We show that two related classes of algorithms, stable algorithms and Boolean circuits with bounded depth, cannot produce an approximate sample from the uniform measure over the set of solutions to the symmetric binary perceptron model at any constraint-to-variable density. This result is in contrast to the question of finding \emph{a} solution to the same problem, where efficient (and stable) algorithms are known to succeed at sufficiently low density. This result suggests that the solutions found efficiently -- whenever this task is possible -- must be highly atypical, and therefore provides an example of a problem where search is efficiently possible but approximate sampling from the set of solutions is not, at least within these two classes of algorithms.

翻译：我们证明了两类相关算法——稳定算法和有界深度布尔电路——无法在任意约束变量密度下，从对称二元感知机模型的解集上均匀测度中生成近似样本。该结论与同一问题的寻解任务形成鲜明对比：已知在足够低的密度下，高效（且稳定）的算法能够成功寻解。这一结果表明，当寻解任务可行时，高效算法所找到的解必然具有高度非典型性，从而提供了一个问题实例，说明在该问题中高效搜索是可能的，但至少在上述两类算法框架下，从解集进行近似采样是不可行的。