How does the concept of convexity in optimization relate to finding the global minimum in a non-linear cost function?

Why non-convex loss landscapes are hard: many local minima and saddle points

Non-convex landscapes have numerous local minima and saddle points, complicating optimization

Why proximal gradient descent is needed for L1 optimization

Proximal gradient descent handles non-differentiable L1 regularization, enabling sparse solutions

What is the primary objective of using the gradient descent optimization algorithm in training machine learning models?

Minimize the loss function to find optimal model parameters

What Rawls' difference principle says — inequality is just only if it benefits the least advantaged

Rawls' difference principle permits inequality if it improves the situation of the least well-off

What mixup does: trains on convex combinations of pairs: x̃=λx_i+(1-λ)x_j

Trains on convex combinations of pairs: x̃=λx_i+(1-λ)x_j represents a weighted average of two points in a convex set

How does the concept of 'function approximation' in machine learning algorithms relate to the idea of capturing the underlying patterns or functions within a dataset, and what are the primary mathematical techniques used to achieve this?

Function approximation in machine learning models captures dataset patterns using techniques like linear regression, neural networks, and kernel methods