Prerequisites for Preconditioned Optimizers: Shampoo, K-FAC, and Natural Gradient

Direct prerequisites (4)

1. Convex Optimization Basicslayer 1, tier 1
2. Fisher Information: Curvature, KL Geometry, and the Natural Gradientlayer 0B, tier 1
3. The Hessian Matrixlayer 0A, tier 1
4. Conjugate Gradient Methodslayer 2, tier 2

Reachable through the chain (52)

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.

• Differentiation in Rⁿlayer 0A, tier 1
• Sets, Functions, and Relationslayer 0A, tier 1
• Basic Logic and Proof Techniqueslayer 0A, tier 2
• Vectors, Matrices, and Linear Mapslayer 0A, tier 1
• Continuity in Rⁿlayer 0A, tier 1
• Metric Spaces, Convergence, and Completenesslayer 0A, 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
• Integration and Change of Variableslayer 0A, tier 2
• Measure-Theoretic Probabilitylayer 0B, tier 1
• Cardinality and Countabilitylayer 0A, tier 2
• Kolmogorov Probability Axiomslayer 0A, tier 1
• Random Variableslayer 0A, tier 1
• Zermelo-Fraenkel Set Theorylayer 0A, tier 2
• 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
• The Jacobian Matrixlayer 0A, tier 1
• 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
• Vector Calculus Chain Rulelayer 0A, tier 1
• Maximum Likelihood Estimation: Theory, Information Identity, and Asymptotic Efficiencylayer 0B, tier 1
• Central Limit Theoremlayer 0B, tier 1
• Law of Large Numberslayer 0B, tier 1
• Expectation, Variance, Covariance, and Momentslayer 0A, tier 1
• Joint, Marginal, and Conditional Distributionslayer 0A, tier 1
• Triangular Distributionlayer 0A, tier 2
• 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
• KL Divergencelayer 1, tier 1
• Information Theory Foundationslayer 0B, tier 2
• Distance Metrics Comparedlayer 1, tier 2
• Non-Euclidean and Hyperbolic Geometrylayer 1, tier 2
• Total Variation Distancelayer 1, tier 1
• Method of Momentslayer 0B, tier 2
• Radon-Nikodym and Conditional Expectationlayer 0B, tier 1
• Basu's Theoremlayer 0B, tier 3
• Sufficient Statistics and Exponential Familieslayer 0B, tier 2
• Line Search Methodslayer 2, tier 2
• Newton's Methodlayer 1, tier 1
• Numerical Linear Algebralayer 1, tier 2