Numpy만으로 2층신경망짜기(DNN)
처음부터 하나씩 머릿 속으로 그리고 스케치하며 작동원리를 생각했다. tensor 차원을 다루는 방법을 알았으며 몇 가지 신기한 테크닉 또한 배웠다.
오차역전파를 통한 빠른 학습이 중앙차분으로 코딩한 미분보다 훨씬 빠른 것을 보고 굉장히 놀랬다.
풀어야 하는 궁금증 : Affine class에서 Bias를 나타내는 b를 보면 broad cast를 사용한다. mini_batch로 데이터를 받는다면 데이터 1개씩 차례대로 계산되는 것인지 (이게 맞는 것 같음) 아니면 200개를 한 번에 계산하는지 (이렇게 되면 bias가 broadcast 작동으로 공통의 bias를 공유하게 된다 데이터끼리) 알아봐야함.
entire code:
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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) #여기가 이해가 안되네 self.db = np.sum(dout, axis=0) 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 #----------------------------------2층 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 #------------------------2층 신경망으로 mnist 학습하기------------------ from keras.datasets import mnist (x_train, y_train), (x_test, y_test) = mnist.load_data() num = np.unique(y_train) num = num.shape[0] y_train = np.eye(num)[y_train] num = np.unique(y_test) num = num.shape[0] y_test = np.eye(num)[y_test] x_train = x_train / 255. x_test = x_test / 255. x_train = x_train.reshape(x_train.shape[0], -1) x_test = x_test.reshape(x_test.shape[0], -1) epoch_cycle = 20 batch_size = 200 learning_rate = 0.1 network = TwoLayerNet(input_size=784, hidden_size=300, output_size=10) for i in range(epoch_cycle): for x_batch, y_batch in mini_batch(x_train,y_train): grad = network.gradient(x_batch,y_batch) for key in ['W1','b1','W2','b2']: 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) |
result : 
