Hamiltonian Monte Carlo frames sampling from a probability distribution... as a physics problem. By endowing "particles" with momentum and simulating their energy and motion through Hamilton's equations you can efficiently explore a distribution.show 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

Random Walks aim to explore a distribution through random... perturbations. This is likely to move into low density regions, which is inefficient. Hamiltonian MC sails through a distribution much more rapidly by incorporating the distribution's structure into proposals.show more

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

KIMI K3 VS OPUS 4.8 SIMULATING A 3D PARTICLE... SYSTEM same prompt, same target: thousands of particles reacting to gravity and to each other in real time → K3: more organic distribution, smoother motion, particles actually cluster and drift like something physical → Opus: more rigid pattern, less natural, movement reads more like a grid than a simulation K3: $0.65 in API. Opus 4.8: ~$1.30 this is simulated physics, not just aesthetics, and it's the kind of detail that separates a demo from something you'd actually shipshow 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

Web3 brands have a distribution problem. For Memeland ❤️... Memecoin and $MEME, distribution is our moat through our existing audience and 9GAG ❤️ Memeland. An extension of this is partnerships with Web2 brands/ products with the Potatoz IP being integrated. Stay tuned. 🥔show more

Did you know you can create the Maxwell-Boltzmann distribution... with just some balls and a motor? I built this simple device to illustrate it. This is how it works: A spinning agitator pumps energy into ~400 balls, so they bounce around and collide like gas particles in a box. They escape one at a time through a tiny hole, then fall a fixed gap into bins below. Since the hole is so small, every ball leaves with no vertical speed and takes the same time to fall. Constant fall time means how far a ball flies sideways is set purely by its speed. A faster ball goes into a further bin. So each bin is really a speed. Tally all 400 and you get the Maxwell-Boltzmann distribution.show more

ReViV reconstructs viewer-centric human motion (body, hand, and gaze)... and view-centric scene geometry (camera and depth) from a single egocentric RGB video in a unified feed-forward model. It formulates the task as learning the full joint probability distribution over multimodal signals, including RGB video, camera trajectory, gaze direction, full-body motion, hand motion, and depth. Powered by a Masked Generative Egocentric Transformer, ReViV operates within a single feed-forward architecture to simultaneously reconstruct the temporally consistent 4D reconstruction across the viewer and the view with fast inference speed. Paper Title: ReViV: Reconstructing the Viewer and the View in 4D from Monocular Project: Link:show more

This simulation visualizes the Maxwell Boltzmann distribution by showing... how gas particles move at different speeds. The emerging bell curve highlights the statistical probability of finding molecules at specific velocity states.show more

A discrete Markov chain is basically a random walk... on a graph, where each outgoing edge has a fixed probability. Cool fact: any initial distribution on a sufficiently nice* Markov chain converges to its stationary distribution after many steps—because it's a contraction mapping.show more

The physics of load distribution

One reaction changed everything. From human to pure energy,... science became the future Created with Seedance 2.0 on WaveSpeedAI Prompt: A cinematic ultra-realistic sequence inside a futuristic high-tech chemistry laboratory. A brilliant young scientist wearing a white lab coat carefully pours a glowing blue serum into a transparent glass flask. Suddenly, the unstable chemical reaction erupts into an intense burst of golden, cyan, and violet energy. The scientist is engulfed in the radiant explosion as their body begins dissolving into billions of glowing atoms, molecules, and quantum particles. The camera performs a dramatic 360° orbit while every atom separates in slow motion, connected by luminous chemical bonds and streams of plasma energy. The particles travel through a breathtaking microscopic molecular universe filled with floating DNA helices, orbiting electrons, crystal lattices, colorful chemical reactions, and glowing periodic elements. The energy stream accelerates through a cosmic tunnel of atoms before converging again. Every molecule perfectly reassembles into the scientist, who now appears as an upgraded futuristic version wearing a sleek nanotech suit with glowing blue energy lines. Their eyes emit a soft electric glow as waves of molecular energy ripple across the laboratory. The room transforms into an advanced AI research facility with holographic chemical formulas floating in the air. The scientist confidently raises a hand, creating a luminous sphere of molecular energy above their palm. Cinematic camera movement, Hollywood VFX, hyper-realistic chemistry simulation, volumetric lighting, particle physics, ultra-detailed molecular animation, seamless transformation, dramatic slow motion, shallow depth of field, 8K, masterpiece, photorealistic, epic sci-fi atmosphere, vertical 16.9show 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

Distribution connection diagram 🔥⚡ A simple visual guide to... understanding electrical distribution connections and how power is safely routed.show more

Messing around with classical mechanics. Here a simple 2D... system with collision detection and conservation of momentum. #creativecoding #particlesshow more