ANN Variable Correlation I am using an ANN for predicting high value customers based on their first 0, 5, 10 days.

I've made 3 variables: PurchasesOnDay0, PurchasesOnDay0to5, PurchasesOnDay0to10.

PurchasesOnDay0to5 will include PurchasesOnDay0 and PurchasesOnDay0to10 will include PurchasesOnDay0to10 and PurchasesOnDay0to5.

My question is, will the ANN pick up the correlation and adjust accordingly or will this be a problem when creating my model?
Generically speaking a neural network can automatically learn the needed feature transformation for a model to perform well.  What tends to matter more is how the features relate to your output.

If you're ever bored, you can run your original matrix, a transformed matrix that has been de-correlated via a principle axis transformation, and the original matrix combined with correlation information.  I suspect performance using the same architecture will be relatively similar.