Can a single projection layer beat fancy regularization? For neural ODEs with autoencoders, respecting global geometry trumps local smoothing for rollouts. latentrepresentation geometricML AI arxiv.org/abs/2603.03238v1

We often hear that Machine Learning models learn patterns in data. But what does that actually look like in Geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a Self-Organizing Map (SOM), a simple unsupervised neural model, learn the shape of a 3D datasets l, one static and the other dynamic. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud. It knows nothing about the structure underneath. Learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. Python code is available for Subscribers. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

We often hear that Machine Learning models learn patterns in data. But what does that look like in geometry? Picture dropping an elastic mesh into a cloud of points and letting it adapt. How would it bend, stretch, and settle so it matches the shape hiding in the data? In this scene we watch a self-organizing map(SOM)...a classic unsupervised neural model...learn a 2D dataset arranged like a spiral arm. Over the points we place a square grid of neurons whose weights live in the same plane. At the start it’s just a flat net drifting across the cloud. No clue what the structure is. Fir the SOM, learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, then nudge that neuron and its neighbours toward the point. Repeat, repeat, repeat...while gradually shrinking how wide the neighbourhood influence spreads. The result is satisfying...the grid stops being a grid and turns into a coordinate sheet wrapped onto the spiral. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML #SelfOrganizingMap #Topology

We often hear that machine learning models "learn patterns in data". But what does that actually look like in geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a self-organizing map...a simple unsupervised neural model...learn the shape of a two-dimensional dataset arranged in a spiral arm. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud...it knows nothing about the structure underneath. Learning is a repeated game: pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

Stuck on spectral reg for manifolds? Heat kernels stall at O(τ²) in curved space. HKR framework: Unifies Tikhonov RG via e^{τ Δ_g} f—~70% heat kernel covered. Python/Torch MVP for PDE/QFT. Feedback? github.com/zeusindomitable-m… [Attach: Demo notebook screenshot] #GeometricML

One clean navigation system. For all robots. Built once. Reused everywhere. Who's in? #Robotics #VisualNavigation #GeometricML

SOVERNA 👁️✨ #Artificial_Intelligence (⚡️ 2-Step SEED→SHIP SUP3R AGENT) 🪄 Drop a thought-fragment → receive a fully-formed, theorem-sealed build. 📜 Formal Chain-of-Thought THEOREM at the heart — every reasoning step is laid bare, proof-first, zero hocus-pocus. 🤖 The SUP3R Co-Creator literally proved itself into existence, then wrote its own specs. Meta-on-meta vibes. 🌐 Runs on the world’s first Continuous-Time Manifold Transformer — geometry-native brains for real-world dynamics. 🚀 Idea in, certified artifact out. Nothing casual, all canonical. #FormalAI #GeometricML #SeedToShip @akashnet @Ultra_io @CUDOS_ @Conste11ation