Algorithmically Aligned Neural Agglomerative Tree Construction

2026-10-05

AI Summary

This study addresses the limitations of traditional hierarchical clustering rules, which struggle to adapt to specific tasks, and existing neural approaches that often sacrifice the efficiency and generalizability of classical algorithms. We propose NN-linkage, a model that rigorously aligns deep neural networks with the Lance-Williams recurrence framework for the first time. By integrating Transformers to encode global dependencies, the model learns local, task-specific merging rules through parameterized recursion, and is proven to be a universal approximator of continuous linkage functions. Evaluated on real-world applications including clock tree routing and phylogenetic reconstruction, NN-linkage significantly outperforms both classical algorithms and neural baselines. Ultimately, this work achieves a unified framework that simultaneously preserves computational efficiency, ensures strong generalization, and enables task-adaptive hierarchical clustering.

Abstract

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.

Problem

• hierarchical clustering
• linkage algorithms
• merge rules
• algorithmic alignment
• size generalization

Innovation

• Hierarchical Clustering
• Algorithmic Alignment
• Lance-Williams Recurrence
• Neural Linkage
• Universal Approximation