Prerequisites for SGD as a Stochastic Differential Equation

Direct prerequisites (4)

1. Stochastic Differential Equationslayer 3, tier 2
2. Stochastic Gradient Descent Convergencelayer 2, tier 1
3. Fokker–Planck Equationlayer 3, tier 2
4. Stochastic Calculus for MLlayer 3, tier 3

Reachable through the chain (66)

These topics are not directly cited as prerequisites but are reached transitively by following the chain upward. Working through the direct prerequisites pulls these in.

• Ito's Lemmalayer 3, tier 2
• Martingale Theorylayer 0B, tier 2
• Measure-Theoretic Probabilitylayer 0B, tier 1
• Cardinality and Countabilitylayer 0A, tier 2
• Sets, Functions, and Relationslayer 0A, tier 1
• Basic Logic and Proof Techniqueslayer 0A, tier 2
• Integration and Change of Variableslayer 0A, tier 2
• Kolmogorov Probability Axiomslayer 0A, tier 1
• Random Variableslayer 0A, tier 1
• Zermelo-Fraenkel Set Theorylayer 0A, tier 2
• Classical ODEs: Existence, Stability, and Numerical Methodslayer 1, tier 1
• Continuity in Rⁿlayer 0A, tier 1
• Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
• The Jacobian Matrixlayer 0A, tier 1
• Differentiation in Rⁿlayer 0A, tier 1
• Vectors, Matrices, and Linear Mapslayer 0A, tier 1
• Gradient Descent Variantslayer 1, tier 1
• Convex Optimization Basicslayer 1, tier 1
• Matrix Operations and Propertieslayer 0A, tier 1
• Linear Independencelayer 0A, tier 1
• Common Inequalitieslayer 0A, tier 1
• Common Probability Distributionslayer 0A, tier 1
• Exponential Function Propertieslayer 0A, tier 1
• Dynamic Programminglayer 0A, tier 1
• Graph Algorithms Essentialslayer 0A, tier 2
• Greedy Algorithmslayer 0A, tier 2
• GraphSLAM and Factor Graphslayer 3, tier 2
• Inverse and Implicit Function Theoremlayer 0A, tier 2
• Positive Semidefinite Matriceslayer 0A, tier 1
• Eigenvalues and Eigenvectorslayer 0A, tier 1
• Inner Product Spaces and Orthogonalitylayer 0A, tier 1
• Matrix Normslayer 0A, tier 1
• Submodular Optimizationlayer 3, tier 3
• Taylor Expansionlayer 0A, tier 1
• The Hessian Matrixlayer 0A, tier 1
• Vector Calculus Chain Rulelayer 0A, tier 1
• Concentration Inequalitieslayer 1, tier 1
• Expectation, Variance, Covariance, and Momentslayer 0A, tier 1
• Joint, Marginal, and Conditional Distributionslayer 0A, tier 1
• Triangular Distributionlayer 0A, tier 2
• Central Limit Theoremlayer 0B, tier 1
• Law of Large Numberslayer 0B, tier 1
• Borel-Cantelli Lemmaslayer 0B, tier 1
• Modes of Convergence of Random Variableslayer 0B, tier 1
• Characteristic Functionslayer 1, tier 1
• Moment Generating Functionslayer 0A, tier 2
• Radon-Nikodym and Conditional Expectationlayer 0B, tier 1
• Skewness, Kurtosis, and Higher Momentslayer 1, tier 1
• Coordinate Descentlayer 2, tier 2
• Mirror Descent and Frank-Wolfelayer 3, tier 2
• Convex Dualitylayer 2, tier 1
• Subgradients and Subdifferentialslayer 1, tier 1
• Online Convex Optimizationlayer 3, tier 2
• No-Regret Learninglayer 3, tier 2
• Projected Gradient Descentlayer 2, tier 2
• Proximal Gradient Methodslayer 2, tier 1
• Quasi-Newton Methodslayer 2, tier 1
• Newton's Methodlayer 1, tier 1
• Line Search Methodslayer 2, tier 2
• Secant Methodlayer 1, tier 2
• PDE Fundamentals for Machine Learninglayer 1, tier 2
• Fast Fourier Transformlayer 1, tier 2
• Complex Numbers for Fourierlayer 0A, tier 2
• Functional Analysis Corelayer 0B, tier 2
• Divergence, Curl, and Line Integralslayer 0A, tier 2
• Feynman–Kac Formulalayer 3, tier 2