Riemannian geometry for Compound Gaussian distributions: application to recursive change detection

Riemannian stochastic recursive momentum method for non-convex optimization

We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a near-optimal complexity of $\tilde{\mathcal{O}}(ε^{-3})$ to find $ε$-approximate solution with one sample. That is, our method requires $\mathcal{O}(1)$ gradient evaluations per iteration and does not require restarting with a large batch gradient, which is commonly used to obtain the faster rate. Extensive experiment results demonstrate the superiority of our proposed algorithm.

Black Box Recursive Translations for Molecular Optimization

Machine learning algorithms for generating molecular structures offer a promising new approach to drug discovery. We cast molecular optimization as a translation problem, where the goal is to map an input compound to a target compound with improved biochemical properties. Remarkably, we observe that when generated molecules are iteratively fed back into the translator, molecular compound attributes improve with each step. We show that this finding is invariant to the choice of translation model, making this a "black box" algorithm. We call this method Black Box Recursive Translation (BBRT), a …

递归训练的扩散模型：限制崩溃分布与谱特征

Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization

研究递归训练扩散模型时的分布崩溃问题，证明即使完美学习也会因早期停止导致漂移，并收敛到唯一极限分布，该分布具有低通滤波谱特性。

条件核均值嵌入的递归估计

Recursive Estimation of Conditional Kernel Mean Embeddings

本文提出一种在Bochner空间中递归估计条件核均值映射的新算法，将Stone定理推广到局部紧波兰空间上的希尔伯特空间值回归，证明了弱与强L2一致性并给出强渐近界，在欧氏空间、黎曼流形和函数空间子集上验证了效果。