arXiv:2512.10656v3 Announce Type: replace Abstract: As context windows in large language models continue to expand, it is essential to characterize how attention behaves at extreme sequence lengths. We introduce token sample complexity: the rate at which attention computed on $n$ tokens converges to its infinite-token limit. We estimate finite-$n$ convergence bounds at two levels: pointwise uniform convergence of the attention map, and convergence of moments for the transformed token distribution. For compactly supported (and more generally sub-Gaussian) distributions, our first result shows t
The continuous expansion of context windows in large language models necessitates a deeper understanding of attention mechanisms at extreme sequence lengths.
Characterizing the sample complexity of attention helps optimize the design, efficiency, and capabilities of next-generation AI models, especially as they scale.
This research provides theoretical bounds and insights into how attention converges, enabling more predictable and performant large language models.
- · AI researchers
- · Large Language Model developers
- · Cloud AI providers
- · Inefficient AI model architectures
- · Developers ignoring theoretical limits
Improved efficiency and performance of large language models for longer context windows.
Faster development and deployment of more capable AI applications requiring extensive contextual understanding.
Reduced compute costs and energy consumption for advanced AI, potentially impacting the 'energy-bottleneck' narrative positively.
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Read at arXiv cs.LG