记忆具有几何结构：面向长时程个性化AI的非均匀几何记忆
Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI
- The Chinese University of Hong Kong（香港中文大学）
- The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出将长期记忆建模为用户特定的动态状态空间，以非均匀几何结构捕捉稳定与易变区域，并将记忆访问视为轨迹条件下的状态重建，以支持长时程个性化AI。
AI中文摘要：
长期记忆正成为个性化AI的核心基础，然而大多数系统仍将个性化表示为大致静态潜在空间中的离散记录，并在单一全局相似性概念下进行访问。对于数据挖掘而言，这造成了一种错配：证据是时间事件流，而主导抽象是可搜索的记录集。我们认为，长时程个性化应转而将记忆建模为具有局部异质几何结构的用户特定动态状态空间。这里的几何是一种计算语言，而非关于认知的字面主张：它捕捉稳定与易变区域、变速率漂移、异质邻域以及关于当前用户状态的不确定性。轮廓和孤立事件作为点仍然有用，但交互、反馈和经过的时间会引发轨迹。记忆访问因此成为轨迹条件下的相关用户状态重建，而不仅仅是最近邻查找。
英文摘要：
Long-term memory is becoming a core substrate for personalized AI, yet most systems still represent personalization as discrete records in a largely static latent space, accessed under one global similarity notion. For data mining, this creates a mismatch: the evidence is a temporal event stream, while the dominant abstraction is a searchable record set. We argue that long-horizon personalization should instead model memory as a user-specific dynamical state space with locally heterogeneous geometry. Geometry here is a computational language, not a literal claim about cognition: it captures stable versus volatile regions, variable-rate drift, heterogeneous neighborhoods, and uncertainty about current user state. Profiles and isolated events remain useful as points, but interaction, feedback, and elapsed time induce trajectories. Memory access then becomes trajectory-conditioned reconstruction of the relevant user state, not only nearest-neighbor lookup.
