We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1-\alpha$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the statistical accuracies and computational efficiency of these algorithms depend on the degree of supervision, which is quantified by $\alpha$. In this paper, we characterize the effect of $\alpha$ by establishing the information-theoretic and computational boundaries, namely, the minimax-optimal statistical accuracy that can be achieved by all algorithms, and polynomial-time algorithms under an oracle computational model. For small $\alpha$, our result shows a gap between these two boundaries, which represents the computational price of achieving the information-theoretic boundary due to the lack of supervision. Interestingly, we also show that this gap narrows as $\alpha$ increases. In other words, having more supervision, i.e., more correct labels, not only improves the optimal statistical accuracy as expected, but also enhances the computational efficiency for achieving such accuracy.

In this paper, we adapt Mamba, a state-space language model, into VMamba, a vision backbone with linear time complexity.

The process for calculating these metrics is described in Appendix C. Moreover, to ensure the comparability between prediction performance metrics and driving performance metrics in the radar plot, we normalize all metrics to the scale of [0, 1]. In the subsequent section, we provide an overview of the DESPOT planner. These two values can only be inferred from history. The safety is represented by the normalized collision rate.

Success stories of deep reinforcement learning (RL) from high dimensional inputs such as pixels or large spatial layouts include achieving superhuman performance on Atari games [30, 37, 1], grandmaster levelinStarcraft II[50]andgrasping adiverse setofobjects with impressivesuccess rates and generalization with robots in the real world [21].

Spiking neural networks have attracted increasing attention in recent years due to their potential of handling time-dependent data.