7 ms·
NoiseLang: Where N = 5 is a Dirac delta
- bradrn 2mo agoReminds me of Haskell’s monad-bayes: https://monad-bayes.netlify.app/ https://monad-bayes.netlify.app/
- manucorporat 2mo agooh! that's awesome, i had no idea haskell could express this things
- tengwar2 2mo agoMy system is blocking that site as it is on the HaGeZi blocklist. I don't have any further information, and I'm not expressing an opinion on the site. An alternative might be https://noiselang.com https://noiselang.com, which is not on the blocklist.
- manucorporat 2mo agommmh i can't see the domain blocked in the list, it's my personal blog, i don't even have tracking other than server-side stats. could it be because using netlify dns?
- tengwar2 2mo agoFirstly, I'm not intending any slight on you personally! In fact this might be more of an issue for you interacting with the site than for people just reading an article. There are multiple versions of the list. The authoritative site appears to be https://github.com/hagezi/dns-blocklists https://github.com/hagezi/dns-blocklists, and making a fairly random choice, I used the "medium" version of the "Threat intelligence feed", and specifically the one marked "Link" for AdBlock. That took me to https://cdn.jsdelivr.net/gh/hagezi/dns-blocklists@latest/adblock/tif.medium.txt https://cdn.jsdelivr.net/gh/hagezi/dns-blocklists@latest/adb..., and manualmeida.dev does appear in that list. The software I'm using is Little Snitch on a Mac, but since the entry is in the list, that's not the problem.
- manucorporat 2mo agoThis is great! thank you for the digging, gonna figuring out how it end up there
- tengwar2 2mo agoJust checked, and it's gone from the list. Did you happen to find out what the problem was?
- manucorporat 2mo agoSent issue: https://github.com/hagezi/dns-blocklists/issues/10759 https://github.com/hagezi/dns-blocklists/issues/10759
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- aslushnikov 2mo agoThis reminds me of https://mc-stan.org https://mc-stan.org
- qarl2 2mo agoYou should read the part of the article where the author compares his work to Stan.
- aslushnikov 2mo agoThank you for pointing!
- chrisra 2mo agoIt might be worth looking into probabilistic programming languages. I'm out of date, but I remember webppl, stan, anglican, pymc (a python library). Seems worth an investigation and maybe mention on the article.
- ljwolf 2mo agoif you read the website, the author explicitly mentions stan in the comparison at the end ;^)
- esafak 2mo agoIt says Stan and PyMC beat Noise at the thing they’re built for, fitting a posterior to lots of continuous data with their HMC/NUTS samplers, and NumPy beats it at raw array crunching. Conditioning in Noise is rejection-based, so it works great for a handful of discrete observations but becomes useless for ten thousand continuous measurements, and there is no stateful simulation yet (no Markov chains yet). Where Noise wins when you have a probability question and you wanna know the answer without much hassle. So use Noise for the whiteboard stage of a problem, when you want to run the math you just wrote, and move to Stan or PyMC when you need a real posterior, or to NumPy and JAX when you need to go to production.
- qdotme 2mo agoNice! I’ve dabbled with something similar on my own lately (originally wrote/vibed to explain some concepts that came up when discussing D&D) at diceplots.com - different approach, keeping the distributions exactly analytical at every step, never sampling.
- xyzsparetimexyz 2mo agoI'd have just written this as a Python library that lazily evaluates expression via numpy personally. The API is useful, language is not
- mswphd 2mo agothat has some technical limitations. For example, their impl can compile to wasm, which makes giving an online interpreter simpler/lighter weight than relying on running python in the browser.
- kccqzy 2mo agoPeople do this kind of computation using numpy all the time. If you weren’t developing a new language with a new syntax, there really isn’t much of a library to write. At that point it’s just using numpy.
