Lectures related to Saddle point

Why are there so many saddle points?: Loss landscape and optimization methods

Explores the reasons behind the abundance of saddle points in deep learning optimization, emphasizing statistical and geometric arguments.

Stationary Points and Saddle Points

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

Lipschitz Gradient Theorem

Covers the Lipschitz gradient theorem and its applications in function optimization.

Gradient Descent: Lipschitz Continuity

Explores Lipschitz continuity in gradient descent optimization and its implications on function optimization.

Twisted Partition Function: Instanton Pre-factor

Explores the instanton pre-factor, twisted partition function, and zero mode integration.

Local Extremum Points Determination

Focuses on determining local extremum points of functions through various examples.

Local Extremums of Functions in Multivariable Calculus

Revisits local and absolute extremums of multivariable functions, emphasizing critical points and their classification.

Nature of Extremum Points

Covers the nature of extremum points and their classification as stationary or saddle points.

Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

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Local Inversion Theorem

Explores the Local Inversion Theorem and extremum points in functions.

Functions: Parametric, Integrals, Multi-variable

Covers parametric functions, integrals, and the origin of plasticity in metals.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Extrema of Functions in Several Variables

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Nature of Extremum Points

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.

Mathematical Methods for Materials Science: Integrals, Exact Differentials

Explores limits, derivation rules, integrals, and exact differentials for practical applications.

Implicit Functions Theorem

Explores the Implicit Functions Theorem and properties of hypersurfaces and matrices.

Lagrange Multipliers: Extremum Points

Explains Lagrange multipliers for extremum points and multiple integration methods for volume and area calculations.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.