fashion_mnist.model')
# Predict on the image
confidences = model.predict(image_data)
# Get prediction instead of confidence levels
predictions = model.output_layer_activation.predictions(confidences)
# Get label name from label index
prediction = fashion_mnist_labels[predictions[0]]
print(prediction)

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本章的章节代码、更多资源和勘误表：https://nnfs.io/ch22

到此为止，整个系列更新完毕！感谢收看！