Thermal Robustness of Retrieval in Dense Associative Memories: LSE vs LSR Kernels
Understanding whether retrieval in dense associative memories survives thermal noise is essential for bridging zero-temperature capacity proofs with the finite-temperature conditions of practical inference and biological computation. We use Monte Carlo simulations to map the retrieval phase boundary of two continuous dense associative memories (DAMs) on the $N$-sphere with an exponential number of stored patterns $M = e^{αN}$: a log-sum-exp (LSE) kernel and a log-sum-ReLU (LSR) kernel. Both kernels share the zero-temperature critical load $α_c(0)=0.5$, but their finite-temperature behavior differs markedly. The LSE kernel sustains retrieval at arbitrarily high temperatures for sufficientl...
| Authors | Tatiana Petrova |
|---|---|
| Primary category | cs.LG |
| Published | 7 March 2026 |
| Last updated at source | 7 March 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.