aiqbench analysis
This research addresses a fundamental bottleneck in compositional reasoning by replacing non-convex energy landscapes with input-convex neural networks, enabling deterministic optimization and zero-shot transfer to larger combinatorial problems. The proposed Convex Compositional Energy Minimization (CCEM) framework demonstrates that preserving convexity under summation allows models trained on small instances to generalize effectively without retraining.
Convex Compositional Reasoning Models
arXiv:2605.23395v3 Announce Type: replace Abstract: Compositional energy-based models can generalize to larger combinatorial reasoning problems by reusing a learned factor energy across many local constraints. In our paper, we show that a key bottleneck in compositional reasoning is not composition itself, but the non-convex geometry of the learned energy landscape. To solve this problem, we introduce Convex Compositional Energy Minimization (CCEM), a framework that parameterizes each factor with an input-convex neural network and optimizes the composed energy over a tight convex relaxation of the feasible set. Because convexity is preserved under summation, the global relaxed objective remains convex, enabling deterministic projected first-order optimization. CCEM is trained in two stages: factor-level contrastive learning to shape local energy basins, followed by end-to-end refinement through an unrolled projected solver. Our experiments show that our models trained on small subproblems or a single problem size transfer to larger instances without retraining.
Abstract:Compositional energy-based models can generalize to larger combinatorial reasoning problems by reusing a learned factor energy across many local constraints. In our paper, we show that a key bottleneck in compositional reasoning is not composition itself, but the non-convex geometry of the learned energy landscape. To solve this problem, we introduce Convex Compositional Energy Minimization (CCEM), a framework that parameterizes each factor with an input-convex neural network and optimizes the composed energy over a tight convex relaxation of the feasible set. Because convexity is preserved under summation, the global relaxed objective remains convex, enabling deterministic projected first-order optimization. CCEM is trained in two stages: factor-level contrastive learning to shape local energy basins, followed by end-to-end refinement through an unrolled projected solver. Our experiments show that our models trained on small subproblems or a single problem size transfer to larger instances without retraining.
Machine Learning (cs.LG)
arXiv:2605.23395 [cs.LG]
(or arXiv:2605.23395v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.23395 Focus to learn more arXiv-issued DOI via DataCite
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