Opponents Artist David KittDavid Kitt (born 1975 in Dublin Ireland) isan Irishmusician.

We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters, characterizing precisely how regularity conditions govern statistical performance. We also propose a bandwidth selection heuristic using derivative information, which shows promise in numerical experiments.

We thank the reviewers for their insightful comments. In this rebuttal, we respond to remarks from reviews. Remark 1 The work lacks discussion about the comparison of interpretability with BSP-Net. Moreover, their CSG structure is fixed by definition. CSG trees for different instances (see Figure on the right). Remark 2 Only a single instance of CSG visualization for each class is shown.

R3 asked why more CoDA samples don't always increase performance. This is all we meant by Remark 3.1: that within We agree our "intuitive" explanation of minimality might mislead in the way RL/Causal literatures, we show a broad application of causal techniques yielding empirical sample efficiency in RL. The "mental ignorance" comment at the end of Remark B's actual thoughts (but not agent A's belief about agent B's thoughts), and other true facts that agent A is ignorant of. We did not try the delta state trick; this is a helpful suggestion (thanks!) that we Note that CoDA + MBPO were complementary in the Batch RL case.

We would like to thank all reviewers for their comments and questions. We appreciate your recommendation about reordering the paper. Y our example is correct. We will rephrase this remark to make it more clear. Nguyen et al. [25] recognize the fact that for a strongly-convex Hence, like Nguyen et al. [25], Theorem 1 (iii) avoids the incompatible bounded-gradients assumption

Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and generating diverse samples, achieving state-of-the-art performance across domains such as computer vision, audio generation, reinforcement learning, and computational biology. Despite their empirical success, existing Wasserstein-2 convergence analysis typically assume strong regularity conditions-such as smoothness or strict log-concavity of the data distribution-that are rarely satisfied in practice. In this work, we establish the first non-asymptotic Wasserstein-2 convergence guarantees for SGMs targeting semiconvex distributions with potentially discontinuous gradients. Our upper bounds are explicit and sharp in key parameters, achieving optimal dependence of $O(\sqrt{d})$ on the data dimension $d$ and convergence rate of order one. The framework accommodates a wide class of practically relevant distributions, including symmetric modified half-normal distributions, Gaussian mixtures, double-well potentials, and elastic net potentials. By leveraging semiconvexity without requiring smoothness assumptions on the potential such as differentiability, our results substantially broaden the theoretical foundations of SGMs, bridging the gap between empirical success and rigorous guarantees in non-smooth, complex data regimes.