Numpy 만으로 신경망구현하기 (일반 기본 DNN)
저번에 2층 DNN 구현을 한 것에 이어 일반화하여 hidden layer의 수를 n개 수용할 수 있는 DNN 을 구현했다. 추가된 것으로 활성화 함수로 relu 와 sigmoid 를 선택할 수 있고 L2 regularization 기능이 추가됐다. 또한 가중치들의 초기화로 relu 는 he 초기화, sigmoid 는 xavier 초기화가 된다.
라이브러리 코드 :
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# coding: utf-8 import numpy as np from collections import OrderedDict #--------------------functions--------------------- def identity_function(x): return x def step_function(x): return np.array(x > 0, dtype=np.int) def sigmoid(x): return 1 / (1 + np.exp(-x)) def sigmoid_grad(x): return sigmoid(x) * (1.0 - sigmoid(x)) def softmax(x): if x.ndim == 2: x = x.T x = x - np.max(x, axis=0) y = np.exp(x) / np.sum(np.exp(x), axis=0) return y.T x = x - np.max(x) return np.exp(x) / np.sum(np.exp(x)) def mean_squared_error(y,t): return 0.5 * np.sum((y-t)**2) def cross_entropy_error(y,t): if y.ndim == 1: y = y.reshape(1,-1) t = t.reshape(1,-1) if t.size == y.size: t = t.argmax(axis=1) batch_size = y.shape[0] return -np.sum(np.log(y[np.arange(batch_size),t] + 1e-7)) / batch_size def softmax_loss(x,t): y = softmax(x) return cross_entropy_error(y,t) def _numerical_gradient_1d(f,x): h = 1e-4 grad = np.zeros_like(x) for idx in range(x.size): tmp_val = x[idx] x[idx] = float(tmp_val) + h f1 = f(x) x[idx] = tmp_val - h f2 = f(x) grad[idx] = (f1 - f2) / (2*h) x[idx] = tmp_val return grad def numerical_gradient_2d(f,X): if X.ndim == 1: return _numerical_gradient_1d(f,X) else: grad = np.zeros_like(X) for i,x in enumerate(X): grad[i] = _numerical_gradient_1d(f,x) return grad def numerical_gradient(f,x): h = 1e-4 grad = np.zeros_like(x) it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite']) while not it.finished: idx = it.multi_index tmp_value = x[idx] x[idx] = float(tmp_value) + h f1 = f(x) x[idx] = tmp_value - h f2 = f(x) grad[idx] = (f1 - f2) / (2*h) x[idx] = tmp_value it.iternext() return grad def mini_batch(x_train, y_train, batch_size=200): random_lenght = np.random.permutation(x_train.shape[0]) mod = x_train.shape[0] // float(batch_size) for idx in np.array_split(random_lenght,mod): x_batch, y_batch = x_train[idx], y_train[idx] yield x_batch, y_batch #----------------------------------layers-------------------------------- class Relu: def __init__(self): self.mask = None def forward(self,x): self.mask = (x <= 0) out = x.copy() out[self.mask] = 0 return out def backward(self,dout): dout[self.mask] = 0 dx = dout return dx class Sigmoid: def __init__(self): self.out = None def forward(self,x): out = sigmoid(x) self.out = out return out def backward(self,dout): dx = dout * self.out * (1.0 - self.out) return dx class Affine: def __init__(self,W,b): self.W = W self.b = b self.original_x_shape = None self.x = None self.dW = None self.db = None def forward(self,x): self.original_x_shape = x.shape x = x.reshape(x.shape[0],-1) self.x = x out = np.dot(self.x,self.W) + self.b return out def backward(self,dout): dx = np.dot(dout,self.W.T) self.dW = np.dot(self.x.T,dout) self.db = np.sum(dout, axis=0) #편향 공유 데이터끼리 dx = dx.reshape(*self.original_x_shape) return dx class SoftmaxWithLoss: def __init__(self): self.y = None self.t = None self.loss = None def forward(self,x,t): self.y = softmax(x) self.t = t self.loss = cross_entropy_error(self.y,self.t) return self.loss def backward(self,dout=1): batch_size = self.t.shape[0] if self.y.size == self.t.size: dx = (self.y - self.t) / batch_size else: dx = self.y.copy() dx[np.arange(batch_size), self.t] -= 1 dx = dx / batch_size return dx class Dropout: def __init__(self, dropout_ratio=0.5): self.dropout_ratio = dropout_ratio