https://ihebgafsi.tn Notes on geometric deep learning, representation learning, and applied research. en Thu, 23 Jul 2026 15:02:01 +0000 https://ihebgafsi.tn/post.html?slug=augmented-neural-odes-topology augmented-neural-odes-topology Sat, 01 Aug 2026 00:00:00 +0000 Neural ODE flows are homeomorphisms of the state space, an ODE's trajectories cannot cross, which makes concentric classes unsolvable at any training budget, not just hard. Works through the adjoint method, an exact vector-field example, an explicit inseparable dataset, and Augmented Neural ODEs as the actual fix. https://ihebgafsi.tn/post.html?slug=superposition-more-features-than-neurons superposition-more-features-than-neurons Wed, 01 Jul 2026 00:00:00 +0000 The grandmother-cell intuition (one neuron, one concept) is wrong, and interpretability research shows why: networks pack more features than they have dimensions by using almost-orthogonal directions instead of one-per-neuron, a real trick backed by concentration of measure. Includes an actual Monte Carlo experiment showing random vectors becoming orthogonal as dimension grows. https://ihebgafsi.tn/post.html?slug=why-gimbal-lock-cannot-be-fixed why-gimbal-lock-cannot-be-fixed Wed, 01 Jul 2026 00:00:00 +0000 A short, checkable proof that no three-number coordinate system for 3D rotations can ever avoid a singularity, why compactness is the entire reason, where Euler angles and rotation vectors each hide theirs, the hairy ball theorem as a sibling fact, and why this is the exact same theorem that makes every map of the Earth distorted somewhere. https://ihebgafsi.tn/post.html?slug=so3-se3-elegant-groups so3-se3-elegant-groups Wed, 01 Jul 2026 00:00:00 +0000 What makes SO(3) a group, the tangent space and exponential map, exactly why Euler angles hit gimbal lock at pitch = 90 degrees, the SU(2) double cover, and how SE(3) extends all of it to rigid motion. https://ihebgafsi.tn/post.html?slug=elegant-representation-learning-history elegant-representation-learning-history Wed, 01 Jul 2026 00:00:00 +0000 From SIFT and bag-of-words, through word2vec and distributional semantics, to contrastive and masked self-supervision, to choosing embedding geometry (hyperbolic, equivariant) on purpose. Same question throughout: what should the representation space look like. https://ihebgafsi.tn/post.html?slug=beyond-the-grid-geometric-deep-learning beyond-the-grid-geometric-deep-learning Wed, 01 Jul 2026 00:00:00 +0000 Convolutions assume a grid. Graphs, point clouds, and meshes don't have one. A walkthrough of equivariance, permutation-invariant message passing, receptive field growth on real vs small-world topology, and where rotation equivariance connects back to the orientation-fusion project. https://ihebgafsi.tn/post.html?slug=geodesic-averaging-demo geodesic-averaging-demo Wed, 01 Jul 2026 00:00:00 +0000 A template post showing every supported block: KaTeX math, a Mermaid diagram, a Plotly chart, and a code block. Delete once you've read data/posts.json and README.md.