4 ms·

Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is

Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation.

t_mann 2y ago
It seems like you're asking for quite a lot here. Are there any examples of common interpretable ML methods that would give you anything like that answer? The most common methods that are called interpretable would give you hints like "Mass and distance matter for gravity, color doesn't" or "Gravity gets stronger with mass and weaker with distance". Both are clearly less informative than the formula. The only way I could think of to get anywhere near such an answer would be to use symbolic regression first and then ask an LLM to interpret the result. And that would probably take quite some more original research to get it anywhere near working, and even then probably primarily for problems where the answer is already known. I agree that this kind of answer would be useful, but we also have to be honest that that's not what currently meant by interpretability. And that's what should matter for evaluating the claim - it's not misleading if it delivers what one can reasonably expect. Whether we should update our interpretability definitions is a different (interesting) discussion.
dataflow 2y ago
> Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation. I used to think the same, but don't the weak and strong forces decay differently?
- nathan_compton 2y ago
  Sort of, but the same sort of thinking is involved in both at a fundamental level. Most of the coefficients in a QFT expansion can almost be guessed by just considering dimensional analysis. Like the "force laws" of those two theories derive from the dimensionality of space time, the symmetry group involved (which is itself just an irreducible representation of rotations in the spacetime) and then some details having to do with symmetry breaking and the fact that gluons carry charge. Not that all of that is simple, but it doesn't invalidate the logic which gives us the 1/r^2 force law in the classical regimes of gravity and E&M.

Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation.

t_mann 2y ago

It seems like you're asking for quite a lot here. Are there any examples of common interpretable ML methods that would give you anything like that answer? The most common methods that are called interpretable would give you hints like "Mass and distance matter for gravity, color doesn't" or "Gravity gets stronger with mass and weaker with distance". Both are clearly less informative than the formula. The only way I could think of to get anywhere near such an answer would be to use symbolic regression first and then ask an LLM to interpret the result. And that would probably take quite some more original research to get it anywhere near working, and even then probably primarily for problems where the answer is already known. I agree that this kind of answer would be useful, but we also have to be honest that that's not what currently meant by interpretability. And that's what should matter for evaluating the claim - it's not misleading if it delivers what one can reasonably expect. Whether we should update our interpretability definitions is a different (interesting) discussion.

dataflow 2y ago

> Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation. I used to think the same, but don't the weak and strong forces decay differently?

nathan_compton 2y ago
Sort of, but the same sort of thinking is involved in both at a fundamental level. Most of the coefficients in a QFT expansion can almost be guessed by just considering dimensional analysis. Like the "force laws" of those two theories derive from the dimensionality of space time, the symmetry group involved (which is itself just an irreducible representation of rotations in the spacetime) and then some details having to do with symmetry breaking and the fact that gluons carry charge. Not that all of that is simple, but it doesn't invalidate the logic which gives us the 1/r^2 force law in the classical regimes of gravity and E&M.