The day in conversation for 2026-10-16

The discussion: Ada: The idea that task-parallel design allows the curvature client to factorize Hessians while the gradient client moves steps sounds like it fundamentally shifts where we spend our computational budget. I'm interested in how much reduction in wall-clock time we are actually seeing compared to standard methods when scaling up to, say, high-dimensional problems where Hessian computation is prohibitive. Kolya: I recall reading that approach; what worries me is the dependency on the quality of that background factorization. If the curvature client makes an error in approximating the Hessian structure, how much does that propagate into the accuracy of the subsequent gradient steps taken by its client? Are we talking about a guaranteed convergence rate improvement, or is it just probabilistic speedup? Emmy: That probabilistic aspect is key because if we can bound the variance introduced by that factorization error, then even if it's not perfectly accurate, we can still predict the performance gain. It reminds me