标题： 二阶神经控制器策略剪枝的闭式鲁棒性边界 显示英文标题

标题： Closed-Form Robustness Bounds for Second-Order Pruning of Neural Controller Policies

摘要： 深度神经策略为四旋翼飞行器解锁了敏捷飞行，为机械臂实现了自适应抓取，并为地面机器人提供了可靠的导航，但其数百万个权重与嵌入式微控制器的紧密内存和实时约束相冲突。 二阶剪枝方法，如最优脑损伤（OBD）及其变体，包括最优脑手术（OBS）和最近的SparseGPT，通过利用局部Hessian矩阵在单次传递中压缩网络，实现的稀疏性远高于幅度阈值法。 尽管它们在视觉和语言领域取得了成功，但这种权重移除对闭环稳定性、跟踪精度和安全性的影响仍然不清楚。 我们提出了对非线性离散时间控制中二阶剪枝的第一个数学严格鲁棒性分析。 系统在连续转移映射下演化，而控制器是一个$L$层的多层感知器，具有全局1-Lipschitz类型的ReLU激活函数。 剪枝层$k$的权重矩阵将$W_k$替换为$W_k+\delta W_k$，产生扰动参数向量$\widehat{\Theta}=\Theta+\delta\Theta$和剪枝后的策略$\pi(\cdot;\widehat{\Theta})$。 对于每个输入状态$s\in X$，我们推导出闭式不等式$ \|\pi(s;\Theta)-\pi(s;\widehat{\Theta})\|_2 \le C_k(s)\,\|\delta W_k\|_2, $，其中常数$C_k(s)$仅依赖于未剪枝的谱范数和偏置，并且可以从一次前向传递中以闭式求得。 所推导的界限在领域部署之前指定了与预定控制误差阈值兼容的最大可接受剪枝幅度。 通过将二阶网络压缩与闭环性能保证联系起来，我们的工作缩小了现代深度学习工具与安全关键自主系统鲁棒性需求之间的关键差距。 显示英文摘要

摘要： Deep neural policies have unlocked agile flight for quadcopters, adaptive grasping for manipulators, and reliable navigation for ground robots, yet their millions of weights conflict with the tight memory and real-time constraints of embedded microcontrollers. Second-order pruning methods, such as Optimal Brain Damage (OBD) and its variants, including Optimal Brain Surgeon (OBS) and the recent SparseGPT, compress networks in a single pass by leveraging the local Hessian, achieving far higher sparsity than magnitude thresholding. Despite their success in vision and language, the consequences of such weight removal on closed-loop stability, tracking accuracy, and safety have remained unclear. We present the first mathematically rigorous robustness analysis of second-order pruning in nonlinear discrete-time control. The system evolves under a continuous transition map, while the controller is an $L$-layer multilayer perceptron with ReLU-type activations that are globally 1-Lipschitz. Pruning the weight matrix of layer $k$ replaces $W_k$ with $W_k+\delta W_k$, producing the perturbed parameter vector $\widehat{\Theta}=\Theta+\delta\Theta$ and the pruned policy $\pi(\cdot;\widehat{\Theta})$. For every input state $s\in X$ we derive the closed-form inequality $ \|\pi(s;\Theta)-\pi(s;\widehat{\Theta})\|_2 \le C_k(s)\,\|\delta W_k\|_2, $ where the constant $C_k(s)$ depends only on unpruned spectral norms and biases, and can be evaluated in closed form from a single forward pass. The derived bounds specify, prior to field deployment, the maximal admissible pruning magnitude compatible with a prescribed control-error threshold. By linking second-order network compression with closed-loop performance guarantees, our work narrows a crucial gap between modern deep-learning tooling and the robustness demands of safety-critical autonomous systems.