Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI

Summary

The paper argues that long-term memory is becoming a core substrate for personalized AI, but existing systems usually treat personalization as discrete records stored in a largely static latent space and retrieved with one global similarity measure. This abstraction does not match the underlying evidence, which arrives as a temporal stream of interactions and events. The authors propose representing each user’s memory as a dynamical state space with locally heterogeneous geometry. In this computational framing, different regions can be stable or volatile, user state can drift at different rates, neighborhoods can vary, and the current state can remain uncertain; the geometry is not presented as a literal model of human cognition. Profiles and isolated events remain useful as points, while interactions, feedback, and elapsed time create trajectories. Memory access is therefore framed as trajectory-conditioned reconstruction of the relevant user state, rather than simple nearest-neighbor lookup.