发表机构
University of California San Diego; University of Washington（加州大学圣迭戈分校; 华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出NN-linkage，一种算法对齐Lance-Williams递推的神经网络模型，用于学习任务特定的层次聚类合并规则，兼具经典算法的效率与规模泛化，并在时钟树布线和系统发育重建中优于现有方法。
AI 中文摘要
用于层次聚类（HC）的链接算法是构建聚类树的一个强大且高效的框架，然而对于给定的数据集或任务，通常不清楚哪种合并规则最为合适。相比之下，神经方法可以从数据中学习，但往往无法保留经典算法的效率和规模泛化能力。我们引入了NN-linkage，一种神经网络（NN）模型，它能够学习特定于任务和局部依赖的合并规则，同时保留经典链接算法的递归结构和高效推理。特别是，我们的模型在算法上与Lance-Williams（LW）递推对齐，这是一个用于定义凝聚HC的广泛连续链接规则族的参数化框架。诸如单链接（SL）、全链接（CL）和平均链接等经典方法在该更广泛族中表现为离散选择。我们证明NN-linkage是连续链接函数（包括LW递推）的通用逼近器，并且当与变压器编码器配对时，还可以逼近全局依赖规则，如鲁棒单链接。我们进一步证明，NN-linkage可以在所有输入规模上精确实现任何对称常系数LW递推。在实证方面，我们在实际应用中评估了NN-linkage，包括时钟树布线和系统发育重建，使用合成和真实数据集，展示了其相对于经典算法和其他神经方法的有效性。通过直接从目标树学习合并规则，NN-linkage将高效HC扩展到现有手工设计的链接规则未能充分捕捉的科学和工程目标。
英文摘要
Linkage algorithms for hierarchical clustering (HC) are a powerful and efficient framework for constructing clustering trees, yet it is often unclear which merge rule best suits a given dataset or task. In contrast, neural approaches can learn from data, but often fail to retain the efficiency and size generalization of classical algorithms. We introduce NN-linkage, a neural network (NN) model that can learn task-specific and locally dependent merge rules while retaining the recursive structure and efficient inference of classical linkage algorithms. In particular, our model is algorithmically aligned with the Lance-Williams (LW) recurrence, a parameterized framework for defining a broad, continuous family of linkage rules for agglomerative HC. Classical methods such as single linkage (SL), complete linkage (CL), and average linkage arise as discrete choices within this broader family. We show that NN-linkage is a universal approximator for continuous linkage functions, including LW recurrences, and, when paired with a transformer encoding, can also approximate globally dependent rules such as robust single-linkage. We further show that NN-linkage can exactly implement any symmetric constant-coefficient LW recurrence across all input sizes. On the empirical front, we evaluate NN-linkage in real-world applications, clock-tree routing and phylogenetic reconstruction, using both synthetic and real datasets, demonstrating its effectiveness over both classical algorithms and other neural approaches. By learning merge rules directly from target trees, NN-linkage extends efficient HC to scientific and engineering objectives not adequately captured by existing hand-designed linkage rules.
