Great idea! My intuition says this won’t work, as you’ll just capture half of the mechanism of the type of chaotic attractor we want. This will give you the “stretching” of points close in phase space to some elongated section, but not by itself the folding over of that stretched section, which at least in my current thinking is necessary. But it’s definitely worth trying, I could very well be wrong! Thanks for the idea :)
Similarly it’s not obvious to me that constraining the lyapanov exponent to a certain value gives you the correct “structure”. For instance, if instead of ..01R… I wanted to train on …10R… Or …11R… Etc. But maybe the training of the lyapanov would just be one part of the optimization, and then other factors could play into it.
This will give you the “stretching” of points close in phase space to some elongated section, but not by itself the folding over of that stretched section, which at least in my current thinking is necessary.
I mean, the only way to have “stretching” of ‘most’ points in phase space is to have some sort of ‘folding over’.
Of course, it’s an entirely different matter as to if a standard optimizer can actually make any headway in figuring that out.
Great idea! My intuition says this won’t work, as you’ll just capture half of the mechanism of the type of chaotic attractor we want. This will give you the “stretching” of points close in phase space to some elongated section, but not by itself the folding over of that stretched section, which at least in my current thinking is necessary. But it’s definitely worth trying, I could very well be wrong! Thanks for the idea :)
Similarly it’s not obvious to me that constraining the lyapanov exponent to a certain value gives you the correct “structure”. For instance, if instead of ..01R… I wanted to train on …10R… Or …11R… Etc. But maybe the training of the lyapanov would just be one part of the optimization, and then other factors could play into it.
I mean, the only way to have “stretching” of ‘most’ points in phase space is to have some sort of ‘folding over’.
Of course, it’s an entirely different matter as to if a standard optimizer can actually make any headway in figuring that out.