提出凸组合推理模型，让小规模训练的模型直接解决更大问题。
Convex Compositional Reasoning Models
- 用输入凸神经网络建模局部能量，保证整体优化凸性
- 在不重新训练情况下，从小问题推广到大问题
- 适合需要快速泛化到大规模推理任务的研究者
组合能量模型可通过复用学习到的局部能量项来泛化至更大的组合推理问题。本文指出，组合推理的关键瓶颈并非组合本身，而是学习到的能量景观的非凸几何结构。为此，我们提出凸组合能量最小化（CCEM）框架：将每个因子参数化为输入凸神经网络，并在可行集的紧凸松弛上优化组合能量。由于凸性在求和下保持不变，全局松弛目标仍为凸，从而支持确定性的投影一阶优化。CCEM采用两阶段训练：先进行因子级对比学习以塑造局部能量谷，再通过展开的投影求解器进行端到端微调。实验表明，基于小规模子问题或单一问题规模训练的模型可直接推广至更大实例，无需重新训练。
原文摘要 · Abstract (English)
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.
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