softmax.py

from builtins import range
import numpy as np
from random import shuffle
from past.builtins import xrange

def softmax_loss_naive(W, X, y, reg):
    """
    Softmax loss function, naive implementation (with loops)

    Inputs have dimension D, there are C classes, and we operate on minibatches
    of N examples.

    Inputs:
    - W: A numpy array of shape (D, C) containing weights.
    - X: A numpy array of shape (N, D) containing a minibatch of data.
    - y: A numpy array of shape (N,) containing training labels; y[i] = c means
      that X[i] has label c, where 0 <= c < C.
    - reg: (float) regularization strength

    Returns a tuple of:
    - loss as single float
    - gradient with respect to weights W; an array of same shape as W
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)
    n = X.shape[0]
    classes = W.shape[1]
    #############################################################################
    # TODO: Compute the softmax loss and its gradient using explicit loops.     #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    scores = np.dot(X, W)
    scores -= np.max(scores, axis=1)[:, None]

    for i in range(n):
        loss += -scores[i][y[i]] + np.log(np.exp(scores[i]).sum())
        dW += X[i][:, None] * np.exp(scores[i]) / np.exp(scores[i]).sum()
        dW[:, y[i]] -= X[i]

    loss /= n
    dW /= n

    loss += reg * np.sum(W ** 2)
    dW += reg * 2 * W
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
    return loss, dW


def softmax_loss_vectorized(W, X, y, reg):
    """
    Softmax loss function, vectorized version.

    Inputs and outputs are the same as softmax_loss_naive.
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)
    n = X.shape[0]

    #############################################################################
    # TODO: Compute the softmax loss and its gradient using no explicit loops.  #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    scores = np.dot(X, W)
    scores -= np.max(scores, axis=1)[:, None]
    loss = (-scores[range(n), y] + np.log(np.sum(np.exp(scores), axis=1))).sum()

    coef = np.exp(scores) / np.sum(np.exp(scores), axis=1)[:, None]
    coef[np.arange(n), y] -= 1
    dW = np.dot(X.T, coef)

    loss /= n
    dW /= n

    loss += reg * np.sum(W*W)
    # print('reg', W.shape, (W ** 2)[-1])
    dW += reg * 2 * W
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW