Determining the capacity $\alpha_c$ of the Binary Perceptron is a long-standing problem. Krauth and Mezard (1989) conjectured an explicit value of $\alpha_c$, approximately equal to .833, and a rigorous lower bound matching this prediction was recently established by Ding and Sun (2019). Regarding the upper bound, Kim and Roche (1998) and Talagrand (1999) independently showed that $\alpha_c$ < .996, while Krauth and Mezard outlined an argument which can be used to show that $\alpha_c$ < .847. The purpose of this expository note is to record a complete proof of the bound $\alpha_c$ < .847. The proof is a conditional first moment method combined with known results on the spherical perceptron

翻译：确定二元感知器的容量$\alpha_c$是一个长期存在的问题。Krauth和Mezard（1989）推测了$\alpha_c$的显式值，约为0.833，而Ding和Sun（2019）近期建立了与这一预测匹配的严格下界。关于上界，Kim和Roche（1998）以及Talagrand（1999）分别证明了$\alpha_c$ < 0.996，而Krauth和Mezard概述了一个可用于证明$\alpha_c$ < 0.847的论证。本说明性注释旨在记录关于$\alpha_c$ < 0.847边界的完整证明。该证明采用条件一阶矩方法，并结合了关于球面感知器的已知结果。