- manucorporat 2mo agothe language can do a lot of very expressive things, every language feature works in your favor too, but agree with you, i would not use my own language for anything production. like this: D ~ unif_int(1, 6); Print("P(rolled a 6 | rolled > 3) =", P(D == 6 | D > 3)); or: loss ~ unif(0, 1000); claim = if loss > 200 { loss - 200 } else { 0 }; p = P(claim > 0); Print("P(insurer pays a claim) =", p) notice that "claim" is also a random variable! result of a if expression
- kccqzy 2mo agoYeah sure this is how numpy people would do it: N = 10**6 D = np.random.randint(1, 6, N) print("P(rolled a 6 | rolled > 3) =", ((D == 6) | (D > 3)).mean()) loss = np.random.uniform(0, 1000, N) claim = np.where(loss > 200, loss - 200, 0) p = (claim > 0).mean() print("P(insurer pays a claim) =", p) It’s concise enough that people generally wouldn’t bother writing a library. Unless they really want their custom syntax, then perhaps they write a parser.
- torginus 2mo agoInterestingly, shading languages started out like this - way before consumer GPUs. I remember encountering this idea written in a book written by Ed Catmull of Pixar fame (can't find the title sorry, but it was written in the 80s), but generally comes from signal processing as a way of avoiding aliasing artifacts.. The core idea is to make programming, which is a discrete and discontinuous domain, into a well-behaved band limited signal. Otherwise you get aliasing (or jaggies), which can happen even INSIDE a surface, if the shader's like that. The code idea for this is the step function which is the integral of the dirac delta. step(x) returns 1 for all x >0 and 0 otherwise. Step is not a well-behaved function in the sense, that it changes infinitely quickly at x=0. But once we know what we want, we can replace it with something like that, that's well behaved. Consider the example pseudocode color = x> 5? green:blue; can be rewritten as color = blue + step(x-5)(green-blue) With the two being equivalent. Now if we put the code into a shader, we get jaggies. So to combat the value changing infinitely fast, we go for a function that's like step, but changes smoothly* from 0 to 1 around x=0. Enter smoothstep: color = blue + smoothstep(x-(5+EPSILION),(x-EPSILON), x)*(green-blue) And so we defined a 'transition zone' of +-EPSILON(an arbitrary number). While any smooth function can work, smoothstep is chosen because it has a smooth first and second derivative (meaning even if you want to get the rate of change, something that often pops up in computer graphics, the result will be still well behaved). Pixar's Renderman shading language (which is remarkably similar to GLSL/HLSL/C), used to do this automatically for you. Essentially it could take arbitrary code peppered with if statements, and turn it into a continuous function. Which is kinda cool imo. It's also a cool trick in the age of AI. Since you have a function that's well-behaved, you can do things like gradient descent to train an AI to synthetize a function for you. You can even say, that you don't need exact results, you can accept some error. In this case your program optimization problem can be reframed from doing idempotent transformations on the list of instructions, to getting a program that generates a target function whose error is no greater than some (mathematical) reference function.
- mswphd 2mo agonote that similar concepts appear in mathematics. Generally the term for it is a "mollified" function. applied to the step function, you would get a smooth cutoff function https://en.wikipedia.org/wiki/Mollifier#Smooth_cutoff_functions https://en.wikipedia.org/wiki/Mollifier#Smooth_cutoff_functi... this is also related somewhat to the notion of differentiable programming. RELU is (roughly) the same as x * step(x). In differentiable programming one can replace it with smooth approximations, cf "softplus" https://arxiv.org/pdf/2403.14606 https://arxiv.org/pdf/2403.14606 That book also has a chapter on control flow, which is very similar to what you're talking about. Unrolling an if statement into x = b (result of one branch) + (1-b) (result of the other branch) is also incredibly common in cryptography. If `b` is a "secret" variable, an if statement may leak the value of it via the branch predictor/speculative execution. The way around this is to compute both branches, and then select them with the above arithmetic expression. This mostly works, though compilers are tediously smart, and so one often has to be careful how with how you precisely do it.
- sidmohanty11 2mo agoWOWW!!!!!
