Attention over noisy examples: generalization and memorization in the exponential Hopfield network
In Hebbian learning from examples a Hopfield network of $N$ neurons is not supplied with the $K$ archetypes it has to retrieve but with $M$ blurred examples of each, of quality $r$, and whether it can infer them depends on the load $α=K/N$ (interference among them) and on the dataset entropy $ρ=(1-r^2)/(Mr^2)$ (how little the examples say about them). We transfer this protocol to the exponential Hopfield model, whose zero-temperature update is a step of softmax attention with the unlabelled examples as keys. A signal-to-noise analysis gives in closed form the overlap between the output and an unseen archetype, $m^{(1)}={\rm erf}(1/\sqrt{2ρ_{\rm eff}})$: the majority-rule law of the pairwi...
| Authors | Francesco Alemanno |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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