4 ms·

Also did a bit of QC research. Since I'm tipsy, I skimmed the Twitter post. Here's a pdf on arxiv about HMC (2017) which I found in 20 seconds: https://arxiv.o

Also did a bit of QC research. Since I'm tipsy, I skimmed the Twitter post. Here's a pdf on arxiv about HMC (2017) which I found in 20 seconds: https://arxiv.org/abs/1701.02434 https://arxiv.org/abs/1701.02434 Seems like Claude3 is decently logical in paraphrasing key parts of text in a good order, but with repetition scattered everywhere. Also Monte Carlo is something which sounds cool but is literally just conceptual dart-throwing. I've always hated the name.

amluto 3y ago
However you feel about the term Monte Carlo, MCMC (Markov chain Monte Carlo) is a nifty algorithm. You’re also welcome to say “Metropolis-Hastings algorithm” (assuming that’s the specific algorithm you’re using). I was personally entertained when I learned that the algorithm formerly known as the Metropolis algorithm had nothing to do with cities. And MCMC really is like throwing darts. Except that, when done right, it throws darts in a distribution of your choice, and, critically, you don’t need to be able to normalize the distribution or integrate it to find the CDF. This turns out to be extremely useful. So you can think of it as a sort of bizarre way to numerically integrate gnarly functions. If you already knew the inverse CDF of a distribution, you could directly sample it. But if you don’t, either because it’s hard to integrate or because you’re getting the probabilities or probability densities, unnormalized, from a black box, you can still run MCMC. I bet you could have some fun taking a small ML model, using it to compute probabilities of strings of tokens, and using MCMC to sample the distribution of likely strings as seen by the model. The challenging part will be coming up with a remotely credible random walk that efficiently explores the space. NB: everyone loves saying “log-likelihood”. This is essentially the same thing. The log is nice because otherwise the numbers end up awkwardly small.
- winwang 3y ago
  Great comment! I didn't mean to suggest Monte Carlo isn't incredibly clever and nice. I just get intimidated by cool-sounding names :)
  - amluto 3y ago
    I used to imagine that the domain was a sprawling metropolis and that you explored it by randomly walking through its streets, elevators and skybridges, but that, on every step, you briefly contemplate whether that step was good and backtrack if it wasn’t. At some point, someone mentioned Nicholas Metropolis, and I was slightly disappointed :)

amluto 3y ago

However you feel about the term Monte Carlo, MCMC (Markov chain Monte Carlo) is a nifty algorithm. You’re also welcome to say “Metropolis-Hastings algorithm” (assuming that’s the specific algorithm you’re using). I was personally entertained when I learned that the algorithm formerly known as the Metropolis algorithm had nothing to do with cities. And MCMC really is like throwing darts. Except that, when done right, it throws darts in a distribution of your choice, and, critically, you don’t need to be able to normalize the distribution or integrate it to find the CDF. This turns out to be extremely useful. So you can think of it as a sort of bizarre way to numerically integrate gnarly functions. If you already knew the inverse CDF of a distribution, you could directly sample it. But if you don’t, either because it’s hard to integrate or because you’re getting the probabilities or probability densities, unnormalized, from a black box, you can still run MCMC. I bet you could have some fun taking a small ML model, using it to compute probabilities of strings of tokens, and using MCMC to sample the distribution of likely strings as seen by the model. The challenging part will be coming up with a remotely credible random walk that efficiently explores the space. NB: everyone loves saying “log-likelihood”. This is essentially the same thing. The log is nice because otherwise the numbers end up awkwardly small.

winwang 3y ago
Great comment! I didn't mean to suggest Monte Carlo isn't incredibly clever and nice. I just get intimidated by cool-sounding names :)
- amluto 3y ago
  I used to imagine that the domain was a sprawling metropolis and that you explored it by randomly walking through its streets, elevators and skybridges, but that, on every step, you briefly contemplate whether that step was good and backtrack if it wasn’t. At some point, someone mentioned Nicholas Metropolis, and I was slightly disappointed :)