Low-rank matrix recovery is a fundamental problem in machine learning with numerous applications.

Let M denote M = 2 1 1 2 1 . . . . . . . . . 1 2 1 1 2 R

These theoretical findings are supported by experimental results.

Most of the breeds will have the first type of collapse as in Figure 5, 6, and 7. Figure 5, 6 shows the

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional `Pre-train \& Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning.

Massively parallel GPU simulation environments have accelerated reinforcement learning (RL) research by enabling fast data collection for on-policy RL algorithms like Proximal Policy Optimization (PPO). To maximize throughput, it is common to use short rollouts per policy update, increasing the update-to-data (UTD) ra- tio. However, we find that, in this setting, standard synchronous resets introduce harmful nonstationarity, skewing the learning signal and destabilizing training. We introduce staggered resets, a simple yet effective technique where environments are initialized and reset at varied points within the task horizon. This yields training batches with greater temporal diversity, reducing the nonstationarity induced by synchronized rollouts. We characterize dimensions along which RL environments can benefit significantly from staggered resets through illustrative toy environ- ments. We then apply this technique to challenging high-dimensional robotics environments, achieving significantly higher sample efficiency, faster wall-clock convergence, and stronger final performance. Finally, this technique scales better with more parallel environments compared to naive synchronized rollouts.

We first introduce necessary notations as follows. "LB" is lower bound while "UB" is upper bound. Quantity µ is the PL constant. These rates are derived under the strongly-convex assumption, not the general PL condition. This rate is achieved by utilizing increasing (non-constant) mini-batch sizes.

Parallelization is a popular strategy for improving the performance of iterative algorithms.