Beyond Fixed Points: Superpolynomial Capacity of Asymmetric Hopfield Networks
Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical synchronous asymmetric networks, however, has remained a challenge. We present a simple and robust construction within the classical asymmetric Hopfield model with binary neurons and synchronous updates, that allows $n$ neurons to support $\exp\!\big(Ω(n/(\log n)^2)\big)$ distinct limit-cycle attractors, each with period $\exp\!\big(Ω(\sqrt n/\log n)\big)$ and robust to random noise with flip probability up to $\frac12-o(1)$, yielding superpolynomial capacity...
| Authors | Aakash Kumar, Anatoly Khina, Frederik Mallmann-Trenn et al. |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 23 May 2026 |
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