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

saddle points are more common than local minima in high dimensions

Saddle points arise due to mixed partial derivatives being zero, leading to more complex curvature in high dimensions

Convex optimization

Convex functions have only one global minimum

t-SNE preserves local structure

t-SNE preserves local structure by converting distances to probabilities and minimizing Kullback-Leibler divergence

the Johnson-Lindenstrauss lemma says

Random projection reduces dimensionality while approximately preserving pairwise distances

Graph (abstract data type)

Time complexity of BFS and DFS: O(V + E)

random projection to O(log n/ε²) dimensions preserves pairwise distances within 1±ε

Random projection reduces dimensionality while preserving pairwise distances within ε² due to the Johnson-Lindenstrauss lemma