PaTH Attention: Position Encoding via Accumulating Householder Transformations

• URL: http://arxiv.org/abs/2505.16381v1
• Date: Thu, 22 May 2025 08:36:09 GMT
• Title: PaTH Attention: Position Encoding via Accumulating Householder Transformations
• Authors: Songlin Yang, Yikang Shen, Kaiyue Wen, Shawn Tan, Mayank Mishra, Liliang Ren, Rameswar Panda, Yoon Kim,
• Abstract summary: PaTH is a flexible data-dependent position encoding scheme based on accumulated products of Householder transformations.<n>We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices.
• Score: 56.32365080761523
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The attention mechanism is a core primitive in modern large language models (LLMs) and AI more broadly. Since attention by itself is permutation-invariant, position encoding is essential for modeling structured domains such as language. Rotary position encoding (RoPE) has emerged as the de facto standard approach for position encoding and is part of many modern LLMs. However, in RoPE the key/query transformation between two elements in a sequence is only a function of their relative position and otherwise independent of the actual input. This limits the expressivity of RoPE-based transformers. This paper describes PaTH, a flexible data-dependent position encoding scheme based on accumulated products of Householder(like) transformations, where each transformation is data-dependent, i.e., a function of the input. We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices, and implement a FlashAttention-style blockwise algorithm that minimizes I/O cost. Across both targeted synthetic benchmarks and moderate-scale real-world language modeling experiments, we find that PaTH demonstrates superior performance compared to RoPE and other recent baselines.

Related papers

• Context-aware Rotary Position Embedding [0.0]
  Rotary Positional Embeddings (RoPE) have become a widely adopted solution due to their compatibility with relative position encoding and computational efficiency.<n>We propose CARoPE (Context-Aware Rotary Positional Embedding), a novel generalization of RoPE that dynamically generates head-specific frequency patterns conditioned on token embeddings.<n>CaroPE consistently outperforms RoPE and other common positional encoding baselines, achieving significantly lower perplexity, even at longer context lengths.
  arXiv  Detail & Related papers  (2025-07-30T20:32:19Z)
• SeqPE: Transformer with Sequential Position Encoding [76.22159277300891]
  SeqPE represents each $n$-dimensional position index as a symbolic sequence and employs a lightweight sequential position encoder to learn their embeddings.<n> 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--but also enables seamless generalization to multi-dimensional inputs without requiring manual architectural redesign.
  arXiv  Detail & Related papers  (2025-06-16T09:16:40Z)
• Revisiting LRP: Positional Attribution as the Missing Ingredient for Transformer Explainability [53.21677928601684]
  Layer-wise relevance propagation is one of the most promising approaches to explainability in deep learning.<n>We propose specialized theoretically-grounded LRP rules designed to propagate attributions across various positional encoding methods.<n>Our method significantly outperforms the state-of-the-art in both vision and NLP explainability tasks.
  arXiv  Detail & Related papers  (2025-06-02T18:07:55Z)
• Rethinking Addressing in Language Models via Contexualized Equivariant Positional Encoding [89.52931576290976]
  Transformers rely on both content-based and position-based addressing mechanisms to make predictions.<n>TAPE is a novel framework that enhances positional embeddings by incorporating sequence content across layers.<n>Our method can be easily integrated into pre-trained transformers, offering parameter-efficient fine-tuning with minimal overhead.
  arXiv  Detail & Related papers  (2025-01-01T03:23:00Z)
• DAPE V2: Process Attention Score as Feature Map for Length Extrapolation [63.87956583202729]
  We conceptualize attention as a feature map and apply the convolution operator to mimic the processing methods in computer vision. The novel insight, which can be adapted to various attention-related models, reveals that the current Transformer architecture has the potential for further evolution.
  arXiv  Detail & Related papers  (2024-10-07T07:21:49Z)
• PoPE: Legendre Orthogonal Polynomials Based Position Encoding for Large Language Models [0.0]
  Polynomial Based Positional gonal (PoPE) encodes positional information by Orthogonal Legendres. We show that transformer models PoPE outperform baseline transformer models on the $Multi30k$ English-to-German translation task. We will present novel theoretical perspectives on position encoding based on the superior performance of PoPE.
  arXiv  Detail & Related papers  (2024-04-29T10:30:59Z)
• How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations [98.7450564309923]
  This paper takes initial steps on understanding in-context learning (ICL) in more complex scenarios, by studying learning with representations. We construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size.
  arXiv  Detail & Related papers  (2023-10-16T17:40:49Z)
• Rethinking and Improving Relative Position Encoding for Vision Transformer [61.559777439200744]
  Relative position encoding (RPE) is important for transformer to capture sequence ordering of input tokens. We propose new relative position encoding methods dedicated to 2D images, called image RPE (iRPE)
  arXiv  Detail & Related papers  (2021-07-29T17:55:10Z)
• Conformer-based End-to-end Speech Recognition With Rotary Position Embedding [11.428057887454008]
  We introduce rotary position embedding (RoPE) in the convolution-augmented transformer (conformer) RoPE encodes absolute positional information into the input sequence by a rotation matrix, and then naturally incorporates explicit relative position information into a self-attention module. Our model achieves a relative word error rate reduction of 8.70% and 7.27% over the conformer on test-clean and test-other sets of the LibriSpeech corpus respectively.
  arXiv  Detail & Related papers  (2021-07-13T08:07:22Z)
• Stable, Fast and Accurate: Kernelized Attention with Relative Positional Encoding [63.539333383965726]
  We propose a novel way to accelerate attention calculation for Transformers with relative positional encoding (RPE) Based upon the observation that relative positional encoding forms a Toeplitz matrix, we mathematically show that kernelized attention with RPE can be calculated efficiently using Fast Fourier Transform (FFT)
  arXiv  Detail & Related papers  (2021-06-23T17:51:26Z)
• Relative Positional Encoding for Transformers with Linear Complexity [30.48367640796256]
  relative positional encoding (RPE) was proposed as beneficial for classical Transformers. RPE is not available for the recent linear-variants of the Transformer, because it requires the explicit computation of the attention matrix. In this paper, we present precisely what is precisely what is a way to generate PE that can be used as a replacement to the classical additive (sinusoidal) PE and provably behaves like RPE.
  arXiv  Detail & Related papers  (2021-05-18T09:52:32Z)
• RoFormer: Enhanced Transformer with Rotary Position Embedding [9.01819510933327]
  We propose a novel method named Rotary Position Embedding(RoPE) to effectively leverage the positional information. RoPE encodes the absolute position with a rotation matrix and meanwhile incorporates the explicit relative position dependency in self-attention formulation. We evaluate the enhanced transformer with rotary position embedding, also called RoFormer, on various long text classification benchmark datasets.
  arXiv  Detail & Related papers  (2021-04-20T09:54:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.