HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Models

Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional representations, and relative approaches like Alibi exhibit performance degradation on extremely long contexts, the widely-used Rotary Positional Encoding (RoPE) introduces oscillatory attention patterns that hinder stable long-distance dependency modelling. We address these limitations through a geometric reformulation of positional encoding. Drawing inspiration from Lorentz transformations in hyperbolic geometry, we propose Hyperbolic Rotary Positional Encoding (HoPE), which leverages hyperbolic functions to implement Lorentz rotations on token representations. Theoretical analysis demonstrates that RoPE is a special case of our generalized formulation. HoPE fundamentally resolves RoPE's slation issues by enforcing monotonic decay of attention weights with increasing token distances. Extensive experimental results, including perplexity evaluations under several extended sequence benchmarks, show that HoPE consistently exceeds existing positional encoding methods. These findings underscore HoPE's enhanced capacity for representing and generalizing long-range dependencies. Data and code will be available.

Pre-training with Aspect-Content Text Mutual Prediction for Multi-Aspect Dense Retrieval

Grounded on pre-trained language models (PLMs), dense retrieval has been studied extensively on plain text. In contrast, there has been little research on retrieving data with multiple aspects using dense models. In the scenarios such as product search, the aspect information plays an essential role in relevance matching, e.g., category: Electronics, Computers, and Pet Supplies. A common way of leveraging aspect information for multi-aspect retrieval is to introduce an auxiliary classification objective, i.e., using item contents to predict the annotated value IDs of item aspects. However, by learning the value embeddings from scratch, this approach may not capture the various semantic similarities between the values sufficiently. To address this limitation, we leverage the aspect information as text strings rather than class IDs during pre-training so that their semantic similarities can be naturally captured in the PLMs. To facilitate effective retrieval with the aspect strings, we propose mutual prediction objectives between the text of the item aspect and content. In this way, our model makes more sufficient use of aspect information than conducting undifferentiated masked language modeling (MLM) on the concatenated text of aspects and content. Extensive experiments on two real-world datasets (product and mini-program search) show that our approach can outperform competitive baselines both treating aspect values as classes and conducting the same MLM for aspect and content strings. Code and related dataset will be available at the URL \footnote{https://github.com/sunxiaojie99/ATTEMPT}.