We show how the differentiability method employed in the paper ``Differentiable Integer Linear Programming'', Geng, et al., 2025 as shown in its theorem 5 is incorrect. Moreover, there already exists some downstream work that inherits the same error. The underlying reason comes from that, though being continuous in expectation, the surrogate loss is discontinuous in almost every realization of the randomness, for the stochastic gradient descent.

翻译：我们证明，Geng等人于2025年发表的论文《可微整数线性规划》中定理5所采用的可微性方法是错误的。此外，已有若干后续研究沿袭了同一错误。其根本原因在于：尽管在期望意义上连续，但该替代损失函数在随机梯度下降的几乎每次随机实现中均不连续。