cs231n_2017_gradient_check

关于梯度检测的一些代码及使用示例：

五种gradient_check:

from __future__ import print_function
from builtins import range

import numpy as np
from random import randrange

def eval_numerical_gradient(f, x, verbose=True, h=0.00001):
    """
    a naive implementation of numerical gradient of f at x
    - f should be a function that takes a single argument
    - x is the point (numpy array) to evaluate the gradient at
    """

    fx = f(x) # evaluate function value at original point
    grad = np.zeros_like(x)
    # iterate over all indexes in x
    it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
    while not it.finished:

        # evaluate function at x+h
        ix = it.multi_index
        oldval = x[ix]
        x[ix] = oldval + h # increment by h
        fxph = f(x) # evalute f(x + h)
        x[ix] = oldval - h
        fxmh = f(x) # evaluate f(x - h)
        x[ix] = oldval # restore

        # compute the partial derivative with centered formula
        grad[ix] = (fxph - fxmh) / (2 * h) # the slope
        if verbose:
            print(ix, grad[ix])
        it.iternext() # step to next dimension

    return grad


def eval_numerical_gradient_array(f, x, df, h=1e-5):
    """
    Evaluate a numeric gradient for a function that accepts a numpy
    array and returns a numpy array.
    """
    grad = np.zeros_like(x)
    it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
    while not it.finished:
        ix = it.multi_index

        oldval = x[ix]
        x[ix] = oldval + h
        pos = f(x).copy()
        x[ix] = oldval - h
        neg = f(x).copy()
        x[ix] = oldval

        grad[ix] = np.sum((pos - neg) * df) / (2 * h)
        it.iternext()
    return grad


def eval_numerical_gradient_blobs(f, inputs, output, h=1e-5):
    """
    Compute numeric gradients for a function that operates on input
    and output blobs.

    We assume that f accepts several input blobs as arguments, followed by a
    blob where outputs will be written. For example, f might be called like:

    f(x, w, out)

    where x and w are input Blobs, and the result of f will be written to out.

    Inputs:
    - f: function
    - inputs: tuple of input blobs
    - output: output blob
    - h: step size
    """
    numeric_diffs = []
    for input_blob in inputs:
        diff = np.zeros_like(input_blob.diffs)
        it = np.nditer(input_blob.vals, flags=['multi_index'],
                       op_flags=['readwrite'])
        while not it.finished:
            idx = it.multi_index
            orig = input_blob.vals[idx]

            input_blob.vals[idx] = orig + h
            f(*(inputs + (output,)))
            pos = np.copy(output.vals)
            input_blob.vals[idx] = orig - h
            f(*(inputs + (output,)))
            neg = np.copy(output.vals)
            input_blob.vals[idx] = orig

            diff[idx] = np.sum((pos - neg) * output.diffs) / (2.0 * h)

            it.iternext()
        numeric_diffs.append(diff)
    return numeric_diffs


def eval_numerical_gradient_net(net, inputs, output, h=1e-5):
    return eval_numerical_gradient_blobs(lambda *args: net.forward(),
                inputs, output, h=h)


def grad_check_sparse(f, x, analytic_grad, num_checks=10, h=1e-5):
    """
    sample a few random elements and only return numerical
    in this dimensions.
    """

    for i in range(num_checks):
        ix = tuple([randrange(m) for m in x.shape])

        oldval = x[ix]
        x[ix] = oldval + h # increment by h
        fxph = f(x) # evaluate f(x + h)
        x[ix] = oldval - h # increment by h
        fxmh = f(x) # evaluate f(x - h)
        x[ix] = oldval # reset

        grad_numerical = (fxph - fxmh) / (2 * h)
        grad_analytic = analytic_grad[ix]
        rel_error = (abs(grad_numerical - grad_analytic) /
                    (abs(grad_numerical) + abs(grad_analytic)))
        print('numerical: %f analytic: %f, relative error: %e'
              %(grad_numerical, grad_analytic, rel_error))

使用示例：

# Test the affine_backward function
np.random.seed(231)
x = np.random.randn(10, 2, 3)
w = np.random.randn(6, 5)
b = np.random.randn(5)
dout = np.random.randn(10, 5)

dx_num = eval_numerical_gradient_array(lambda x: affine_forward(x, w, b)[0], x, dout)
dw_num = eval_numerical_gradient_array(lambda w: affine_forward(x, w, b)[0], w, dout)
db_num = eval_numerical_gradient_array(lambda b: affine_forward(x, w, b)[0], b, dout)

_, cache = affine_forward(x, w, b)
dx, dw, db = affine_backward(dout, cache)

# The error should be around 1e-10
print('Testing affine_backward function:')
print('dx error: ', rel_error(dx_num.reshape(dx_num.shape[0],-1), dx))
print('dw error: ', rel_error(dw_num, dw))
print('db error: ', rel_error(db_num, db))

rel_error函数:

def rel_error(x, y):
  """ returns relative error """
  return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))