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📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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⚙️AlgorithmAdvanced

Natural Gradient Method

Natural gradient scales the ordinary gradient by the inverse Fisher information matrix to account for the geometry of probability distributions.

#natural gradient#fisher information#empirical fisher+12
∑MathAdvanced

Lie Groups & Lie Algebras

Lie groups model continuous symmetries like rotations and rigid-body motions, combining algebra (group law) and calculus (smooth manifolds).

#lie group
Advanced
Group:
Differential Geometry
#lie algebra
#so(3)
+12
∑MathAdvanced

Curvature

Curvature measures how a geometric object bends, and it comes in several flavors: Gaussian, sectional, and Ricci curvature.

#gaussian curvature#sectional curvature#ricci curvature+11
∑MathAdvanced

Geodesics & Exponential Map

Geodesics are the “straightest possible” paths on curved spaces (manifolds) and locally minimize distance.

#geodesic#exponential map#riemannian metric+12
∑MathIntermediate

Riemannian Metrics & Geometry

A Riemannian metric assigns an inner product to each tangent space, giving you a way to measure lengths and angles on curved spaces (manifolds).

#riemannian metric#metric tensor#christoffel symbols+12
∑MathAdvanced

Smooth Manifolds & Tangent Spaces

A smooth manifold is a space that looks like ordinary Euclidean space when you zoom in, glued together using charts that transition smoothly.

#smooth manifolds#tangent space#chart+11