def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a tuple of:
- loss: Scalar giving the loss
"""
N = x.shape[0]
C = x.shape[1]
if len(y.shape) == 1:
#convert it to one hot encoding
onehot_y = np.zeros([N, C])
np.onehot_encode(y, onehot_y)
else:
onehot_y = y
probs = x - np.max(x, axis=1, keepdims=True)
loss = -np.sum(probs * onehot_y) / N
loss += np.sum(np.log(np.sum(np.exp(probs), axis=1, keepdims=True))) / N
return loss
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a tuple of:
- loss: Scalar giving the loss
"""
N = x.shape[0]
C = x.shape[1]
if len(y.shape) == 1:
#convert it to one hot encoding
onehot_y = np.zeros([N, C])
np.onehot_encode(y, onehot_y)
else:
onehot_y = y
probs = x - np.max(x, axis=1, keepdims=True)
loss = -np.sum(probs * onehot_y) / N
loss += np.sum(np.log(np.sum(np.exp(probs), axis=1, keepdims=True))) / N
return loss
def softmax_cross_entropy(prob, label):
"""
Computes the cross entropy for softmax activation.
Inputs:
- prob: Probability, of shape (N, C) where x[i, j] is the probability for the jth class
for the ith input.
- label: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a Value:
- cross_entropy
"""
N = prob.shape[0]
C = prob.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
return -np.sum(np.log(prob) * onehot_label) / N
def softmax_loss(x, label):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a tuple of:
- loss: Scalar giving the loss
"""
N = x.shape[0]
C = x.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
prob = np.softmax_output(x, onehot_label)
return softmax_cross_entropy(prob, onehot_label)
def softmax_cross_entropy(prob, label):
"""
Computes the cross entropy for softmax activation.
Inputs:
- prob: Probability, of shape (N, C) where x[i, j] is the probability for the jth class
for the ith input.
- label: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a Value:
- cross_entropy
"""
N = prob.shape[0]
C = prob.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
return -np.sum(np.log(prob) * onehot_label) / N
def softmax_probability(p, channel):
N, C = p.shape
p -= np.max(p, axis=1).reshape((N, 1))
code = np.zeros((N, C))
np.onehot_encode(channel, code)
p = np.exp(p)
selected_p = p * code
total_p = np.sum(p, axis=1).reshape((N, 1))
return np.sum(selected_p / total_p, axis=1)
def softmax_cross_entropy(prob, label):
N = prob.shape[0]
C = prob.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
return -np.sum(np.log(prob) * onehot_label) / N
def softmax_cross_entropy(prob, label):
N = prob.shape[0]
C = prob.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
return -np.sum(np.log(prob) * onehot_label) / N
def l2_loss(x, label):
"""
The Mean Square Error loss for regression.
"""
N = x.shape[0]
C = x.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
return np.sum((x - onehot_label)**2) / N
def l2_loss(x, label):
"""
The Mean Square Error loss for regression.
"""
N = x.shape[0]
C = x.shape[1]
if len(label.shape) == 1:
#convert it to one hot encoding
onehot_label = np.zeros([N, C])
np.onehot_encode(label, onehot_label)
else:
onehot_label = label
return np.sum((x - onehot_label) ** 2) / N
