4 ms·

First, I think you mean associative. That's true, but I don't think that's likely to be the problem here? If the limits of floating point resolution cause such

First, I think you mean associative. That's true, but I don't think that's likely to be the problem here? If the limits of floating point resolution cause such a big change (~80k deaths) in the simulation output, then I'd have bigger questions than the non-determinism. Yes, you can get chaotic behavior solving certain PDEs and stuff; but what in the mathematics of what's basically an extended SIR model could generate a sensitivity like that? I agree that the non-determinism may be pseudo-random numbers used in a differing order, whether from differing seeds or from differing scheduling of multiple threads. Ideal practice would be to correct for these--a thread-safe RNG, an unsafe RNG per thread, seed saved in output files for restart, etc. That they didn't do that doesn't mean their model is wrong, just that it's harder to show that it's right. Note that even in your quote above, they hedged with "might".

eesmith 6y ago
Derp! Yes, associative. Lots of equations are quite sensitive. You don't need PDEs. The original Lorenz equations are only three ordinary differential equations - https://en.wikipedia.org/wiki/Lorenz_system#Overview https://en.wikipedia.org/wiki/Lorenz_system#Overview , and that's enough to give chaos. > Ideal practice would be to correct for these--a thread-safe RNG, an unsafe RNG per thread, seed saved in output files for restart, etc. If you want to reproduce a simulation (assuming it doesn't have issues like IEEE math ordering), then you need to repeat the entire simulation process. You can't expect that steps A + save checkpoint + B is the same as load checkpoint + B. If you want people to be able to reproduce from a checkpoint, then you need to do step A + checkpoint, then exit, the run checkpoint + B. That makes "A + checkpoint" as one reproducible and "checkpoint + B" another. Perhaps that's what they did? I don't know. I only read that single issue, plus HN commentary. And that issue doesn't appear to highlight anything novel or unexpected for this sort of simulation. > they hedged with "might" Yes, and that's the mentality drilled into researchers. Because perhaps that code is wrong. But the internal RNG state difference seems much more likely to me.
- tripletao 6y ago
  Agreed that chaotic behavior shows up in unexpected places, but I'd still find it hard to believe here. What kind of state variable could show a sensitivity like that? If they're stuff like numbers of people, then at most they're going from one to the full population, many of orders of magnitude less than a double mantissa. And I'm not sure I'd be totally reassured that the simulation is deterministic when run single-threaded in a single start, if they run it multi-threaded for real? How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory? With some effort, it should be possible to make the multi-threaded simulation deterministic too. If you want to run the simulation in multiple starts, then you can make that deterministic by saving the final seed in the intermediate output file and restarting from that. I've seen stuff like that in other non-deterministic code, and I'd find it (a) an unreasonable degree of rigor to expect from random academic code, and (b) a quite reasonable degree of rigor to expect in code whose output helps make decisions determining the safety and freedom of billions of people. But (a) and (b) unexpectedly became one and the same, so here we are.
  - eesmith 6y ago
    You are making what is sometimes called an "argument from incredulity". Just because you find it hard to believe doesn't mean it's true. This issue parallels the foundational story of chaos theory. Quoting https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory : > [Lorenz] wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather the machine began to predict was completely different from the previous calculation. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome. At the very least it shows that it's easy for intuition to be wrong. Do you accept that "issues with random seeds and parallel floating point reductions are extremely widespread, and a great deal of science gets done with non-deterministic simulations", re-quoting Carmack? That holds with my own experience. You ask "How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory?" You cannot. Rather, how can you be sure that any program is bug-free? The question is, can you be confident enough to use it to make policy statements? Eg, people use imperfect models all the time when making laws.

eesmith 6y ago

Derp! Yes, associative. Lots of equations are quite sensitive. You don't need PDEs. The original Lorenz equations are only three ordinary differential equations - https://en.wikipedia.org/wiki/Lorenz_system#Overview https://en.wikipedia.org/wiki/Lorenz_system#Overview , and that's enough to give chaos. > Ideal practice would be to correct for these--a thread-safe RNG, an unsafe RNG per thread, seed saved in output files for restart, etc. If you want to reproduce a simulation (assuming it doesn't have issues like IEEE math ordering), then you need to repeat the entire simulation process. You can't expect that steps A + save checkpoint + B is the same as load checkpoint + B. If you want people to be able to reproduce from a checkpoint, then you need to do step A + checkpoint, then exit, the run checkpoint + B. That makes "A + checkpoint" as one reproducible and "checkpoint + B" another. Perhaps that's what they did? I don't know. I only read that single issue, plus HN commentary. And that issue doesn't appear to highlight anything novel or unexpected for this sort of simulation. > they hedged with "might" Yes, and that's the mentality drilled into researchers. Because perhaps that code is wrong. But the internal RNG state difference seems much more likely to me.

tripletao 6y ago
Agreed that chaotic behavior shows up in unexpected places, but I'd still find it hard to believe here. What kind of state variable could show a sensitivity like that? If they're stuff like numbers of people, then at most they're going from one to the full population, many of orders of magnitude less than a double mantissa. And I'm not sure I'd be totally reassured that the simulation is deterministic when run single-threaded in a single start, if they run it multi-threaded for real? How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory? With some effort, it should be possible to make the multi-threaded simulation deterministic too. If you want to run the simulation in multiple starts, then you can make that deterministic by saving the final seed in the intermediate output file and restarting from that. I've seen stuff like that in other non-deterministic code, and I'd find it (a) an unreasonable degree of rigor to expect from random academic code, and (b) a quite reasonable degree of rigor to expect in code whose output helps make decisions determining the safety and freedom of billions of people. But (a) and (b) unexpectedly became one and the same, so here we are.
- eesmith 6y ago
  You are making what is sometimes called an "argument from incredulity". Just because you find it hard to believe doesn't mean it's true. This issue parallels the foundational story of chaos theory. Quoting https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory : > [Lorenz] wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather the machine began to predict was completely different from the previous calculation. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome. At the very least it shows that it's easy for intuition to be wrong. Do you accept that "issues with random seeds and parallel floating point reductions are extremely widespread, and a great deal of science gets done with non-deterministic simulations", re-quoting Carmack? That holds with my own experience. You ask "How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory?" You cannot. Rather, how can you be sure that any program is bug-free? The question is, can you be confident enough to use it to make policy statements? Eg, people use imperfect models all the time when making laws.