One of the simplest algorithms for sampling from a... probability distribution is Random Walk Metropolis-Hastings. It proposes new samples by taking Gaussian-distributed steps, accepting or rejecting them to maintain the target distribution. I call this pdf the "fidget spinner".show more

Flow Matching aims to learn a "flow" that transforms... a simple source distribution (e.g. Gaussian) to an arbitrarily complex target distribution. This video shows the evolution of the marginal probability path as a source distribution is transformed to a target distribution.show more

A basic strategy for drawing from a random distribution... is to first generate uniformly-distributed points, then "warp" these points so they're spread out according to the target distribution. For example, the Box-Muller transform takes uniform points to normally-distributed onesshow more

Langevin Monte Carlo allows you to draw samples from... a probability distribution using its log gradient ∇ log p(x). By performing a sort of gradient ascent with noise you can navigate around the distribution. Langevin MC is heavily related to modern diffusion models.show more

This animation shows how a uniform grid of points... is deformed by a flow matching model. The visualization highlights how the learned flow warps the underlying space—stretching, compressing, and bending it—to transform one probability distribution into another.show more

A high-dimensional Gaussian is a soap bubble: the densest... point is the emptiest place. In high dimensions, density and mass diverge completely. For a d-dimensional standard Gaussian distribution, nearly all probability mass is concentrated in a "thin shell" or annulus with radius √d, rather than near the center. The mode has the highest density, but every sample you'll ever draw lives on a thin shell at radius √d. The typical point and the most probable point are in completely different places. Today was the n-th time this has tripped me up, so to commemorate it, I just created this visualization. 🫠show more

this is my app "Kairo Alarm" i fought the... urge to keep polishing it, and shipped it in 7 days. if you're starting a new app: → build the fastest polished version possible → ship in 7–14 days max → go all-in on distribution distribution is what matters early onshow more

✨ New samwho visual essay o'clock! ✨ Reservoir sampling... is one of my favourite algorithms. It allows you to sample from a set without knowing the size of that set. I assume no prior knowledge, and use no math notation. Just beautiful visuals. Let me know what you think! ❤️show more

Israel is wiping out the bridges of South Lebanon... — one by one. Not for military necessity, but to isolate an entire population. To trap them. To starve them. To cut them off from hospitals, food, and aid. Call it what it is: A crime against humanity.show more

This is completely inappropriate for a police officer from... Merseyside police force to call a member of the public a nonce. Extremely unprofessional or is this just the new standard practice from our police service.show more

Great example of old vs. new values By the... eye test, this is a marvelous catch, the kind fans are glad they paid money to see By analytics, this had an 85% catch probability per The WARmonger & only looked hard because of a bad jump Is it good or bad?show more

Is this the new Green Legacy initiative by the... #TPLF in Tigray? Or is it intended to make them invisible to drones? The wonders of Africa never cease!”show more

Our analysis of Israel’s so-called ‘humanitarian bubbles’ indicates that... this new system of aid distribution is simply an extension of the existing architecture of spatial control. The routes established for civilian access to these aid distribution centres (in blue) are continuous with Israeli military raid routes (in red), forming a militarised network designed to facilitate forced displacement and population control.show more

Highlight Queens: This Officiating is Raising Eyebrows... 👀 Did... the Officials Get This One Wrong? 😳 Aliyah Boston Was Called for Traveling After Taking One Step, But Olivia Miles Appeared to Take Multiple Steps with No Whistle. The Controversial Sequence Has Indiana Fever Fans Questioning the Consistency of the Officiating. Watch the Play and Decide for Yourself - Was It Simply a Missed Call, Or Something More? Link: #CC22 #CaitlinClark #NowYouKnow #FeverRising #IndianaFever #WNBAshow more

🌟 Welcome to the Era of Gems 🌟 This... August, embark upon a mystical voyage as we unveil the hidden jewels of our realm. Receive your allotment of GEMS this month. You will soon be able to spend them in our marketplace and incorporate them into our games. Rest assured, this initial distribution is just the beginning. We will conduct a precise count once global distribution is complete, ensuring that every adventurer is treated fairly. Stay tuned for a month filled with discovery and wonder as we explore the mysteries and magic of our world. Ashes Of Idunn™ #EraOfGems #AshesOfIdunnshow more

Initia VIP is live on Leap 🕴️ Use Leap... to maximise your Initia wins in three simple steps 1️⃣ access & use Initia 🪢 rollups using the dApp browser 2️⃣ track your VIP points and rewards in the app why does this matter to you? 🤑 ~560k esINIT distributed to users across 11 apps in the previous stage 💸 25% INIT supply locked for Initia rollup users 💰 free & fair token distribution for everyone this is the new meta, don't miss it! join Initia VIP with Leap today 🏆show more