CS231N Assignment1 softmax 笔记

• -为Softmax分类器实现完全矢量化的损失函数
• -实现解析梯度完全矢量化的表达式
• 使用数值梯度检查实现结果
• 使用验证集调整学习率和正则化强度
• 使用SGD优化损失函数
• 可视化最终学习的权重

softmax.ipynb

库、绘图设置和数据的导入和SVM一样

Train data shape:  (49000, 3073)
Train labels shape:  (49000,)
Validation data shape:  (1000, 3073)
Validation labels shape:  (1000,)
Test data shape:  (1000, 3073)
Test labels shape:  (1000,)
dev data shape:  (500, 3073)
dev labels shape:  (500,)

Softmax Classifier

 `cs231n/classifiers/softmax.py`

首先完成带嵌套循环的softmax_loss_naive

def softmax_loss_naive(W, X, y, reg):
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W) #创建一个与W具有相同形状的全零数组。

    N = X.shape[0]
    for i in range(N):
        score = X[i].dot(W) #长度为C?
        exp_score = np.exp(score - np.max(score)) #防止溢出
        loss += -np.log(exp_score[y[i]]/np.sum(exp_score)) / N #复刻公式
        #loss += (-np.log(exp_score[y[i]])+ np.log(np.sum(exp_score))) / N #展开
        dexp_score = np.zeros_like(exp_score)
        dexp_score[y[i]] -= 1/exp_score[y[i]]/N
        dexp_score += 1 /np.sum(exp_score) / N
        dscore = dexp_score *exp_score
        dW += X[[i]].T.dot([dscore])
    loss +=reg*np.sum(W**2)
    dW += 2*reg*W
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW

注意使用exp避免数值溢出之后要用本地梯度乘上游梯度得到梯度值。

向量化的softmax_loss_vectorized

def softmax_loss_vectorized(W, X, y, reg):

    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)
                                                      #

    scores = X.dot(W)
    #exp_score = np.exp(score - np.max(score))
    scores -= np.max(scores, axis=1, keepdims=True)#保持dim
    exp_scores = np.exp(scores)

    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)

    # Compute the loss
    N = X.shape[0]  #有点不熟悉这个维度012的顺序
    loss = np.sum(-np.log(probs[np.arange(N), y])) / N
    loss +=  reg * np.sum(W * W) #正则化强度的系数其实无所谓？只要不太小应该效果都差不多

    # Compute the gradient
    dscores = probs
    dscores[np.arange(N), y] -= 1
    dscores /= N

    dW = X.T.dot(dscores)
    dW += reg * W

    return loss, dW

超参数调试

# Use the validation set to tune hyperparameters (regularization strength and
# learning rate). You should experiment with different ranges for the learning
# rates and regularization strengths; if you are careful you should be able to
# get a classification accuracy of over 0.35 on the validation set.

from cs231n.classifiers import Softmax
results = {}
best_val = -1
best_softmax = None

################################################################################
# TODO:                                                                        #
# Use the validation set to set the learning rate and regularization strength. #
# This should be identical to the validation that you did for the SVM; save    #
# the best trained softmax classifer in best_softmax.                          #
################################################################################

# Provided as a reference. You may or may not want to change these hyperparameters
learning_rates = [3e-7,4e-7,5e-7]
regularization_strengths = [0.5e4, 1e4,1.5e4,2e4]

# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

# Iterate over all hyperparameter combinations
for lr in learning_rates:
    for reg in regularization_strengths:
        # Create a new Softmax classifier
        softmax = Softmax()

        # Train the classifier on the training set
        softmax.train(X_train, y_train, learning_rate=lr, reg=reg, num_iters=1000)

        # Evaluate the classifier on the training and validation sets
        train_accuracy = np.mean(softmax.predict(X_train) == y_train)
        val_accuracy = np.mean(softmax.predict(X_val) == y_val)

        # Save the results for this hyperparameter combination
        results[(lr, reg)] = (train_accuracy, val_accuracy)

        # Update the best validation accuracy and best classifier
        if val_accuracy > best_val:
            best_val = val_accuracy
            best_softmax = softmax

# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

# Print out results.
for lr, reg in sorted(results):
    train_accuracy, val_accuracy = results[(lr, reg)]
    print('lr %e reg %e train accuracy: %f val accuracy: %f' % (
                lr, reg, train_accuracy, val_accuracy))

print('best validation accuracy achieved during cross-validation: %f' % best_val)

目前调出来比较好一点的是

lr 5.000000e-07 reg 5.000000e+03 train accuracy: 0.386000 val accuracy: 0.392000

最后看看在test上的准确率

# evaluate on test set
# Evaluate the best softmax on test set
y_test_pred = best_softmax.predict(X_test)
test_accuracy = np.mean(y_test == y_test_pred)
print('softmax on raw pixels final test set accuracy: %f' % (test_accuracy, ))

softmax on raw pixels final test set accuracy: 0.384000

对比一下不同步数的权重图像差异

100	500	1000
1500	3000	5000

（多整了一些）噪点的减少还是非常明显的，虽然1500之后准确率没太大区别