Lipschitz continuity

Formal sciences
Mathematics
Analysis
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Stochastic Differential Equations

Explores Stochastic Differential Equations, discussing existence, uniqueness, Lipschitz properties, and explicit solutions.

Advanced Analysis II: Differential Equations

Explores Lipschitz conditions in differential equations and their implications on solutions and properties.

Applying the learning bound to kernel regression

Discusses the application of the main theorem to least square regression in a RKHS, focusing on LR of the Rademacher bound and Lipschitz constant.

Existence Unicité

Explores the Lipschitz condition for functions and its implications on the uniqueness of solutions to the Cauchy problem.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Intermediate value theorem

Explores uniform continuity, Lipschitz functions, and the intermediate value theorem with examples and proofs.

Diffusion Models and Robustness

Explores diffusion models, GAN training challenges, SDE-based generative models, and robustness in deep learning.

Existence and Uniqueness Theorem

Explores the existence and uniqueness theorem of maximal solutions to Cauchy problems within specific intervals.

Local Lipschitz Functions

Explores locally Lipschitz functions, discussing differentiability, unique solutions, and function reduction.

Projected Gradient Descent: Quadratic Penalty

Covers projected gradient descent with a focus on quadratic penalty and optimality conditions.