Hierarchical Prototype Emergence in Modern Hopfield Models
Hierarchical correlations are a universal feature of any realistic model of data, and the question of how associative memory models may learn these correlations and generalize beyond them to construct new sensible images is an important step towards understanding more complex modern architectures such as diffusion models. We consider a hierarchical model for memories which are sampled and stored in a dense Hopfield network with polynomial activation. We analytically derive conditions for each level of this hierarchy to be locally stable - that is they are local energy minima. We use prototype reconstruction as a minimal model of generalization and we find that it takes only a quasi-polyno...
| Authors | Aditya Cowsik, Adithya Sriram |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 10 September 2026 |
| Last updated at source | 10 September 2026 |
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