Large language models (LLMs) have achieved impressive performance in numerous domains but often struggle to process lengthy inputs effectively and efficiently due to limited length generalization and attention's quadratic computational demands. Many sought to mitigate this by restricting the attention window within the pre-trained length. However, these methods introduce new issues such as ignoring the middle context and requiring additional training. To address these problems, we propose LongHeads, a training-free framework that enhances LLM's long context ability by unlocking multi-head attention's untapped potential. Instead of allowing each head to attend to the full sentence, which struggles with generalizing to longer sequences due to out-of-distribution (OOD) issues, we allow each head to process in-distribution length by selecting and attending to important context chunks. To this end, we propose a chunk selection strategy that relies on the inherent correlation between the query and the key representations, efficiently distributing context chunks to different heads. In this way, each head ensures it can effectively process attended tokens within the trained length, while different heads in different layers can collectively process longer contexts. LongHeads works efficiently in linear time, fits seamlessly with many LLMs that use relative positional encoding. Our extensive empirical analyses verify LongHeads's efficacy in extending the usable context window for existing models, showcasing its promise for enhancing long text understanding.

In recent years, there have been remarkable advancements in the performance of Transformer-based Large Language Models (LLMs) across various domains. As these LLMs are deployed for increasingly complex domains, they often face the need to follow longer user prompts or generate longer texts. In these situations, the $\textit{length generalization failure}$ of LLMs on long sequences becomes more prominent. Most pre-training schemes truncate training sequences to a fixed length. LLMs often struggle to generate fluent and coherent texts after longer contexts, even with relative positional encoding specifically designed to cope with this problem. Common solutions such as finetuning on longer corpora often involve daunting hardware and time costs and require careful training process design. To more efficiently extrapolate existing LLMs' generation quality to longer texts, we theoretically and empirically investigate the main out-of-distribution (OOD) factors contributing to this problem. Inspired by this diagnosis, we propose a simple yet effective solution for on-the-fly length generalization, LM-Infinite. It involves only a $\mathbf{\Lambda}$-shaped attention mask (to avoid excessive attended tokens) and a distance limit (to avoid unseen distances) while requiring no parameter updates or learning. We find it applicable to a variety of LLMs using relative-position encoding methods. LM-Infinite is computationally efficient with $O(n)$ time and space, and demonstrates consistent text generation fluency and quality to as long as 128k tokens on ArXiv and OpenWebText2 datasets, with 2.72x decoding speedup. We will make the codes publicly available following publication.