指出一种看似可微的整数线性规划方法其实不可微，且错误已被后续研究继承。

Differentiable Integer Linear Programming is not Differentiable & it's not a mere technical problem

• 发现原论文中可微化方法在数学上不成立
• 证明其代理损失在实际随机样本中几乎处处不连续
• 提醒相关领域的研究者警惕该错误传播

我们指出《可微整数线性规划》（Geng 等，2025）一文中定理5所采用的可微性方法存在根本性错误。更严重的是，已有下游工作沿用了这一错误。其根本原因在于：尽管代理损失在期望意义下连续，但在随机梯度下降的每一次具体实现中，该损失几乎处处不连续，因此无法真正支持可微优化。这一问题并非单纯技术瑕疵，而是理论基础的缺陷。

原文摘要 · Abstract (English)

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.

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