We used a Gaussian process on the outputs from a CNN, not separately. What I meant by locality is the idea that two points which are close to each other should

We used a Gaussian process on the outputs from a CNN, not separately. What I meant by locality is the idea that two points which are close to each other should also have predictions close to each other, assuming that there is some underlying Gaussian variable we can't see immediately from the data or from the CNN. One example could be housing prices: if your neighbor sold their house, controlled for other factors like square ft or the number of bedrooms, you should value your own house similarly. We assume that there is this underlying quality of the neighborhood, possibly given by distance between houses. The niche that GPs fill is broad. Two applications I've seen were their use in trying to find the missing MH370 flight, and another is in hyperparameter tuning of ML models.