I contribute on all three sites.
There is a large amount of overlap in subject matter, especially between Data Science and Cross Validated regarding machine learning algorithms. When it comes to ML questions, those two sites mainly differ in where the practical lines are drawn between subjectively good/bad and on-topic/off-topic. This is a murky area, and neither site is 100% consistent, because it is driven by individual behaviour and there is not strong consensus yet.
However, my feeling is that Data Science is more accepting of practical implementation issues - whether for code, specific data issues, or specific technologies. Whilst Cross Validated is the go to place for underlying mathematics and theory. Often a question could be valid on both sites at its core, but may need to be phrased differently to fit the culture. Again, my feeling is that CV, as the largest of the three sites, has the strongest internal culture here, and is driving how a lot of the edge cases work.
Meanwhile Artificial Intelligence is still quite a new site and trying to find its voice and community. That means that topics that should logically be very strong for it, such as Reinforcement Learning, often get asked on DS and CV sites, because even though a low fraction of experts on those sites know RL well, a low fraction of CV or DS users is still very competitive with the available experts on AI.
If I were to offer some opinion on the questions you have posted:
How to train the RPN in Faster R CNN? - should be on Data Science, as it is asking for practical advice working with a specific neural network based on reading a paper.
How does region proposal network (RPN) and R-CNN works? despite the upvotes is IMO off-topic on any Stack Exchange network, as it is just asking for external resources and with very little context
Binary score in RPN (Faster-RCNN) could be on any of the three Stack Exchanges, as it could be answered from different perspectives. By posting on AI, the user can currently expect a descriptive, qualitative answer, without maths (because no LaTex implemented yet) or large amounts of detail. Or, sadly, no answer at all, because not enough experts available to cover all possible technical subjects.
Outside of machine learning, I think the sites have some clearer differences, and these can in part be seen by looking at the top 20 tags on each one. The following are all tags in the top 20 of each site, and not on the first page of the other two:
Cross Validated https://stats.stackexchange.com/tags
probability, hypothesis-testing, self-study, distributions, bayesian, correlation, statistical-significance, mathematical-statistics, anova, normal-distribution,
Data Science https://datascience.stackexchange.com/tags
data-mining, scikit-learn, keras, dataset, text-mining, bigdata, pandas
Artificial Intelligence https://ai.stackexchange.com/tags
ai-design, reinforcement-learning, philosophy, genetic-algorithms, ai-basics, game-ai, computer-vision
Of course, that is not to say that Data Science would not consider probability questions, or Cross Validated does not deal with deep learning issues. But I think the differences between the tags do show that a different focus for each community is evident.