Bayesian Attention Mechanism: A Probabilistic Framework for Positional Encoding and Context Length Extrapolation

Arthur S. Bianchessi, Yasmin C. Aguirre, Rodrigo C. Barros, Lucas S. Kupssinskü · May 28, 2025 · Citations: 0

Abstract

Transformer-based language models rely on positional encoding (PE) to handle token order and support context length extrapolation. However, existing PE methods lack theoretical clarity and rely on limited evaluation metrics to substantiate their extrapolation claims. We propose the Bayesian Attention Mechanism (BAM), a theoretical framework that formulates positional encoding as a prior within a probabilistic model. BAM unifies existing methods (e.g., NoPE and ALiBi) and motivates a new Generalized Gaussian positional prior that substantially improves long-context generalization. Empirically, BAM enables accurate information retrieval at $500\times$ the training context length, outperforming previous state-of-the-art context length generalization in long context retrieval accuracy while maintaining comparable perplexity and introducing minimal additional parameters.

Human Data Lens

Uses human feedback: No
Feedback types: None
Rater population: Unknown
Unit of annotation: Unknown
Expertise required: General

Evaluation Lens

Evaluation modes: Automatic Metrics
Agentic eval: None
Quality controls: Not reported
Confidence: 0.45
Flags: low_signal, possible_false_positive

Research Summary

Contribution Summary

Transformer-based language models rely on positional encoding (PE) to handle token order and support context length extrapolation.
However, existing PE methods lack theoretical clarity and rely on limited evaluation metrics to substantiate their extrapolation claims.
We propose the Bayesian Attention Mechanism (BAM), a theoretical framework that formulates positional encoding as a prior within a probabilistic model.

Why It Matters For Eval

However, existing PE methods lack theoretical clarity and rely on limited evaluation metrics to substantiate their extrapolation claims.