So, to check my understanding: You have set up a sort of artificial feedback loop, where there are N overlapping patterns of hills, and each one gets stronger the farther you travel in a particular dimension/direction. So if one or more of these patterns tends systematically to push the ball in the same direction that makes it stronger, you’ll get a feedback loop. And then there is selection between patterns, in the sense that the pattern which pushes the strongest will beat the ones that push more weakly, even if both have feedback loops going.
And then the argument is, even though these feedback loops were artificial / baked in by you, in “natural” search problems there might be a similar situation… what exactly is the reason for this? I guess my confusion is in whether to expect real life problems to have this property where moving in a particular direction strengthens a particular pattern. One way I could see this happening is if the patterns are themselves pretty smart, and are able to sense which directions strengthen them at any given moment. Or it could happen if, by chance, there happens to be a direction and a pattern such that the pattern systematically pushes in that direction and the direction systematically strengthens that pattern. But how likely are these? I don’t know. I guess your case is a case of the second, but it’s rigged a bit, because of how you built in the systematic-strengthening effect.
Thanks, and your summary is correct. You’re also right that this is a pretty contrived model. I don’t know exactly how common demons are in real life, and this doesn’t really shed much light on that question. I mainly thought that it was interesting to see that demon formation was possible in a simple situation where one can understand everything that is going on.
This is awesome, thanks!
So, to check my understanding: You have set up a sort of artificial feedback loop, where there are N overlapping patterns of hills, and each one gets stronger the farther you travel in a particular dimension/direction. So if one or more of these patterns tends systematically to push the ball in the same direction that makes it stronger, you’ll get a feedback loop. And then there is selection between patterns, in the sense that the pattern which pushes the strongest will beat the ones that push more weakly, even if both have feedback loops going.
And then the argument is, even though these feedback loops were artificial / baked in by you, in “natural” search problems there might be a similar situation… what exactly is the reason for this? I guess my confusion is in whether to expect real life problems to have this property where moving in a particular direction strengthens a particular pattern. One way I could see this happening is if the patterns are themselves pretty smart, and are able to sense which directions strengthen them at any given moment. Or it could happen if, by chance, there happens to be a direction and a pattern such that the pattern systematically pushes in that direction and the direction systematically strengthens that pattern. But how likely are these? I don’t know. I guess your case is a case of the second, but it’s rigged a bit, because of how you built in the systematic-strengthening effect.
Am I following, or am I misunderstanding?
Thanks, and your summary is correct. You’re also right that this is a pretty contrived model. I don’t know exactly how common demons are in real life, and this doesn’t really shed much light on that question. I mainly thought that it was interesting to see that demon formation was possible in a simple situation where one can understand everything that is going on.
I have the same confusion