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

arXiv: https://arxiv.org/abs/2609.17969 · HTML: https://mlsanity.com/paper/2609.17969/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 64 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 30 of 52)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Evaluating Very Long-Term Conversational Memory of LLM Agents](https://mlsanity.com/paper/2402.17753/) (2024)
- [LongMemEval: Benchmarking Chat Assistants on Long-Term Interactive Memory](https://mlsanity.com/paper/2410.10813/) (2024)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [A Survey on the Memory Mechanism of Large Language Model based Agents](https://mlsanity.com/paper/2404.13501/) (2024)
- [MemoryBank: Enhancing Large Language Models with Long-Term Memory](https://mlsanity.com/paper/2305.10250/) (2023)
- [Deep Interest Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1706.06978/) (2017)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [LaMP: When Large Language Models Meet Personalization](https://mlsanity.com/paper/2304.11406/) (2023)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Zep: A Temporal Knowledge Graph Architecture for Agent Memory](https://mlsanity.com/paper/2501.13956/) (2025)
- [Deep Interest Evolution Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1809.03672/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Augmenting Language Models with Long-Term Memory](https://mlsanity.com/paper/2306.07174/) (2023)
- [Hello Again! LLM-powered Personalized Agent for Long-term Dialogue](https://mlsanity.com/paper/2406.05925/) (2024)
- [In Prospect and Retrospect: Reflective Memory Management for Long-term Personalized Dialogue Agents](https://mlsanity.com/paper/2503.08026/) (2025)
- [User-LLM: Efficient LLM Contextualization with User Embeddings](https://mlsanity.com/paper/2402.13598/) (2024)
- [A Survey of Personalized Large Language Models: Progress and Future Directions](https://mlsanity.com/paper/2502.11528/) (2025)
- [Aligning LLMs with Individual Preferences via Interaction](https://mlsanity.com/paper/2410.03642/) (2024)
- [Towards Lifelong Dialogue Agents via Timeline-based Memory Management](https://mlsanity.com/paper/2406.10996/) (2024)

## Built on by (most cited first, 1 of 1)

- [Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution](https://mlsanity.com/paper/2609.29329/) (2026)

## Abstract (arXiv)

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.