Hebbian Memory Decay: Why Static Vector Databases Fail at Long-Term LLM Context

Static vector databases store embeddings in fixed metric spaces. If a user mentioned a preference 3 months ago, a standard k-NN query might retrieve it with high similarity even if it has been rendered obsolete by recent interactions.

Neurons That Fire Together, Wire Together

Spector implements Hebbian Memory Decay, a biologically-inspired mathematical model where memory weights dynamically adjust based on two factors:

$$\Delta W_{ij} = \eta \cdot R_{i} \cdot R_{j} - \gamma \cdot (t - t_{last})$$

1. Reinforcement ($R$): Frequent activation of related memories strengthens edge weights.
2. Temporal Decay ($\gamma$): Unreferenced memories naturally decay in weight over time, preserving relevant recent context while retaining deep foundation nodes.