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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.

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Alec Helbling

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168,757 görüntüleme • 10 ay önce •via X (Twitter)

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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.
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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.

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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.
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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.

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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".
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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".

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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 ship

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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. 🥔

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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.

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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:

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When a nuclear reactor powers on for the first time, the core fills with a deep blue glow that feels almost unreal as it rises through the water in a quiet surge of energy. The light is Cherenkov radiation, created when charged particles move through the water faster than light can travel in that medium, a discovery made in the 1930s that revealed a new way to see high energy reactions. Every appearance of this glow is a reminder of how powerful atomic reactions can be, showing a rare moment where raw physics becomes something visible and strangely beautiful.

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