- seanhunter 2mo agoDoes it still count as a Dirac delta when it’s a discrete distribution? (The distributions in TFA are not continuous - they are things like a roll of 1d6 etc)
- manucorporat 2mo agoYes, a Dirac delta is just "all the weight on one point", and that works fine on a die. For the scope of the language it never even comes up, because Noise is a simulator, it does not evaluate densities, it draws samples. The point is that every value goes through the same operators. Add them, compare them, pass them to a function, put one in the condition of an if. You can even use a random variable to define another random variable: bias ~ unif(0, 1) flips ~[10] bernoulli(bias) // bernoulli just took a distribution where a number normally goes. and in if-stataments: DistributionC = if DistributionA < DistributionB { 0 } else { 1 } But you right, dirac only applies to continuous functions, in Noise is only refers to the dirac measure. I found this article a fun/nerd to make my point that everything "acts" as a distribution from the DX perspective, but under the hood 5 is just 5. And a constant collapses back to a plain integer in the graph anyway, so 5 costs nothing.
- seanhunter 2mo agoI like the “everything is a distribution” approach a lot[1]. Looks great. I’m looking forward to actually having a chance to mess around with it. [1] And feels philosophically like the unification in the underlying maths between discrete and continuous probability that you get when you apply measure theory
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- ajkjk 2mo agoSome people would call it a Kronecker delta instead, but imo they are exactly the same concept. The Kronecker delta is the indicator for a single value, like 1_{x=0}, while the Dirac delta is the indicator for a single 'dx' partition, divided by the width of the partition: δ(x) = 1_{0 in (x, x+dx)}/|dx| which is why integrating it ∫ δ(x) dx = ∫ 1_{0 in (x, x+dx)}/|dx| = ±1 (depending on the orientation of the integral). The Kronecker can sorta be viewed as the same thing but with dx=1, although that is kinda silly because usually you would intentionally evaluate it on a discrete measure anyway.
- kccqzy 2mo agoI didn’t really see loops being handled here. As far as I understand, the biggest technical difficulty with this kind of probabilistic programming language is handling loops, including infinite loops and almost surely terminating loops. I did a bit of research earlier in my life[0] to study the handling of loops and without using Monte Carlo simulation. The result was actually workable if incredibly resource intensive to the point of being impractical. If I had chosen to do it again, I might’ve accepted using Monte Carlo simulations while still supporting loops. [0]: https://github.com/kccqzy/probabilistic-program-inference/blob/master/README.md https://github.com/kccqzy/probabilistic-program-inference/bl... Shameless self promotion I know! I put quite a bit of effort into that README and the code.
- jlaporte 2mo agoBeautiful!
- manucorporat 2mo agoI started this about 9 years ago and never finished it. The idea comes from a course in my telecom degree called "Señales Aleatorias y Ruido" (Random Signals and Noise), I spent so many evenings writing probability by hand, and every time I wanted to check a result with a computer it was a ton of boilerplate. The engine is Rust, the JIT is built on Cranelift, there is also a WASM backend so everything runs in the browser too. Full disclosure, I could only finish it now because of AI agents. In my experience they are amazing at the runtime and the numerical code, but pretty bad at language design, so I kept that part for myself. It's a toy language. Ask me anything!
- roger_ 2mo agoDefinitely going to play around with this, thanks for posting. I know MCMC isn’t your goal, but seems like this could be used for ABC-MCMC (as is?) Would also be nice to have an option to plot using a KDE vs histograms. (Also your FM example seems to be technically PM)
- manucorporat 2mo agooh! that is very interesting. I was not aware of I could simulate markov chains with Approximate Bayesian, I have some good reading to do this weekend! indeed, expressions like P(D == 8 | D > 3) are already natively supported: https://noiselang.com/play/#x=conditional_bayes https://noiselang.com/play/#x=conditional_bayes Fair! My thinking was that PM of a single tone signal (the one i use in the demo is equivalent to FM, but shifted a bit). And implementing real FM for decoding is a lot more noisy, but I will add some callout in the article. Truth be told, you motivated me to write the exact FM with the differenciation, maybe. Could be interesting to simulate PM vs FM for non single tone signals, to see how FM does even better!
- qarl2 2mo agoBe warned - by using AI like this you've made yourself a lightning rod for the people who really really really dislike AI.
- 2mo ago