对比两种记忆核在热噪声下的检索能力，发现一种能稳定工作于高温。
Thermal Robustness of Retrieval in Dense Associative Memories: LSE vs LSR Kernels
- 用蒙特卡洛模拟对比LSE与LSR两种核在高维球面上的检索表现
- LSE核在低负载时可耐受任意高温，而LSR核在低负载下实现完美检索
- 适合研究神经网络鲁棒性或生物计算的学者参考
理解密集关联记忆在热噪声下的检索能力，对连接零温容量理论与实际推理及生物计算的有限温度条件至关重要。我们通过蒙特卡洛模拟，绘制了两种连续密集关联记忆（DAM）在N-球面上的检索相边界，其存储模式数为指数级 $M = e^{αN}$：一种是对数求和指数（LSE）核，另一种是对数求和修正线性单元（LSR）核。两者在零温下的临界负载均为 $α_c(0)=0.5$，但在有限温度下行为迥异。LSE核在低负载时可维持检索能力于任意高温；而LSR核存在一个有限支持阈值，低于该阈值时可在任意温度下实现完美检索；对于典型锐度值，该阈值趋近于 $α_c$，使检索在全负载范围内几乎完美。我们还对比了测得的平衡对齐与检索域内解析的玻尔兹曼预测。
原文摘要 · Abstract (English)
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 sufficiently low load, whereas the LSR kernel exhibits a finite support threshold below which retrieval is perfect at any temperature; for typical sharpness values this threshold approaches $α_c$, making retrieval nearly perfect across the entire load range. We also compare the measured equilibrium alignment with analytical Boltzmann predictions within the retrieval basin.
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