通过组合子问题能量函数，实现推理模型的可扩展泛化。
Generalizable Reasoning through Compositional Energy Minimization
- 将复杂推理拆解为子问题，学习其能量景观以构建全局解空间。
- 在测试时组合多个子问题能量函数，支持新约束与更大规模问题求解。
- 引入并行能量最小化提升样本质量，适用于需要强泛化的推理任务。
泛化是机器学习中推理任务的核心挑战，模型需解决训练时未见过的更复杂问题。现有方法多采用端到端训练，直接从输入映射到解，虽能学习数据中的启发式规则，但泛化能力受限于训练分布。本文提出一种新方法：在小型可处理子问题上学习解空间的能量景观，并在测试时通过组合多个子问题的能量函数构建全局能量景观。该组合方式允许在推断阶段引入额外约束，从而应对日益复杂的任务。为提升由此生成的样本质量，引入并行能量最小化（PEM）。我们在多种推理任务上评估该方法，结果优于现有最先进模型，证明其在更大、更复杂问题上的泛化能力。项目网站见：https://alexoarga.github.io/compositional_reasoning/
原文摘要 · Abstract (English)
Generalization is a key challenge in machine learning, specifically in reasoning tasks, where models are expected to solve problems more complex than those encountered during training. Existing approaches typically train reasoning models in an end-to-end fashion, directly mapping input instances to solutions. While this allows models to learn useful heuristics from data, it often results in limited generalization beyond the training distribution. In this work, we propose a novel approach to reasoning generalization by learning energy landscapes over the solution spaces of smaller, more tractable subproblems. At test time, we construct a global energy landscape for a given problem by combining the energy functions of multiple subproblems. This compositional approach enables the incorporation of additional constraints during inference, allowing the construction of energy landscapes for problems of increasing difficulty. To improve the sample quality from this newly constructed energy landscape, we introduce Parallel Energy Minimization (PEM). We evaluate our approach on a wide set of reasoning problems. Our method outperforms existing state-of-the-art methods, demonstrating its ability to generalize to larger and more complex problems. Project website can be found at: https://alexoarga.github.io/compositional_reasoning/
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