self.mask = None def forward(self,x,train_flg=True): if train_flg: self.mask = np.random.rand(*x.shape) > self.dropout_ratio return x * self.mask else: return x * (1.0 - self.dropout_ratio) def backward(self,dout): return dout * self.mask #---------------------------------- 신경망 구현 -------------------------- class TwoLayerNet: def __init__(self,input_size, hidden_size, output_size, weight_init_std=0.01): self.params = {} self.params['W1'] = weight_init_std * np.random.randn(input_size, hidden_size) self.params['b1'] = np.zeros(hidden_size) self.params['W2'] = weight_init_std * np.random.randn(hidden_size, output_size) self.params['b2'] = np.zeros(output_size) self.layers = OrderedDict() self.layers['Affine1'] = Affine(self.params['W1'], self.params['b1']) self.layers['Relu'] = Relu() self.layers['Affine2'] = Affine(self.params['W2'], self.params['b2']) self.last_layer = SoftmaxWithLoss() def predict(self,x): for layer in self.layers.values(): x = layer.forward(x) return x def loss(self,x,t): y = self.predict(x) return self.last_layer.forward(y,t) def accuracy(self,x,t): y = self.predict(x) y = np.argmax(y, axis=1) if t.ndim != 1 : t = np.argmax(t, axis=1) accuracy = np.sum(y==t) / float(x.shape[0]) return accuracy def numerical_gradient(self,x,t): loss_W = lambda W : self.loss(x,t) grads = {} grads['W1'] = numerical_gradient(loss_W, self.params['W1']) grads['b1'] = numerical_gradient(loss_W, self.params['b1']) grads['W2'] = numerical_gradient(loss_W, self.params['W2']) grads['b2'] = numerical_gradient(loss_W, self.params['b2']) return grads def gradient(self,x,t): self.loss(x,t) dout = 1 dout = self.last_layer.backward(dout) layers = list(self.layers.values()) layers.reverse() for layer in layers: dout = layer.backward(dout) grads = {} grads['W1'] = self.layers['Affine1'].dW grads['b1'] = self.layers['Affine1'].db grads['W2'] = self.layers['Affine2'].dW grads['b2'] = self.layers['Affine2'].db return grads #--------------------------다층신경망------------------------------- class MultiLayerNet: """완전연결 다층 신경망 Parameters ---------- input_size : 입력 크기（MNIST의 경우엔 784） hidden_size_list : 각 은닉층의 뉴런 수를 담은 리스트（e.g. [100, 100, 100]） output_size : 출력 크기（MNIST의 경우엔 10） activation : 활성화 함수 - 'relu' 혹은 'sigmoid' weight_init_std : 가중치의 표준편차 지정（e.g. 0.01） 'relu'나 'he'로 지정하면 'He 초깃값'으로 설정 'sigmoid'나 'xavier'로 지정하면 'Xavier 초깃값'으로 설정 weight_decay_lambda : 가중치 감소(L2 법칙)의 세기 """ def __init__(self,input_size, hidden_size_list, output_size, activation='relu',weight_init_std='relu', weight_decay_lambda=0): self.input_size = input_size self.output_size = output_size self.hidden_size_list = hidden_size_list self.hidden_layer_num = len(hidden_size_list) self.weight_decay_lambda = weight_decay_lambda self.params = {} #가중치 초기화 self.__init_weight(weight_init_std) # __init_weight 이 뭐야? #계층 생성 activation_layer = {'sigmoid' : Sigmoid, 'relu' : Relu} self.layers = OrderedDict() for idx in range(1, self.hidden_layer_num+1): self.layers['Affine' + str(idx)] = Affine(self.params['W' + str(idx)], self.params['b' + str(idx)]) self.layers['Activation_function' + str(idx)] = activation_layer[activation]() idx = self.hidden_layer_num + 1 self.layers['Affine' + str(idx)] = Affine(self.params['W' + str(idx)], self.params['b' + str(idx)]) self.last_layer = SoftmaxWithLoss() def __init_weight(self, weight_init_std): """가중치 초기화 Parameters ---------- weight_init_std : 가중치의 표준편차 지정（e.g. 0.01） 'relu'나 'he'로 지정하면 'He 초깃값'으로 설정 'sigmoid'나 'xavier'로 지정하면 'Xavier 초깃값'으로 설정 """ all_size_list = [self.input_size] + self.hidden_size_list + [self.output_size] for idx in range(1, len(all_size_list)): scale = weight_init_std if str(weight_init_std).lower() in ('relu', 'he'): scale = np.sqrt(2.0 / all_size_list[idx - 1]) # ReLU를 사용할 때의 권장 초깃값 elif str(weight_init_std).lower() in ('sigmoid', 'xavier'): scale = np.sqrt(1.0 / all_size_list[idx - 1]) # sigmoid를 사용할 때의 권장 초깃값 self.params['W' + str(idx)] = scale * np.random.randn(all_size_list[idx - 1], all_size_list[idx]) self.params['b' + str(idx)] = np.zeros(all_size_list[idx]) def predict(self, x): for layer in self.layers.values(): x = layer.forward(x) return x def loss(self, x, t): """손실 함수를 구한다. Parameters ---------- x : 입력 데이터 t : 정답 레이블 Returns ------- 손실 함수의 값 """ y = self.predict(x) weight_decay = 0 for idx in range(1, self.hidden_layer_num + 2): W = self.params['W' + str(idx)] weight_decay += 0.5 * self.weight_decay_lambda * np.sum(W ** 2) return self.last_layer.forward(y, t) + weight_decay def accuracy(self, x, t): y = self.predict(x) y = np.argmax(y, axis=1) #index를 뱉어 if t.ndim != 1: t = np.argmax(t, axis=1) accuracy = np.sum(y == t) / float(x.shape[0]) return accuracy def numerical_gradient(self, x, t): """기울기를 구한다(수치 미분). Parameters ---------- x : 입력 데이터 t : 정답 레이블 Returns ------- 각 층의 기울기를 담은 딕셔너리(dictionary) 변수 grads['W1']、grads['W2']、... 각 층의 가중치 grads['b1']、grads['b2']、... 각 층의 편향 """ loss_W = lambda W: self.loss(x, t) grads = {} for idx in range(1, self.hidden_layer_num + 2): grads['W' + str(idx)] = numerical_gradient(loss_W, self.params['W' + str(idx)]) grads['b' + str(idx)] = numerical_gradient(loss_W, self.params['b' + str(idx)]) return grads def gradient(self, x, t): """기울기를 구한다(오차역전파법). Parameters ---------- x : 입력 데이터 t : 정답 레이블 Returns ------- 각 층의 기울기를 담은 딕셔너리(dictionary) 변수 grads['W1']、grads['W2']、... 각 층의 가중치 grads['b1']、grads['b2']、... 각 층의 편향 """ # forward self.loss(x, t) # backward dout = 1 dout = self.last_layer.backward(dout) layers = list(self.layers.values()) #list로 만들어줘야 가능 layers.reverse() for layer in layers: dout = layer.backward(dout) # 결과 저장 grads = {} for idx in range(1, self.hidden_layer_num + 2): grads['W' + str(idx)] = self.layers['Affine' + str(idx)].dW + self.weight_decay_lambda * self.layers[ 'Affine' + str(idx)].W grads['b' + str(idx)] = self.layers['Affine' + str(idx)].db return grads |
MNIST 히든레이어 2층 신경망 구현
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# -*- coding: utf-8 -*- #import pymysql import sys, os sys.path.append(os.pardir) import numpy as np from keras.datasets import mnist from collections import OrderedDict from code1 import * (X_train,y_train),(X_test, y_test) = mnist.load_data() # data normalization X_train = X_train / 255. X_test = X_test / 255. X_train = X_train.reshape(-1,28*28) X_test = X_test.reshape(-1,28*28) hidden_size_list = [300,100] network = MultiLayerNet(input_size=784,hidden_size_list=hidden_size_list,output_size=10,activation='relu') iters_num = 50 train_size = X_train.shape[0] batch_size = 200 learning_rate = 0.1 train_loss_list = [] train_acc_list = [] test_acc_list = [] iter_per_epoch = max(train_size / batch_size, 1) # 키 리스트 생성 key_list = [] for i in range(1,len(hidden_size_list)+2): key_list.append('W' + str(i)) key_list.append('b' + str(i)) for i in range(iters_num): for X_batch, y_batch in mini_batch(X_train,y_train,batch_size=batch_size): grad = network.gradient(X_batch,y_batch) for key in key_list: network.params[key] -= learning_rate * grad[key] if i % 5 == 0: train_acc = network.accuracy(X_train, y_train) test_acc = network.accuracy(X_test, y_test) print("train acc : ", train_acc) print("test acc : ", test_acc) |
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