Autoregressive Differentiable Method for Integer Programming

Ouns El Harzli; Yudong Cao

Home/Archive/arXiv

arXiv · 2610.02528

Autoregressive Differentiable Method for Integer Programming

Ouns El Harzli·Yudong Cao

View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce an autoregressive differentiable method to solve 0-1 integer programs. We fix an arbitrary order of the binary variables and we train a transformer to predict the next bit while remaining in the feasible set. Our method is first trained on feasible incumbents provided by any solver, thus allowing us to initialize the transformer in the feasible set. Our procedure then implements a Lagrangian penalty to penalize infeasible solutions, and the transformer is further trained to explore the feasible set using Gumbel-softmax activations on the relaxed objective. We have tested our method on non-convex instances of quadratic knapsack problem and demonstrated consistent improvement upon state-of-the-art open-source solvers for dense problems up to 10,000 binary variables. In particular, we empirically demonstrate a phenomenon akin to a tunneling effect where the effective change of variables from binary variable to the continuous weights of the transformer that the method implements enables crossing barriers in the relaxed objective landscape.

Explore related subjects

cs.LG math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ouns El Harzli, Yudong Cao. 2026-10-01. Autoregressive Differentiable Method for Integer Programming. https://arxiv.org/abs/2610.02528

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

CHAOSMINING: Benchmarking Post-Hoc Attribution with Sparse Informative Features in High Dimensions

Post-hoc attribution is widely used to identify important model inputs, but evaluating whether these attributions identify truly informative features is difficult because real datasets rarely provide reliable ground truth. We introduce a multimodal benchmark containing symbolic tabular, vision, and audio tasks with known informative feature sets. In the main benchmark conditions, informative variables, spatial regions, or channels occupy fixed input coordinates while the remaining inputs provide irrelevant or distracting information. We use the benchmark to study how attribution quality depends on predictive performance, irrelevant-feature burden and structure, model configuration, and attribution mechanism, while separately measuring identification, stability, and computational cost. In most symbolic-data sweeps, informative-set identification co-varies with predictive performance, while the relative ordering of attribution methods remains largely stable. Across modalities, no method dominates all architectures and conditions, and greater attribution complexity does not consistently improve identification. Simple gradient attribution is often competitive at lower computational cost, while the vision and audio results show that architecture and the form of irrelevant content materially affect attribution quality.

cs.LG↗

arXiv2026

HardCore Generation: Generating Hard UNSAT Problems for Data Augmentation

Efficiently determining the satisfiability of a boolean equation -- known as the SAT problem for brevity -- is crucial in various industrial problems. Recently, the advent of deep learning methods has introduced significant potential for enhancing SAT solving. However, a major barrier to the advancement of this field has been the scarcity of large, realistic datasets. The majority of current public datasets are either randomly generated or extremely limited, containing only a few examples from unrelated problem families. These datasets are inadequate for meaningful training of deep learning methods. In light of this, researchers have started exploring generative techniques to create data that more accurately reflect SAT problems encountered in practical situations. These methods have so far suffered from either the inability to produce challenging SAT problems or time-scalability obstacles. In this paper we address both by identifying and manipulating the key contributors to a problem's ``hardness'', known as cores. Although some previous work has addressed cores, the time costs are unacceptably high due to the expense of traditional heuristic core detection techniques. We introduce a fast core detection procedure that uses a graph neural network. Our empirical results demonstrate that we can efficiently generate problems that remain hard to solve and retain key attributes of the original example problems. We show via experiment that the generated synthetic SAT problems can be used in a data augmentation setting to provide improved prediction of solver runtimes.

cs.LG↗

arXiv2026

How Vulnerable Is My Learned Policy? Universal Adversarial Perturbation Attacks On Modern Behavior Cloning Policies

Imitation learning, also known as learning from demonstrations, is a popular approach to train AI models; however, the vulnerability of these models to adversarial attacks remains underexplored. We present the first systematic study of adversarial attacks, across a range of both classic and recently proposed imitation learning algorithms, including Vanilla Behavior Cloning (Vanilla BC), LSTM-GMM, Implicit Behavior Cloning (IBC), Diffusion Policy (DP), and Vector-Quantized Behavior Transformer (VQ-BET). We study the vulnerability of these methods to white-box, grey-box and black-box adversarial perturbations. Our experiments reveal that most existing methods are highly vulnerable to these attacks, including black-box transfer attacks that transfer across algorithms. White-box attacks cause at least a 65% reduction in average task success across all evaluated tasks and algorithms, while the black-box transfer attacks reduce task success by up to 88% on Lift, 99% on Can, and 100% on Square. To the best of our knowledge, we are the first to study and compare the vulnerabilities of different popular imitation learning algorithms to both white-box and black-box attacks. Our findings highlight the vulnerabilities of modern imitation learning algorithms, paving the way for future work in addressing such limitations. Videos and code are available at https://sites.google.com/view/uap-attacks-on-bc.

cs.LG↗