KERPLE: Kernelized Relative Positional Embedding for Length Extrapolation

Ta-Chung Chi · Ting-Han Fan · Peter J Ramadge · Alexander Rudnicky

Hall J #440

Keywords: [ kernel method ] [ Transformer Language Modeling ] [ Length Extrapolation ]

[ Abstract ]
[ Paper [ OpenReview
Thu 1 Dec 2 p.m. PST — 4 p.m. PST


Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at~\url{}.

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