# How to measure co-adaptation occuring in a multi-layer perceptron neural network that does not use a drop out?

The dropout proposed by Hinton is said to prevent co-adaptation. My question is how can I measure the co-adaptation that occurs in a multi-layer perceptron that does not use a drop out?

To compute the hidden layer covariance, just take your trained MLP and find a stack of data. Run the data through the MLP until you compute the activations for the hidden layer of interest: $$H = \sigma(WX + B)$$ for an MLP with one hidden layer and activation function $\sigma$. Once you have these values, just compute their covariance: $$S = \frac{1}{n}(H-\bar{H})(H-\bar{H})^\top.$$
To get a single numeric metric from the hidden feature covariance, you could use lots of different things, but I think it's convenient to compute the norm of the covariance less the identity matrix (i.e., the amount of "non-identity stuff" in the observed covariance matrix): $$\ell = \|S-I\|_F.$$