Gist for medium post "Just another post about grad descend"

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=0.0):
    """
    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)

    #############################################################################
    # 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)*****
    D, C = W.shape
    N, D = X.shape
    F = X @ W ## N x C
    S = np.exp(F) / np.sum(np.exp(F), axis=1, keepdims=True)
    for i in range(N):
        s = S[i, :]
        loss -= np.log(s[y[i]])
    loss /= N

    dS = np.copy(S)
    for i in range(N):
        dS[i, y[i]] -= 1
    dW = X.T @ dS
    dW /= N
    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW


def softmax_loss_vectorized(W, X, y, reg=0.0):
    """
    Softmax loss function, vectorized version.

    Inputs and outputs are t he 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)*****

    D, C = W.shape
    N, D = X.shape

    F = X @ W
    F -= np.max(F, axis=1, keepdims=True)
    S = np.exp(F) / np.sum(np.exp(F), axis=1, keepdims=True)
    loss -= np.mean(np.log(S[np.arange(N), y]))

    dS = np.copy(S)
    dS[np.arange(N), y] -= 1
    dW = X.T @ dS
    dW /= N

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

    return loss, dW

softmax_debugging_v1.ipynb