📅 Date: Monday, May 18, 2026
🕚 Time: 15:00 – 16:00
Location: Heinzel Seminar Room, Office Building West
Speaker: David Robin (Dauphine)
Title: Kurdyka-Lojasiewicz integration, convergence to global optima without convexity
Abstract:
We show why convexity assumptions are too rigid to describe properly the convergence properties of gradient flows (and gradient descent more generally), and how to construct proof tactics stable under deformations. Using local integration techniques, we prove that satisfaction of Kurdyka-Lojasiewicz inequalities in a large region is sufficient to ensure convergence to global optima of gradient flows initialized in that region. Delving into more geometrical arguments, we explain why neural networks with strong approximation properties will automatically satisfy such inequalities near initialization, and under which assumptions this can be extended to the entire training trajectory. This enables the construction of convergence proofs without convexity assumptions and permits predictions of rich convergence speeds beyond the linear convergence of PL assumptions, reflecting the more complicated landscape of neural network optimization outside a nearly-convex regime.