I am running a neural net to predict used car prices, sample size is 800. Using both 10-fold cross validation (10 times) and 1/3 holdback (10 times), the $R^2$ for training is about 0.60 and for validation is about 0.68 for all 20 runs. The smallest difference in the 20 runs is training $R^2$ = 0.64 and validation $R^2$ = 0.68, so the training $R^2$ is always less than the validation $R^2$.
I am very used to seeing training $R^2$ bigger than validation $R^2$, which means overfitting. In the past when I have seen training $R^2$ less than validation $R^2$, it has been a transient phenomenon that disappeared when I re-ran the model. This is the first time that I have seen validation $R^2$ systematically larger than training $R^2$.
I have no idea what this means. Any thoughts?