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)
    num_train = X.shape[0]
    num_dims = W.shape[0]
    num_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)*****

    for training_example_index in range(num_train):
        # Compute cross-entropy loss
        raw_scores = X[training_example_index].dot(W)
        raw_scores -= np.max(raw_scores)    # Prevent numerical instability for Softmax computation
        softmax_scores = np.exp(raw_scores) / np.sum(np.exp(raw_scores))
        loss += -np.log(softmax_scores[y[training_example_index]])

        # Compute gradient. Mathematical explanation here: https://stackoverflow.com/a/67046905/13220395
        for dimension in range(num_dims):
            for class_index in range(num_classes):
                if class_index == y[training_example_index]:
                    dW[dimension,class_index] += X[training_example_index, dimension] * (softmax_scores[class_index] - 1)
                else:
                    dW[dimension, class_index] += X[training_example_index, dimension] * softmax_scores[class_index]
    
    # Average loss & add regularization
    loss /= num_train
    loss += reg * np.sum(W*W)
    
    # Average gradient & add regularization
    dW /= num_train
    dW += 2 * reg * 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)
    #############################################################################
    # 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)*****
    num_train = X.shape[0]
    
    raw_scores = X.dot(W)
    raw_scores -= np.max(raw_scores)
    softmax_scores = np.exp(raw_scores) / np.sum(np.exp(raw_scores), axis = 1, keepdims=True)
    loss = np.sum(-np.log(softmax_scores[range(num_train), y]))
    loss /= num_train
    loss += reg * np.sum(W*W)
    
    dscores = softmax_scores
    dscores[range(num_train), y] -= 1
    dW = np.dot(X.T, dscores)
    dW /= num_train
    dW += 2 * reg * W
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW