MATLAB：矢量化反向传播（没有循环训练示例）

Question

在 MATLAB/Octave 中，如何在训练示例上不进行任何循环的情况下实现反向传播？

This answer 讲了并行理论，但是如何在实际的 Octave 代码中实现呢？

Answer 1

对我来说，最后一块拼图来自computing sum of outer products。

这是我想出的：

% X is a {# of training examples} x {# of features} matrix
% Y is a {# of training examples} x {# of output neurons} matrix
% Theta is a cell matrix containing Theta{1}...Theta{n}

% Number of training examples
m = size(X, 1);

% Get h(X) and z (non-activated output of all neurons in network)
[hX, z, activation] = predict(Theta, X);

% Get error of output layer
layers = 1 + length(Theta);
d{layers} = hX - Y;

% Propagate errors backwards through hidden layers
for layer = layers-1 : -1 : 2
  d{layer} = d{layer+1} * Theta{layer};
  d{layer} = d{layer}(:, 2:end); % Remove "error" for constant bias term
  d{layer} .*= sigmoidGradient(z{layer});
end

% Calculate Theta gradients
for l = 1:layers-1
  Theta_grad{l} = zeros(size(Theta{l}));

  % Sum of outer products
  Theta_grad{l} += d{l+1}' * [ones(m,1) activation{l}];

  % Add regularisation term
  Theta_grad{l}(:, 2:end) += lambda * Theta{l}(:, 2:end);
  Theta_grad{l} /= m;
end