We propose and analyze a conservative drifting method for one-step generative modeling. The method replaces the original displacement-based drifting velocity by a kernel density estimator (KDE)-gradient velocity, namely the difference of the kernel-smoothed data score and the kernel-smoothed model score. This velocity is a gradient field, addressing the non-conservatism issue identified for general displacement-based drifting fields. We prove continuous-time finite-particle convergence bounds for the conservative method on $\R^d$: a joint-entropy identity yields bounds for the empirical Stein drift, the smoothed Fisher discrepancy of the KDE, and the squared center velocity. The main finite-particle correction is a reciprocal-KDE self-interaction term, and we give deterministic and high-probability local-occupancy conditions under which this term is controlled. We keep the quadrature constants explicit and track their possible bandwidth dependence: the root residual-velocity rate $N^{-1/(d+4)}$ holds under an additional $h$-uniform quadrature regularity condition, while a more general growth condition yields the optimized root rate $N^{-(2-β)/(2(d+4-β))}$, where $0\le β<2$. We also analyze the non-conservative drifting method with Laplace kernel, corresponding to the original displacement-based velocity proposed in Deng et al., 2026 (arxiv:2602.04770). For this method, a sharp companion kernel decomposes the velocity into a positive scalar preconditioning of a sharp-score mismatch plus a Laplace scale-mismatch residual, producing an analogous finite-particle rate with an unavoidable residual term. Finally, we explain how the continuous-time residual-velocity bounds translate into one-step generation guarantees through the explicit drift size $η$.

In contrast, otheraugmentations ("Coarser" / "Rand") underperform.

Unsurprisingly, this approach performed poorly. Interpretable policy's dependence on demonstrator identity - Discretized PNTs learn splitting criterion dependent Please see Figure 2 in the supplementary for a depiction. Rephrasing Hypothesis - We thank R3 for these suggestions. "Interpretability" is vaguely defined - We agree that our study left the definition of "interpretability" open to the Details of synthetic schedule generation - This information is located within the supplementary. However, we agree this would be an interesting metric to pursue in future work.

Test-time adaptation (TTA) is a task that continually adapts a pre-trained source model to the target domain during inference. One popular approach involves fine-tuning model with cross-entropy loss according to estimated pseudo-labels. However, its performance is significantly affected by noisy pseudo-labels. This study reveals that minimizing the classification error of each sample causes the cross-entropy loss's vulnerability to label noise. To address this issue, we propose a novel Decoupled Prototype Learning (DPL) method that features prototype-centric loss computation. First, we decouple the optimization of class prototypes. For each class prototype, we reduce its distance with positive samples and enlarge its distance with negative samples in a contrastive manner. This strategy prevents the model from overfitting to noisy pseudo-labels. Second, we propose a memory-based strategy to enhance DPL's robustness for the small batch sizes often encountered in TTA. We update each class's pseudo-feature from a memory in a momentum manner and insert an additional DPL loss. Finally, we introduce a consistency regularization-based approach to leverage samples with unconfident pseudo-labels. This approach transfers feature styles of samples with unconfident pseudo-labels to those with confident pseudo-labels. Thus, more reliable samples for TTA are created. The experimental results demonstrate that our methods achieve state-of-the-art performance on domain generalization benchmarks, and reliably improve the performance of self-training-based methods on image corruption benchmarks. The code will be released.

In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in economics, psychology, and the social sciences. We present a function-specific measure of complexity and use it to prove that our algorithm is information-theoretically near-optimal in a strong, function-specific sense. We also corroborate our theoretical contributions with extensive numerical experiments, finding that our method substantially outperforms passive, uniform sampling for favorable synthetic and data-derived functions in low-noise settings with large sampling budgets. Our results also suggest an idealized `oracle strategy', which we use to gauge the potential for deploying the adaptive-sampling strategy on any function in any particular setting.

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations.