AI 中文总结
本文研究可微逻辑门网络的离散化问题，指出局部离散化可能任务次优，提出利用一阶下游任务信息进行渐进式冻结，并在卷积网络上验证了其局部可靠性。
AI 中文摘要
可微逻辑门网络（DLGNs）通过在训练过程中松弛离散逻辑门并在推理时进行离散化，实现了对高效布尔网络的基于梯度的训练。标准方法通常通过argmax选择以及基于置信度或熵的收敛准则，在局部做出这种离散化决策。我们表明，即使对于全局最优的松弛解，局部离散化也可能在任务上不是最优的，高门置信度并不能提供一般性保证，并且我们推导了将任务感知的门选择与松弛网络中的可处理干预联系起来的界限。受这些结果的启发，我们研究了用于渐进式离散化的一阶下游任务信息，并刻画了这种局部近似何时可靠。在卷积DLGNs上的实验揭示了强烈的局部性依赖：当直接优化非局部干预时，一阶分数变得不可靠，但能准确评估用于渐进冻结的局部argmax决策。
英文摘要
Differentiable logic gate networks (DLGNs) enable gradient-based training of highly efficient Boolean networks by relaxing discrete logic gates during training and discretizing them for inference. Standard approaches make this discretization decision locally, typically through argmax selection and confidence- or entropy-based convergence criteria. We show that local discretization can be task-suboptimal even for globally optimal relaxed solutions, with high gate confidence providing no general guarantee, and derive bounds relating task-aware gate selection to tractable interventions in the relaxed network. Motivated by these results, we study first-order downstream task information for progressive discretization and characterize when this local approximation is reliable. Experiments on convolutional DLGNs reveal a strong locality dependence: first-order scores become unreliable when directly optimized over nonlocal interventions, but accurately assess local argmax decisions for progressive freezing.
