这篇论文把跨会话交接讲透了，给出最小充分交接的比特需求和高斯线性回归的精确结果。做长会话AI应用的值得看看。
该论文将跨会话信息传递形式化为任务相关的上下文学习（ICL）状态交接，并区分了精确恢复早期材料与保留目标分布。在外生性条件下，预测等价性刻画了最粗的确定性充分交接，并给出固定长度的比特需求。作者提出三部分记录：精确存储决策与约束，用任务论证的统计量保存重复证据，并保留未被统计量覆盖的原始观察。高斯线性回归得到精确的有限维交接和有限比特扰动界，非参数回归则给出记忆与平方预测误差之间的上下界。
Handover of In-Context Learning State Across Session Boundaries
This study investigates the methodological and theoretical properties of session handover in applications that use large language models. A task may continue in a new session when the context reaches the model's input limit, when the application restarts, or when another agent is asked to finish the task. The application must then decide which information from the earlier session to pass on. We formulate handover as the transfer of a task-relative in-context learning (ICL) state and distinguish exact recovery of earlier material from preservation of the target distribution. Under an exogeneity condition, predictive equivalence characterizes the coarsest deterministic sufficient handover and gives a fixed-length bit requirement. The analysis isolates the effects of the memory constraint, the writer, and the continuation procedure, and quantifies the cost of writing before the realized downstream query is known. We propose a three-part record that stores decisions and constraints exactly, uses task-justified statistics for repeated evidence, and retains original observations whose effect is not preserved by those statistics. Gaussian linear regression gives an exact finite-dimensional handover and finite-bit perturbation bounds, while nonparametric regression gives upper and lower bounds that relate memory to squared prediction error. These results provide a theory and method for deciding what a handover must retain and how its memory requirement depends on the continuation task.