Memory for All: SAGE — Spatial Associative Geometric Embeddings v2

Every time an AI system needs to learn something new, it must retrain from scratch — consuming months of compute and significant resources, while still forgetting what it knew before. This paper introduces SAGE — Spatial Associative Geometric Embeddings — a memory architecture that stores knowledge as coordinate positions in a 3D geometric cube rather than in weights. Retrieval uses cosine similarity. Learning uses local Hebbian updates. No backpropagation is required at any stage. Six contributions are made: gradient-free 3D coordinate storage; self-organising anti-collision; SAGEDivided working memory with fixed spatial partition; MultiCube horizontal scaling; a hippocampal-inspired consolidation pathway; and SAGESequenceCube — explicit geometric transition memory achieving 100% rollout accuracy — all without backpropagation. Empirical results demonstrate: 92% less forgetting than neural networks (0.049 vs 0.669), 91% less than EWC; perfect retention across 200 continuous learning steps; 0.000% sparsity activation; 87.2% word analogy accuracy using two-stage retrieval across 7,096 questions — reaching 90% of the GloVe oracle ceiling (97.4%); Langevin dynamics (Force 6, V3 architecture) improves retrieval cosine similarity by 20.1%; and negative forgetting under noise — retrieval quality improves rather than degrades when noise is applied. A companion paper demonstrates SAGE powering an autonomous agent that continued operating — zero defaults across 72 steps — even when its language model was disabled. The geometry computes. The weights are not needed. Code: https://github.com/Ivelin2022/sage