Differentiable Integer Linear Programming is not Differentiable & it's not a mere technical problem
This points out a critical flaw in a method that could mislead researchers and practitioners in optimization and machine learning, making it an incremental correction to existing work.
The paper identifies an error in the differentiability method used in a prior work on differentiable integer linear programming, showing that the surrogate loss is discontinuous in almost every realization for stochastic gradient descent, and notes that this error has propagated to downstream research.
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.