提出可保证代数约束满足的神经符号层，适用于安全关键场景
A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction
- 用多项式参数化不等式逻辑组合的分布，实现约束建模
- 通过符号积分实现精确重归一化，训练无需近似
- 适合需严格满足复杂代数约束的自动驾驶等场景
在安全关键应用中，确保连续环境中约束的满足至关重要，例如自主代理不应碰撞障碍物或驶离道路。神经模型在处理包含复杂代数关系的约束时表现不佳。为此，我们提出一种可微的概率层，能够保证连续变量上非凸代数约束的满足。该概率代数层（PAL）可无缝嵌入任意神经架构，并通过最大似然进行训练，无需近似。PAL定义了线性不等式合取与析取的分布，由多项式参数化。该形式支持通过符号积分实现高效且精确的重归一化，可在不同数据点间摊销，并在GPU上轻松并行化。我们在多个代数约束集成基准及真实轨迹数据上展示了PAL及其集成方案的有效性。
原文摘要 · Abstract (English)
In safety-critical applications, guaranteeing the satisfaction of constraints over continuous environments is crucial, e.g., an autonomous agent should never crash into obstacles or go off-road. Neural models struggle in the presence of these constraints, especially when they involve intricate algebraic relationships. To address this, we introduce a differentiable probabilistic layer that guarantees the satisfaction of non-convex algebraic constraints over continuous variables. This probabilistic algebraic layer (PAL) can be seamlessly plugged into any neural architecture and trained via maximum likelihood without requiring approximations. PAL defines a distribution over conjunctions and disjunctions of linear inequalities, parameterized by polynomials. This formulation enables efficient and exact renormalization via symbolic integration, which can be amortized across different data points and easily parallelized on a GPU. We showcase PAL and our integration scheme on a number of benchmarks for algebraic constraint integration and on real-world trajectory data.
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