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

TL;DR

This paper critically examines the differentiability approach used in a prior work on differentiable integer linear programming, revealing fundamental errors and clarifying the true nature of the surrogate loss's discontinuities.

Contribution

It identifies a key flaw in the previous differentiability method for integer linear programming and clarifies that the surrogate loss is discontinuous in almost all realizations, not truly differentiable.

Findings

The differentiability method in Geng et al. 2025 is incorrect.

The surrogate loss is discontinuous in almost every realization.

Existing downstream work inherits the same error.

Abstract

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.