提出新方法突破神经符号推理的计算瓶颈，实现更高效准确的逻辑推断。
On Scaling Neurosymbolic Programming through Guided Logical Inference
- 用基于预言机和递归分解的精确算法绕过复杂公式计算
- 在多个数据集上实现显著性能提升，支持更大规模推理
- 兼顾精度与效率，适合追求可证明推理的高可靠性场景
概率神经符号学习旨在融合神经网络与符号编程。现有先进系统多依赖于将问题转化为概率加权模型计数（PWMC），需计算称为逻辑溯源的布尔公式。然而，PWMC属于\#P难问题，且逻辑溯源公式的子句数量可能呈指数级增长，成为实际应用中的主要瓶颈。本文提出新方法DPNL，采用精确算法绕过逻辑溯源的计算。该方法基于预言机机制与类DPLL递归分解，有效引导并加速逻辑推断。此外，该方法可拓展为带$ε$或$(ε, δ)$保证的近似推理算法ApproxDPNL。实验表明，DPNL显著提升精确推断的可扩展性，获得更高精度模型；ApproxDPNL则通过引入可控近似，在进一步提升可扩展性的基础上，仍能确保推理过程的可证明性。
原文摘要 · Abstract (English)
Probabilistic neurosymbolic learning seeks to integrate neural networks with symbolic programming. Many state-of-the-art systems rely on a reduction to the Probabilistic Weighted Model Counting Problem (PWMC), which requires computing a Boolean formula called the logical provenance.However, PWMC is \\#P-hard, and the number of clauses in the logical provenance formula can grow exponentially, creating a major bottleneck that significantly limits the applicability of PNL solutions in practice.We propose a new approach centered around an exact algorithm DPNL, that enables bypassing the computation of the logical provenance.The DPNL approach relies on the principles of an oracle and a recursive DPLL-like decomposition in order to guide and speed up logical inference.Furthermore, we show that this approach can be adapted for approximate reasoning with $ε$ or $(ε, δ)$ guarantees, called ApproxDPNL.Experiments show significant performance gains.DPNL enables scaling exact inference further, resulting in more accurate models.Further, ApproxDPNL shows potential for advancing the scalability of neurosymbolic programming by incorporating approximations even further, while simultaneously ensuring guarantees for the reasoning process.
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