Convex Compositional Reasoning Models
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arXiv
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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913161094889472 |
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| author | Roketlishvili, Meir Semenov, Semyon Bobrin, Maksim Kovalchuk, Viktor Baichorov, Albert Shtanchaev, Abduragim Karray, Fakhri Dylov, Dmitry V. Takáč, Martin Asadulaev, Arip |
| author_facet | Roketlishvili, Meir Semenov, Semyon Bobrin, Maksim Kovalchuk, Viktor Baichorov, Albert Shtanchaev, Abduragim Karray, Fakhri Dylov, Dmitry V. Takáč, Martin Asadulaev, Arip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex Compositional Reasoning Models Roketlishvili, Meir Semenov, Semyon Bobrin, Maksim Kovalchuk, Viktor Baichorov, Albert Shtanchaev, Abduragim Karray, Fakhri Dylov, Dmitry V. Takáč, Martin Asadulaev, Arip Machine Learning 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. |
| title | Convex Compositional Reasoning Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.23395 |