To solve the NP-hard problems in hardware design and such, you don’t necessarily need a solver that works on all (“random”, “general position”) NP-hard problems. You can find and exploit regularities in the problems that actually arise. We humans seem to do just that: someone who plays chess well can’t easily convert their skill to other chess-like games.
Replying separately to earlier reply since long-time gap will make an edited remark unlikely to be noticed by you.
I just ran across in a completely different context this paper on average difficulty of NP-hard problems. This paper is highly technical and I don’t think I follow all (or even most) of the details, but the upshot seems to be that, roughly speaking, the only way for most instances of fairly natural NP complete problems to be as difficult as the worst case is if NP complete problems are actually easy. This makes your objection all the more powerful because it suggests that it is likely that for specific NP complete problems an AI would need to solve it would not just be able to take advantage of regularity in the specific instances it cares about but it would also be able to rely on the fact that most random instances simply aren’t that tough compared to the very worst case. This issue combined with your remark forces me to update my estimation that a software issues will interfere substantially with FOOMing. Taken together, these issues undermine the arguments I gave for software barriers to FOOM.
Yes, that seems to be a very good point. It is unlikely an AI is going to need to solve arbitrary instances of the traveling salesman or graph coloring.
Replying separately to earlier reply since long-time gap will make an edited remark unlikely to be noticed by you.
I just ran across in a completely different context this paper on average difficulty of NP-hard problems. This paper is highly technical and I don’t think I follow all (or even most) of the details, but the upshot seems to be that, roughly speaking, the only way for most instances of fairly natural NP complete problems to be as difficult as the worst case is if NP complete problems are actually easy. This makes your objection all the more powerful because it suggests that it is likely that for specific NP complete problems an AI would need to solve it would not just be able to take advantage of regularity in the specific instances it cares about but it would also be able to rely on the fact that most random instances simply aren’t that tough compared to the very worst case. This issue combined with your remark forces me to update my estimation that a software issues will interfere substantially with FOOMing. Taken together, these issues undermine the arguments I gave for software barriers to FOOM.
To solve the NP-hard problems in hardware design and such, you don’t necessarily need a solver that works on all (“random”, “general position”) NP-hard problems. You can find and exploit regularities in the problems that actually arise. We humans seem to do just that: someone who plays chess well can’t easily convert their skill to other chess-like games.
Replying separately to earlier reply since long-time gap will make an edited remark unlikely to be noticed by you.
I just ran across in a completely different context this paper on average difficulty of NP-hard problems. This paper is highly technical and I don’t think I follow all (or even most) of the details, but the upshot seems to be that, roughly speaking, the only way for most instances of fairly natural NP complete problems to be as difficult as the worst case is if NP complete problems are actually easy. This makes your objection all the more powerful because it suggests that it is likely that for specific NP complete problems an AI would need to solve it would not just be able to take advantage of regularity in the specific instances it cares about but it would also be able to rely on the fact that most random instances simply aren’t that tough compared to the very worst case. This issue combined with your remark forces me to update my estimation that a software issues will interfere substantially with FOOMing. Taken together, these issues undermine the arguments I gave for software barriers to FOOM.
Yes, that seems to be a very good point. It is unlikely an AI is going to need to solve arbitrary instances of the traveling salesman or graph coloring.
Replying separately to earlier reply since long-time gap will make an edited remark unlikely to be noticed by you.
I just ran across in a completely different context this paper on average difficulty of NP-hard problems. This paper is highly technical and I don’t think I follow all (or even most) of the details, but the upshot seems to be that, roughly speaking, the only way for most instances of fairly natural NP complete problems to be as difficult as the worst case is if NP complete problems are actually easy. This makes your objection all the more powerful because it suggests that it is likely that for specific NP complete problems an AI would need to solve it would not just be able to take advantage of regularity in the specific instances it cares about but it would also be able to rely on the fact that most random instances simply aren’t that tough compared to the very worst case. This issue combined with your remark forces me to update my estimation that a software issues will interfere substantially with FOOMing. Taken together, these issues undermine the arguments I gave for software barriers to FOOM.