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一、参数更新策略
1.SGD
也就是随机梯度下降,最简单的更新形式是沿着负梯度方向改变参数(因为梯度指向的是上升方向,但是我们通常希望最小化损失函数)。假设有一个参数向量x及其梯度dx,那么最简单的更新的形式是:
x += - learning_rate * dx
其中learning_rate是一个超参数,表示的是更新的幅度。这是一个重要的参数,lr过大可能会出现loss异常的情况,过小会使训练时间过长,后面也会介绍lr参数更新的一些trick。
2. Momentum
又被成为动量法,我觉得很多地方对这个方法并没有说清楚,我个人简单的理解是,在更新梯度的时候,我们要注意保留之前的梯度的信息,可以相信,一个梯度一直朝下减小的函数,一般不会遇到突然向左减小,所以加上动量以后,就可以处理这种情况,这个如果知道共轭点的话(不确定是不是这么叫的,也就是一个梯度下降的时候,向下一直减小,但是左右一直变化幅度很大的情况),就知道momentum的强大了。
def sgd_momentum(w, dw, config=None):
"""
Performs stochastic gradient descent with momentum.
config format:
- learning_rate: Scalar learning rate.
- momentum: Scalar between 0 and 1 giving the momentum value.
Setting momentum = 0 reduces to sgd.
- velocity: A numpy array of the same shape as w and dw used to store a moving
average of the gradients.
"""
if config is None: config = {}
config.setdefault(‘learning_rate‘, 1e-2)
config.setdefault(‘momentum‘, 0.9)
v = config.get(‘velocity‘, np.zeros_like(w))
next_w = None
v = config[‘momentum‘] * v - config[‘learning_rate‘] * dw
next_w = w + v
config[‘velocity‘] = v
return next_w, config
3.Nestero
这个是动量法的进阶版,既然我们要用之前梯度的信息,那么为什么不在更新当前梯度的时候,直接取最后的方向呢。
x_ahead = x + mu * v # 计算dx_ahead(在x_ahead处的梯度,而不是在x处的梯度) v = mu * v - learning_rate * dx_ahead x += v
在实际编程的时候,我们采用的是下面的方法,因为这样就可以和之前的代码统一起来了 ,因为一般来说我们只有dx:
v_prev = v # 存储备份 v = mu * v - learning_rate * dx # 速度更新保持不变 x += -mu * v_prev + (1 + mu) * v # 位置更新变了形式
为什么可以这样做?据说只要根据X_ahead=x+mu*v应该是可以换算的,但是我试了一下...没推出来.我怀疑只是实际使用的时候效果相似,不一定推出来,因为你不可能去计算dx_ahead的..
4.RMSProp and Adam
这两个是学习速率的更新策略
def rmsprop(x, dx, config=None): """ Uses the RMSProp update rule, which uses a moving average of squared gradient values to set adaptive per-parameter learning rates. config format: - learning_rate: Scalar learning rate. - decay_rate: Scalar between 0 and 1 giving the decay rate for the squared gradient cache. - epsilon: Small scalar used for smoothing to avoid dividing by zero. - cache: Moving average of second moments of gradients. """ if config is None: config = {} config.setdefault(‘learning_rate‘, 1e-2) config.setdefault(‘decay_rate‘, 0.99) config.setdefault(‘epsilon‘, 1e-8) config.setdefault(‘cache‘, np.zeros_like(x)) next_x = None cache = config[‘cache‘] decay_rate = config[‘decay_rate‘] learning_rate = config[‘learning_rate‘] epsilon = config[‘epsilon‘] cache = decay_rate * cache + (1 - decay_rate) * (dx**2) #用一种更为平滑的方式更新lr,注意到这里是累加的,因为越往后惩罚项越大,lr越小 x += - learning_rate * dx / (np.sqrt(cache) + epsilon) config[‘cache‘] = cache next_x = x return next_x, config def adam(x, dx, config=None): """ Uses the Adam update rule, which incorporates moving averages of both the gradient and its square and a bias correction term. config format: - learning_rate: Scalar learning rate. - beta1: Decay rate for moving average of first moment of gradient. - beta2: Decay rate for moving average of second moment of gradient. - epsilon: Small scalar used for smoothing to avoid dividing by zero. - m: Moving average of gradient. - v: Moving average of squared gradient. - t: Iteration number. """ if config is None: config = {} config.setdefault(‘learning_rate‘, 1e-3) config.setdefault(‘beta1‘, 0.9) config.setdefault(‘beta2‘, 0.999) config.setdefault(‘epsilon‘, 1e-8) config.setdefault(‘m‘, np.zeros_like(x)) config.setdefault(‘v‘, np.zeros_like(x)) config.setdefault(‘t‘, 0) next_x = None m = config[‘m‘] v = config[‘v‘] beta1 = config[‘beta1‘] beta2 = config[‘beta2‘] learning_rate = config[‘learning_rate‘] epsilon = config[‘epsilon‘] t = config[‘t‘] t += 1 m = beta1 * m + (1 - beta1) * dx v = beta2 * v + (1 - beta2) * (dx**2) m_bias = m / (1 - beta1**t) v_bias = v / (1 - beta2**t) x += - learning_rate * m_bias / (np.sqrt(v_bias) + epsilon) next_x = x config[‘m‘] = m config[‘v‘] = v config[‘t‘] = t return next_x, config
