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arXiv 2405.14596cs.LG
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可微树集成中的线性模式连通性

Linear Mode Connectivity in Differentiable Tree Ensembles

National Institute of Informatics(信息学研究所);The Graduate University for Advanced Studies, SOKENDAI(高等研究生院(SOKENDAI))

Ryuichi Kanoh, Mahito Sugiyama

AI总结:

本文研究可微软树集成的线性模式连通性,揭示树排列、子树翻转与分裂顺序不变性的作用,并提出基于决策列表的架构以消除额外不变性同时保持LMC。

摘要:

线性模式连通性(LMC)是指在参数空间中对模型进行线性插值时,性能保持一致的现象。对于从不同随机初始化独立优化得到的模型对,实现LMC被认为对于理解现代机器学习模型中非凸优化稳定成功的原因,以及促进模型合并等实际的基于参数的操作至关重要。尽管通过考虑每个隐藏层中神经元的排列不变性,神经网络已经实现了LMC,但对于其他模型如何实现LMC仍是一个开放问题。本文首次为软树集成实现了LMC,软树集成是实践中广泛使用的基于树的可微模型。我们表明,除了树的排列不变性之外,还有必要纳入两种不变性:子树翻转不变性和分裂顺序不变性;这两种不变性不存在于神经网络中,却是树架构所固有的。此外,我们证明,通过设计基于决策列表的树架构,甚至可以在排除这些额外不变性的同时保持LMC,因为在这种架构中这些不变性按定义并不存在。我们的发现表明,在实现LMC时考虑特定架构的不变性具有重要意义。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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