I just skimmed it a bit so this is what I grok of the big idea:

I'm cramming for a test on similar ish right now so I'm not going to do too much of what they were trying to solve for... which is that when human minds, and neural networks of the sort they were working with, learn about data which is extremely similar the "solution" to that "problem" is overwritten to an extent.

In the case of this paper problem_1 was to solve for a sequence of actions when presented with "objects" presented horizontally, which are identical to a sequence of actions when presented vertically in problem_2. Think of a maze rotated 90 degrees.

If you train this network on problem_1 for awhile, then train it on problem_2 for awhile, it forgets how to solve problem_1.

If you train it on sequences of problem_1, then 2, then 1, then 2, and so on, it learns a solution which applies to both. Essentially some of it's "neurons" learn to rotate the maze depending on orientation. However this isn't how the human mind solves this issue, and solving it that way is impractical especially for a large number of tasks.

What they did instead was to "batch" that retraining by first learning 1 well, then start learning 2, but after say five times through the "maze" of learning problem_2, the network "sleeps" and the firing patterns which were characteristic when solving for problem 1 were replayed by a module which is playing the role of the hippocampus. So rather than replaying the problem, they replay the solution to problem 1.

They show that the results are statistically extremely similar to training on the interleaved approach of 1,2,1,2,1,2, where the network learns that 1 and 2 are essentially the same task with a slight variation. It learns an abstraction essentially to rotate the maze, and does so without having to store the raw data (for interleaving).

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Edit: here's a very relevant paper on how our brains do it and likely what they were trying to mimic https://pubmed.ncbi.nlm.nih.gov/19709631/