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Pre-trained language models (LMs), such as BERT (Devlin et al., 2018) and itsvariants, have led to significant improvements on various NLP tasks in pastyears. However, a theoretical framework for studying their relationships isstill missing. In this paper, we fill this gap by investigating the lineardependency between pre-trained LMs. The linear dependency of LMs is definedanalogously to the linear dependency of vectors. We propose Language ModelDecomposition (LMD) to represent a LM using a linear combination of other LMsas basis, and derive the closed-form solution. A goodness-of-fit metric for LMDsimilar to the coefficient of determination is defined and used to measure thelinear dependency of a set of LMs. In experiments, we find that BERT and eleven(11) BERT-like LMs are 91% linearly dependent. This observation suggests thatcurrent state-of-the-art (SOTA) LMs are highly "correlated". To further advanceSOTA we need more diverse and novel LMs that are less dependent on existingLMs.

Language Model Decomposition: Quantifying the Dependency and Correlation of Language Models