SeqPE: Transformer with Sequential Position Encoding

TL;DR

SeqPE introduces a fully learnable, unified position encoding method for Transformers that improves extrapolation and generalization across modalities by representing positions as symbolic sequences and employing regularization techniques.

Contribution

The paper proposes SeqPE, a novel position encoding framework that enhances extrapolation and adaptability in Transformers through symbolic sequence representation and end-to-end learning.

Findings

Outperforms baselines in perplexity, EM, and accuracy.

Improves extrapolation to longer contexts and multi-dimensional inputs.

Enables seamless generalization without architectural redesign.

Abstract

Since self-attention layers in Transformers are permutation invariant by design, positional encodings must be explicitly incorporated to enable spatial understanding. However, fixed-size lookup tables used in traditional learnable position embeddings (PEs) limit extrapolation capabilities beyond pre-trained sequence lengths. Expert-designed methods such as ALiBi and RoPE, mitigate this limitation but demand extensive modifications for adapting to new modalities, underscoring fundamental challenges in adaptability and scalability. In this work, we present SeqPE, a unified and fully learnable position encoding framework that represents each $n$-dimensional position index as a symbolic sequence and employs a lightweight sequential position encoder to learn their embeddings in an end-to-end manner. To regularize SeqPE's embedding space, we introduce two complementary objectives: a contrastive objective that aligns embedding distances with a predefined position-distance function, and a knowledge distillation loss that anchors out-of-distribution position embeddings to in-distribution teacher representations, further enhancing extrapolation performance. Experiments across language modeling, long-context question answering, and 2D image classification demonstrate that SeqPE not only surpasses strong baselines in perplexity, exact match (EM), and accuracy--particularly under context length extrapolation--but also enables seamless generalization to multi-dimensional inputs without requiring manual architectural redesign. We release our code, data, and checkpoints at https://github.com/ghrua/seqpe.