This page answers four questions about the seven solutions as a group. It is for a reader who has read the short pages of this chapter. Each answer is short. It links to the page that explains the idea in full.
Contents#
- What are the seven solutions, in one line each?
- Why are there seven solutions instead of one good one?
- What does each pair of solutions compare, and why is that worth more than a ranking?
- Why do the learned solutions score below the plain geometry, and what would it take to beat it?
1. What are the seven solutions, in one line each?#
- A printed rule takes the shortest safe push.
- A trained model puts the same safe pushes in order.
- A network copies solution 2's pushes from a picture.
- A learned model predicts each push, and a search picks the best.
- A borrowed robot model is used as it downloads.
- The same borrowed model is trained a little on this cell's pushes.
- A newer, larger borrowed model is trained the same way.
How each one works gives a fuller line for each.
2. Why are there seven solutions instead of one good one?#
One solution would give one score and no reason for it. Seven solutions put the learning in seven different places. Each one is a test of where learning helps. The introduction to this chapter says this in full.
3. What does each pair of solutions compare, and why is that worth more than a ranking?#
Each pair differs in one thing, so the gap in score is that thing's worth. Solution 1 against 2 asks whether ranking safe pushes helps. Solution 3 against 4 asks whether to copy pushes or to plan with a model. Solution 5 against 6 asks what training buys. Solution 6 against 7 asks what a newer, larger model buys. That pair has no answer yet, because solution 7's fits did not learn the task. A ranking says who won. A pair says why. What the comparison says reads each pair.
4. Why do the learned solutions score below the plain geometry, and what would it take to beat it?#
Most of them do. Solutions 3, 5 and 6 rack fewer glasses and topple more. They make the push themselves, and the jaw often comes down on a glass. Solution 4 racks more glasses than the geometry, but it topples 20 where the geometry topples 1. To beat the geometry, a model must learn what the geometry gets wrong: where a pushed glass stops. What the comparison says gives the evidence.
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