神经网络python实现

一时失言乱红尘 2022-05-19 07:28 271阅读 0赞

本文主要内容是使用python实现神经网络。`neural-networks-and-deep-learning`神经网络的实现，虽然在原理上易懂，但是不够模块化，layer、net、loss、optimizer间的耦合性太高。通用的深度学习框架，例如caffe都是将每个模块分离实现，这样提升了代码的可阅读，扩展性。

![这里写图片描述][70]

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### 整体上网络的构建以及运行结果展示 ###

下面先给出整体的代码以及运行结果：

def test_net():
        from load_data import load_mnist
        (X_train, y_train), (X_test, y_test) = load_mnist()
    
        net = Net()
        net.add_layer(FCLayer(28*28, 60, activation=ReLU))
        # net.add_layer(FCLayer(28*28, 20))
        # net.add_layer(FCLayer(20, 10))
        net.add_layer(FCLayer(60, 10, activation=SoftMax))
        # net.add_layer(FCLayer(20, 10))
        net.compile()
    
        net.train(X_train, y_train, X_test, y_test, 100)

运行结果如下：

![这里写图片描述][70 1]

下面给出实现的每一个模块：

##### 激活函数 #####

def sigmoid(z):
        return 1 / (1 + np.exp(-z))
    
    def softmax(z):
        x = z - np.max(z, axis=1, keepdims=True)
        exp_x = np.exp(x)
        s = exp_x / np.sum(exp_x, axis=1, keepdims=True)
        return s
    
    class Sigmoid:
    
        def __init__(self):
            self.last_forward = None
    
        def forward(self, in_data):
            self.last_forward = sigmoid(in_data)
            return self.last_forward
    
        def derivative(self, in_data=None):
            self.last_forward = self.forward(in_data) if in_data else self.last_forward
            return self.last_forward * (1 - self.last_forward)
    
    class SoftMax:
        def __init__(self):
            self.last_forward = None
    
        def forward(self, in_data):
            self.last_forward = softmax(in_data)
            return self.last_forward
    
        def derivative(self, in_data=None):
            last_forward = in_data if in_data else self.last_forward
            return np.ones(last_forward.shape)
    
    class ReLU:
        def __init__(self):
            self.last_forward = None
    
        def forward(self, in_data):
            self.last_forward = in_data
            return np.maximum(0.0, in_data)
    
        def derivative(self, in_data=None):
            res = np.zeros(self.last_forward.shape, dtype='float32')
            res[self.last_forward > 0] = 1.
            return res

##### cost函数 #####

class CrossEntropyCost:
        def __init__(self):
            pass
    
        @staticmethod
        def forward(y, a):
            # return np.sum(np.nan_to_num(-y * np.log(a) - (1 - y) * np.log(1 - a)))
            return np.mean(-np.sum(y * np.log(a), axis=1))
    
        @staticmethod
        def backward(y, a):
            return a - y
    
    
    class QuadraticCost:
        def __init__(self):
            pass
    
        @staticmethod
        def forward(a, y):
            return 0.5 * np.linalg.norm(a - y) ** 2
    
        @staticmethod
        def backward(y, a):
            return a - y

##### Optimizer参数的优化方法例如SGD #####

class Optimizer(object):
        def __init__(self, lr=0.001, clip=-1, decay=0., lr_min=0., lr_max=np.inf):
            self.lr = lr
            self.clip = clip
            self.decay = decay
            self.lr_min = lr_min
            self.lr_max = lr_max
    
            self.iterations = 0
    
        def update(self, params, grads):
            self.iterations += 1
    
            self.lr *= (1. / 1 + self.decay * self.iterations)
            self.lr = np.clip(self.lr, self.lr_min, self.lr_max)
    
    
    class SGD(Optimizer):
        def __init__(self, *args, **kwargs):
            Optimizer.__init__(self)
    
        def update(self, params, grads):
            for p, g in zip(params, grads):
                # p -= 0.3 * g
                p -= self.lr * npdl_clip(g, self.clip)
    
            super(SGD, self).update(params, grads)

##### Layer全连接层 #####

class FCLayer:
        def __init__(self, n_in, n_out, activation=Sigmoid):
    
