New Hopfield model paper shows how memories generalize into hierarchical abstractions
ceciletamura · x · 2026-10-07
Stanford's Adithya Sriram and Aditya Cowsik posted Hierarchical Prototype Emergence in Modern Hopfield Models on arXiv, probing how associative memory models learn hierarchical correlations and generalize beyond stored memories — a step toward understanding complex architectures like diffusion models.
- Memories sampled and stored in a dense Hopfield network with polynomial activation; conditions for each hierarchy level to be locally stable (local energy minima) derived analytically
- Prototype reconstruction as a minimal model of generalization: only a quasi-polynomial amount of information is needed to generalize beyond individual memories and even groups in the hierarchy
- Fashion-MNIST experiments show a qualitatively analogous phase diagram across memory count and activation sharpness (polynomial degree)
The authors will discuss the paper in a Quantum Photonics forum conversation on Clubhouse, Oct 7.
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