Paper List

Journal: ArXiv Preprint
Published: Unknown
BioinformaticsMachine Learning

On the Approximation of Phylogenetic Distance Functions by Artificial Neural Networks

Indiana University, Bloomington, IN 47405, USA

Benjamin K. Rosenzweig, Matthew W. Hahn
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The 30-Second View

IN SHORT: This paper addresses the core challenge of developing computationally efficient and scalable neural network architectures that can learn accurate phylogenetic distance functions from simulated data, bridging the gap between simple distance methods and complex model-based inference.

Innovation (TL;DR)

  • Methodology Introduces minimal, permutation-invariant neural architectures (Sequence networks S and Pair networks P) specifically designed to approximate phylogenetic distance functions, ensuring invariance to taxa ordering without costly data augmentation.
  • Methodology Leverages theoretical results from metric embedding (Bourgain's theorem, Johnson-Lindenstrauss Lemma) to inform network design, explicitly linking embedding dimension to the number of taxa for efficient representation.
  • Methodology Demonstrates how equivariant layers and attention mechanisms can be structured to handle both i.i.d. and spatially correlated sequence data (e.g., models with indels or rate variation), adapting to the complexity of the generative evolutionary model.

Key conclusions

  • The proposed minimal architectures (e.g., Sites-Invariant-S with ~7.6K parameters) achieve results comparable to state-of-the-art inference methods like IQ-TREE on simulated data under various models (JC, K2P, HKY, LG+indels), outperforming classic pairwise distance methods (d_H, d_JC, d_K2P) in most conditions.
  • Architectures incorporating taxa-wise attention, while more memory-intensive, are necessary for complex evolutionary models with spatial dependencies; however, simpler networks suffice for simpler i.i.d. models, indicating an architecture-evolutionary model correspondence.
  • Performance is highly sensitive to hyperparameters: validation error increases sharply with fewer than 4 attention heads or with hidden channel counts outside an optimal range (e.g., 32-128), aligning with theoretical requirements for learning graph-structured data.
Background and Gap： Current supervised ML approaches for phylogenetics struggle with scalability to large numbers of taxa, lack built-in permutation invariance (requiring impractical data augmentation), and often fail to generalize beyond their training simulation conditions, failing to consistently match even simple methods like neighbor-joining with Hamming distances.

Abstract: Inferring the phylogenetic relationships among a sample of organisms is a fundamental problem in modern biology. While distance-based hierarchical clustering algorithms achieved early success on this task, these have been supplanted by Bayesian and maximum likelihood search procedures based on complex models of molecular evolution. In this work we describe minimal neural network architectures that can approximate classic phylogenetic distance functions and the properties required to learn distances under a variety of molecular evolutionary models. In contrast to model-based inference (and recently proposed model-free convolutional and transformer networks), these architectures have a small computational footprint and are scalable to large numbers of taxa and molecular characters. The learned distance functions generalize well and, given an appropriate training dataset, achieve results comparable to state-of-the art inference methods.