Gravitate toward natural-feeling parts of the solution space

Vectornaut commented

2025-02-27 20:25:05 +00:00

Member

Idea

When a constraint problem has a continuum of solutions, some parts of the solution space might feel more natural than others. For example:

[…] try from the default state making Castor and Pollux (externally) tangent, then making them both tangent to Ursa Major, and then making all three tangent to Deimos. I end up with a nearly-planar Ursa Major, which isn't the most cognitively comfortable realization starting with the initial configuration. I more-or-less expected them to just nestle in a tetrahedron, each relatively near its starting size.

It might be useful to identify features that make solutions feel more natural and gravitate toward parts of the solution space where those features are strong. Some relevant features might be:

The assembly having a small diameter, not counting infinite-size elements.
Finite-size elements having similar diameters.

Implementation

This seems like it would require some sort of hierarchical optimization, though maybe not the kind discussed in #39. We want to find a solution where the constraint loss is zero and the naturalness loss is small. One approach might be to start with a loss function that includes both constraint and naturalness terms, and to reduce the weight of the naturalness terms to zero over the course of optimization.

### Idea When a constraint problem has a continuum of solutions, some parts of the solution space might feel more natural than others. For [example](pulls/48#issuecomment-2180): > […] try from the default state making Castor and Pollux (externally) tangent, then making them both tangent to Ursa Major, and then making all three tangent to Deimos. I end up with a nearly-planar Ursa Major, which isn't the most cognitively comfortable realization starting with the initial configuration. I more-or-less expected them to just nestle in a tetrahedron, each relatively near its starting size. It might be useful to identify features that make solutions feel more natural and gravitate toward parts of the solution space where those features are strong. Some relevant features might be: - The assembly having a small diameter, not counting infinite-size elements. - Finite-size elements having similar diameters. ### Implementation This seems like it would require some sort of hierarchical optimization, though maybe not the kind discussed in #39. We want to find a solution where the constraint loss is zero and the naturalness loss is small. One approach might be to start with a loss function that includes both constraint and naturalness terms, and to reduce the weight of the naturalness terms to zero over the course of optimization.

Vectornaut added the

enhancement

label 2025-02-27 20:25:05 +00:00

Vectornaut referenced this issue

2025-02-27 20:41:23 +00:00

Generalize constraints to observables #48

glen commented

2025-03-01 01:14:35 +00:00

Owner

If I understand correctly, "constraints" are just quadratic loss terms. So it seems to me a scheme in which we have terms that (say) start at weight 1 but the weight of which can decay if the optimization becomes stuck in a nonzero loss configuration is already a hierarchical optimization constraint. So this might almost be a duplicate of #39, unless perhaps it is a generalization if the weight of a naturalness term can/does start at less than 1.

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Gravitate toward natural-feeling parts of the solution space #61

Idea

Implementation