Linear Mode Connectivity in Differentiable Tree Ensembles

TL;DR

This paper demonstrates linear mode connectivity in differentiable tree ensembles by incorporating architecture-specific invariances, advancing understanding of model stability and enabling model merging in tree-based models.

Contribution

The paper introduces methods to achieve linear mode connectivity in differentiable tree ensembles by considering invariances unique to tree architectures, such as subtree flip and splitting order invariance.

Findings

LMC achieved for soft tree ensembles with invariance considerations

Design of decision list-based architectures that inherently satisfy LMC

Highlighting the importance of architecture-specific invariances in LMC

Abstract

Linear Mode Connectivity (LMC) refers to the phenomenon that performance remains consistent for linearly interpolated models in the parameter space. For independently optimized model pairs from different random initializations, achieving LMC is considered crucial for understanding the stable success of the non-convex optimization in modern machine learning models and for facilitating practical parameter-based operations such as model merging. While LMC has been achieved for neural networks by considering the permutation invariance of neurons in each hidden layer, its attainment for other models remains an open question. In this paper, we first achieve LMC for soft tree ensembles, which are tree-based differentiable models extensively used in practice. We show the necessity of incorporating two invariances: subtree flip invariance and splitting order invariance, which do not exist in neural networks but are inherent to tree architectures, in addition to permutation invariance of trees. Moreover, we demonstrate that it is even possible to exclude such additional invariances while keeping LMC by designing decision list-based tree architectures, where such invariances do not exist by definition. Our findings indicate the significance of accounting for architecture-specific invariances in achieving LMC.