We study algorithms in the resettable streaming model, where the value of each key can either be increased or reset to zero. The model is suitable for applications such as active resource monitoring with support for deletions and machine unlearning. We show that all existing sketches for this model are vulnerable to adaptive adversarial attacks that apply even when the sketch size is polynomial in the length of the stream. To overcome these vulnerabilities, we present the first adaptively robust sketches for resettable streams that maintain polylogarithmic space complexity in the stream length. Our framework supports (sub) linear statistics including $L_p$ moments for $p\in[0,1]$ (in particular, Cardinality and Sum) and Bernstein statistics. We bypass strong impossibility results known for linear and composable sketches by designing dedicated streaming sketches robustified via Differential Privacy. Unlike standard robustification techniques, which provide limited benefits in this setting and still require polynomial space in the stream length, we leverage the Binary Tree Mechanism for continual observation to protect the sketch's internal randomness. This enables accurate prefix-max error guarantees with polylogarithmic space.

翻译：我们研究可重置流处理模型中的算法，其中每个键的值既可以增加也可以重置为零。该模型适用于支持删除操作的主动资源监控和机器遗忘等应用场景。我们证明该模型所有现有草图算法在面对自适应对抗攻击时都存在脆弱性，即使草图大小与数据流长度呈多项式关系时攻击依然有效。为克服这些脆弱性，我们提出了首个适用于可重置数据流的自适应鲁棒草图算法，该算法在数据流长度上保持多对数空间复杂度。我们的框架支持（亚）线性统计量，包括$p\in[0,1]$时的$L_p$矩（特别是基数与和统计）以及伯恩斯坦统计量。通过设计基于差分隐私强化的专用流处理草图，我们规避了线性可组合草图已知的强不可能性结果。与标准鲁棒化技术（在该场景下收益有限且仍需多项式空间）不同，我们利用持续观测的二叉树机制来保护草图的内部随机性。这使得我们能够在多对数空间复杂度下实现精确的前缀最大误差保证。