Explain PinSage-Style Neighbor Sampling to a Skeptical Interviewer

The interviewer says: "Our item graph has 2 billion nodes and hub items with millions of neighbours. You want a 3-layer GraphSAGE. Explain how you would train it at all, why sampling uniformly is a problem, and what PinSage did differently."

1. Compute the size of the computation tree per target at fan-out (20, 15, 10), and say what that means for memory and for hub items.
2. Explain the variance of a sampled neighbour mean and what doubling the fan-out buys.
3. Describe PinSage's importance-based neighbour selection from memory (state that this is from memory) and do a small worked example with visit counts 12, 7 and 1.
4. Say what you would precompute instead of running a GNN online.