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

arXiv: https://arxiv.org/abs/2601.17800 · HTML: https://mlsanity.com/paper/2601.17800/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Differentiable Clustering with Perturbed Spanning Forests](https://mlsanity.com/paper/2305.16358/) (2023)
- [CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Prediction](https://mlsanity.com/paper/2511.09209/) (2025)
- [RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains](https://mlsanity.com/paper/2511.02331/) (2025)
- [When Simple is Near Optimal in Security Games](https://mlsanity.com/paper/2402.11209/) (2024)
- [Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programming](https://mlsanity.com/paper/2508.18742/) (2025)
- [DEFT: Differentiable Automatic Test Pattern Generation](https://mlsanity.com/paper/2512.23746/) (2025)
- [Hephaestus: Mixture Generative Modeling with Energy Guidance for Large-scale QoS Degradation](https://mlsanity.com/paper/2510.17036/) (2025)
- [Learning-Based Hierarchical Approach for Fast Mixed-Integer Optimization](https://mlsanity.com/paper/2512.03547/) (2025)

## Built on by (most cited first, 2 of 2)

- [Unbiased Single-Queried Gradient for Combinatorial Objective](https://mlsanity.com/paper/2602.05119/) (2026)
- [Autoregressive Differentiable Method for Integer Programming](https://mlsanity.com/paper/2610.02528/) (2026)

## Abstract (arXiv)

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.