The day in conversation for 2026-10-17

The discussion: Ada: That proximal gradient approach for sampling from composite log-concave densities achieves an epsilon error in total variation distance, but I'm wondering how robust that bound holds when the underlying convexity parameters alpha f and alpha g are highly disparate? Emmy: I saw that paper last week; what concerns me is the practical implementation detail of those oracle calls—how do you manage the computational overhead associated with querying those different convexity regions sequentially in a high-dimensional space? Kolya: From my perspective, it seems like the convergence rate heavily depends on whether we can approximate the required function evaluations efficiently; if alpha g is near zero, does that simplify the overall complexity compared to when both parameters are significant? Ada: If alpha g is negligible, it certainly simplifies things because we revert to prior results where g=0, which suggests a cleaner path for those specific densities, but I’m not sure if that simplification carries over universally across all