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Multidimensional statistics for finite orbits of generalised continued fractions
Val\'erie Berth\'e, Stephen Cantrell, Jungwon Lee, Mark Pollicott
https://arxiv.org/abs/2507.11295

Multidimensional statistics for finite orbits of generalised continued fractions
We statistically compare the relationships between frequencies of digits in continued fraction expansions of typical rational points in the unit interval and higher dimensional generalisations. This takes the form of a Large Deviation and Central Limit Theorem, including multidimensional results for random vectors. These results apply to classical multidimensional continued fraction transformations including Brun's algorithm and the Jacobi--Perron algorithm, and more generally for maps satisfyi…

Soft Injection of Task Embeddings Outperforms Prompt-Based In-Context Learning
Jungwon Park, Wonjong Rhee
https://arxiv.org/abs/2507.20906 https://arxiv.or…

Soft Injection of Task Embeddings Outperforms Prompt-Based In-Context Learning
In-Context Learning (ICL) enables Large Language Models (LLMs) to perform tasks by conditioning on input-output examples in the prompt, without requiring any update in model parameters. While widely adopted, it remains unclear whether prompting with multiple examples is the most effective and efficient way to convey task information. In this work, we propose Soft Injection of task embeddings. The task embeddings are constructed only once using few-shot ICL prompts and repeatedly used during inf…