二、Batch Normalization
接下来要介绍两个在训练神经网络的时候,非常有用技巧,首先是batch normalization,简单的解释:在每次NN的输入的时候,我们都知道要进行数据预处理,一般是让数据是zero means和单位方差的,这样对于训练是有好处的,但当数据走过几层以后,就基本不可能还保持这个特性了,BN做的事情就是在每一层的开始,加上这个操作,但是有的数据可能会因此丢失了一些信息,所以再加上beta和gama来恢复原始数据,这里beta和gama是可学习的。
#BN参数的初始化 if self.use_batchnorm and i < len(hidden_dims): self.params[‘gamma‘ + str(i+1)] = np.ones((1, layers_dims[i+1])) self.params[‘beta‘ + str(i+1)] = np.zeros((1, layers_dims[i+1]))
BN的的关键是前向传播,后向传播以及实际使用的。
按照上面推导出来的公式,即可进行BN层的构建:
def batchnorm_forward(x, gamma, beta, bn_param): mode = bn_param[‘mode‘] #因为train和test是两种不同的方法 eps = bn_param.get(‘eps‘, 1e-5) momentum = bn_param.get(‘momentum‘, 0.9) N, D = x.shape running_mean = bn_param.get(‘running_mean‘, np.zeros(D, dtype=x.dtype)) running_var = bn_param.get(‘running_var‘, np.zeros(D, dtype=x.dtype)) out, cache = None, None if mode == ‘train‘: sample_mean = np.mean(x, axis=0, keepdims=True) # [1,D] sample_var = np.var(x, axis=0, keepdims=True) # [1,D] x_normalized = (x - sample_mean) / np.sqrt(sample_var + eps) # [N,D] out = gamma * x_normalized + beta cache = (x_normalized, gamma, beta, sample_mean, sample_var, x, eps) running_mean = momentum * running_mean + (1 - momentum) * sample_mean #通过moument得到最终的running_mean和running_var running_var = momentum * running_var + (1 - momentum) * sample_var elif mode == ‘test‘: x_normalized = (x - running_mean) / np.sqrt(running_var + eps) #test的时候如何通过BN层 out = gamma * x_normalized + beta else: raise ValueError(‘Invalid forward batchnorm mode "%s"‘ % mode) # Store the updated running means back into bn_param bn_param[‘running_mean‘] = running_mean bn_param[‘running_var‘] = running_var return out, cache def batchnorm_backward(dout, cache): dx, dgamma, dbeta = None, None, None x_normalized, gamma, beta, sample_mean, sample_var, x, eps = cache N, D = x.shape dx_normalized = dout * gamma # [N,D] x_mu = x - sample_mean # [N,D] sample_std_inv = 1.0 / np.sqrt(sample_var + eps) # [1,D] dsample_var = -0.5 * np.sum(dx_normalized * x_mu, axis=0, keepdims=True) * sample_std_inv**3 dsample_mean = -1.0 * np.sum(dx_normalized * sample_std_inv, axis=0, keepdims=True) - \ 2.0 * dsample_var * np.mean(x_mu, axis=0, keepdims=True) dx1 = dx_normalized * sample_std_inv dx2 = 2.0/N * dsample_var * x_mu dx = dx1 + dx2 + 1.0/N * dsample_mean dgamma = np.sum(dout * x_normalized, axis=0, keepdims=True) dbeta = np.sum(dout, axis=0, keepdims=True) return dx, dgamma, dbeta
Batch Normalization解决的一个重要问题就是梯度饱和,配合Relu可以说基本解决了梯度饱和的问题。
三、Dropout
dropout是非常好理解的,就是在训练的时候以一定的概率来去每层的神经元,如下图所示:
个人理解:每次训练进行deoptout的操作,可以防止过拟合,为什么呢,因为每次训练的模型都长的不一样,但是他们的参数实际上是共享的,可以简单的理解为是个bagging的操作,众所周知..bagging在machine learning中是防止过拟合的神器,每次限制神经元的数量也防止过大的神经网络对数据集的过拟合。
还可以理解为dropout是一个正则化的操作,他在每次训练的时候,强行让一些feature为0,这样提高了网络的稀疏表达能力
def dropout_forward(x, dropout_param): p, mode = dropout_param[‘p‘], dropout_param[‘mode‘] if ‘seed‘ in dropout_param: np.random.seed(dropout_param[‘seed‘]) mask = None out = None if mode == ‘train‘: mask = (np.random.rand(*x.shape) < p) / p #注意这里除以了一个P,这样在test的输出的时候,维持原样即可 out = x * mask elif mode == ‘test‘: out = x cache = (dropout_param, mask) out = out.astype(x.dtype, copy=False) return out, cache def dropout_backward(dout, cache): dropout_param, mask = cache mode = dropout_param[‘mode‘] dx = None if mode == ‘train‘: dx = dout * mask elif mode == ‘test‘: dx = dout return dx
四、总结
总的来说,很多trick都是在train model的时候很有用,不过向BN已经逐渐要被替代和取消了,所以说明实时的follow最新的会议是多么的重要......然后,一些推导之后还是要在自己做一做,预备在后面复习cs231n的讲义的时候做一遍推导。
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原文地址:http://www.cnblogs.com/daihengchen/p/5769999.html