HigherOrderPatterns are patterns about pattern recognition.

The following is from Chess''''''GrandMasterEliminatesWrongMoves:

First order patterns helps us recognize characters, faces, etc. This is an area where AI has made quite promising progress and it is well understood mathematically. But higher order patterns are patterns about patterns, or patterns about second order effect. 

For example, you may program a chess engine to recognize a typical mate configuration. However, a good chess player will recognize, long before the mating configuration can even occur, that a certain plan will create the conditions for the mate configuration to occur. A chess player will recognize also similarities that go way beyond geometrical/mechanical transformations from one position to another. 

For example, I can teach a kid that when two defender pieces cross paths in their line of defence, sometimes you win by sacrificing a piece where those defenders cross their lines (a trick called '''interference'''. I can show him how it works in one particular position with 2 rooks being the defenders. Not only will he be able later to recognize this when a rook and a bishop are the defenders, but even more amazingly, having learnt 20 or so patterns of attacks, he will be able to '''sense''' in a chess puzzle that that particular configuration is riped [?] for interference of all the combinational patterns he learnt. And this talent is innate to humans, it is absolutely amazing. With a neural network you give it a ton of data, and it crunches it and it reaches a configuration that helps it do OCR or voice recognition. All a good 6 yr old kid needs is usually a handful of positions and the '''logical explanation''', and voila, your higher order pattern recognition is ready to fly. Truly talented kids (I've seen a few) may need as little as 1 position. They will look at it exhaustively, not being aware of the pattern, until they get the eureka moment, and then on their own come back with both the logical explanation and the capacity to apply it in the future. 
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See also PatternMatching
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CategoryPattern