            # self.b = np.random.randn(1, n_out)
            self.b = np.zeros((1, n_out), dtype='float32')
            # self.b = Zero().call((n_out, ))
            # self.w = np.random.randn(n_in, n_out)
            self.w = np.random.randn(n_in, n_out) / np.sqrt(n_in)
    
            self.ac_fn = activation()
    
            self.d_w, self.d_b = None, None
            self.last_input = None
    
            self.b_first_layer = False
    
        def forward(self, in_data):
            self.last_input = in_data
    
            z = np.dot(in_data, self.w) + self.b
            a = self.ac_fn.forward(z)
    
            return a
    
        def backward(self, pre_grad):
            act_grad = pre_grad * self.ac_fn.derivative()
            self.d_w = np.dot(self.last_input.T, act_grad)
            self.d_b = np.mean(act_grad, axis=0)
    
            if not self.b_first_layer:
                # return delta * w
                return np.dot(act_grad, self.w.T)
    
        # The below two function mainly used for update w, b
    
        @property
        def params(self):
            return self.w, self.b
    
        @property
        def grads(self):
            return self.d_w, self.d_b

##### Net网络 #####

class Net:
        def __init__(self):
            self.layers = []
            self.loss = None
            self.optimizer = None
    
        def add_layer(self, layer):
            self.layers.append(layer)
    
        def compile(self, cost=CrossEntropyCost, optimizer=SGD):
            self.cost = cost()
            self.optimizer = optimizer()
    
        def train(self, X_train, y_train, X_test, y_test,
                  epochs=100, lr=0.5, batch_size=100):
    
            method_name = self.optimizer.__class__.__name__
            print "using %s method to train" % method_name
    
            n = len(X_train)
    
            lst_iter, lst_loss, lst_acc = [], [], []
    
            for ep in xrange(epochs):
                np.random.seed(ep)
                arr_idx = np.arange(n)
                np.random.shuffle(arr_idx)
    
                for k in xrange(0, n, batch_size):
    
                    # forward propagation
                    y_pred = self.forward(X_train[k:k+batch_size])
    
                    # backward propagation
                    next_grad = self.cost.backward(y_train[k:k+batch_size], y_pred)
                    for layer in self.layers[::-1]:
                        next_grad = layer.backward(next_grad)
    
                    # get parameter and gradients
                    params = []
                    grads = []
                    for layer in self.layers:
                        params += layer.params
                        grads += layer.grads
    
                    # update parameter
                    self.optimizer.update(params, grads)
    
                # print info
                print "============== epoch %s complete =============" % ep
                cost = self.get_cost(X_train, y_train)
                print "training cost is %s" % cost
    
                right_num = self.get_accuracy(X_test, y_test)
                print "accuracy on test data %s / %s" % (right_num, len(y_test))
    
                lst_iter.append(ep)
                lst_acc.append(1.0 * right_num / len(y_test))
                lst_loss.append(cost)
    
            draw_result(lst_iter, lst_loss, lst_acc, method_name)
    
        def forward(self, x_batch):
            x_in = x_batch
            for layer in self.layers:
                x_in = layer.forward(x_in)
    
            y_pred = x_in
            return y_pred
    
        def get_accuracy(self, X_batch, y_batch):
            rets = [(np.argmax(self.forward(x)), np.argmax(y))
                    for (x, y) in zip(X_batch, y_batch)]
    
            return sum(a == y for (a, y) in rets)
    
        def get_cost(self, X_train, y_train):
            a = self.forward(X_train)
            return self.cost.forward(y_train, a)

##### loss、cost的曲线绘制 #####

曲线的绘制可见[stackoverflow][]

def draw_result(lst_iter, lst_loss, lst_acc, title):
        plt.plot(lst_iter, lst_loss, '-b', label='loss')
        plt.plot(lst_iter, lst_acc, '-r', label='accuracy')
    
        plt.xlabel("n iteration")
        plt.legend(loc='upper left')
        plt.title(title)
        plt.savefig(title+".png")  # should before show method
    
        plt.show()
    
    #对应的测试代码：
    
    def test_draw():
        lst_iter = range(100)
        lst_loss = [0.01 * i - 0.01 * i ** 2 for i in xrange(100)]
        # lst_loss = np.random.randn(1, 100).reshape((100, ))
        lst_acc = [0.01 * i + 0.01 * i ** 2 for i in xrange(100)]
        # lst_acc = np.random.randn(1, 100).reshape((100, ))
        draw_result(lst_iter, lst_loss, lst_acc, "sgd_method")

##### 参考： #####

[http://neuralnetworksanddeeplearning.com/][http_neuralnetworksanddeeplearning.com]

[github][]

[stackoverflow][]

[70]: /images/20220519/191b8e8e29724a8fa453042c845980bf.png
[70 1]: /images/20220519/fb4066a61549490a87a01074a264aee4.png
[stackoverflow]: https://stackoverflow.com/a/51439721/6329006
[http_neuralnetworksanddeeplearning.com]: http://neuralnetworksanddeeplearning.com/
[github]: https://github.com/ouja/NumpDL