AI 中文总结
该研究针对随机正则图上的种植自旋玻璃模型，分析信号结构对贝叶斯推断的影响，发现西村条件下先验的复制对称破缺相可引发后验的静态复制对称破缺，并探讨其对置信传播算法性能的影响。
AI 中文摘要
贝叶斯推断理论模型中的一个常见假设是信号具有独立同分布分量。为研究信号先验中相关性的影响，我们考虑一个最小模型：随机正则图上的种植自旋玻璃，其中信号从耦合为κ的伊辛模型中采样。根据先验的相位，我们发现信号中添加结构既可能促进也可能阻碍推断。在顺磁区，信号中的相关性降低了重建阈值，因此更弱的信号强度即可实现恢复。在铁磁区，仅先验本身就能实现部分恢复，我们确定了观测值提供额外信息的阈值。当先验本身处于复制对称破缺（RSB）相时，我们在西村条件下检测到后验中的静态RSB转变。这提供了一个例子，其中不可分的相关先验在贝叶斯最优推断问题中导致静态RSB。我们讨论了这种玻璃态相对算法性能的影响，特别是对置信传播（Belief Propagation）的影响。
英文摘要
A common assumption in theoretical models of Bayesian inference is that the signal has i.i.d. components. To study the effect of correlations in the signal prior, we consider a minimal model: the planted spin glass on random regular graphs, where the signal is sampled from an Ising model with coupling $κ$. Depending on the phase of the prior, we find that adding structure in the signal can either help or hinder inference. In the paramagnetic regime, correlations in the signal lower the reconstruction threshold, so that weaker signal strength is sufficient for recovery. In the ferromagnetic regime, the prior alone already enables partial recovery, and we identify the threshold above which the observations provide additional information. When the prior itself is in a replica symmetry breaking (RSB) phase, we detect a static RSB transition in the posterior under Nishimori conditions. This provides an example where a non-separable, correlated prior leads to static RSB in a Bayes-optimal inference problem. We discuss the consequences of this glassy phase for algorithmic performance, in particular for Belief Propagation.
Comments31 pages, 11 figures
