提出新型门网络结构，实现150层深度下的稳定训练与性能提升。
On the Depth Scalability of Logic Gate Networks
- 通过输入锚点结构防止输出路径合并，保持每层输入访问。
- 在多个数据集上实现150层深度下准确率持续提升，而传统结构会饱和或下降。
- 适合研究深度神经网络可扩展性及逻辑运算型架构的学者。
逻辑门网络（LGNs）通过布尔运算组合进行计算，但现有方法无法可靠从深度增加中获益。我们识别出两个原因：优化坍缩和拓扑导致的输出特定梯度稀释，即使采用跳跃偏置初始化和直通估计也未能解决。为此提出输入锚定逻辑门网络（IALGN），每个门结合私有隐藏脊柱与直接输入锚点。该结构避免输出路径合并，同时保留每层对输入的访问。梯度诊断显示，随机连接会稀释或冲突输出特定梯度，而IALGN能维持可用且一致的梯度流。随机-kx松弛在不放松脊柱的前提下优化锚点选择。在MNIST、CIFAR-10和CIFAR-100上，IALGN表现出稳定的固定宽度深度-精度扩展，可达150层，而其他拓扑结构则出现饱和或退化。线性探测、拓扑消融与操作感知分析表明，训练后的IALGN保持私有状态并执行稀疏锚点条件更新。结果表明，可扩展的深度依赖于稳定优化与梯度信息的保真访问。
原文摘要 · Abstract (English)
Logic Gate Networks (LGNs) compute through compositions of Boolean operations, yet existing LGNs do not reliably benefit from increased depth. We identify two causes: optimization collapse and topology-induced degradation of output-specific credit that persists even after skip-biased initialization and straight-through estimation stabilize training. We introduce Input-Anchored Logic Gate Networks (IALGNs), in which each gate combines a private hidden spine with a direct input anchor. This topology prevents output-path merging while retaining input access at every layer. Credit diagnostics show that random wiring dilutes or conflicts output-specific gradients, whereas IALGN maintains usable and coherent credit. Random-$k_x$ relaxation improves anchor selection without relaxing the spine. Across MNIST, CIFAR-10, and CIFAR-100, IALGN exhibits consistent fixed-width depth--accuracy scaling up to 150 layers, while alternative topologies saturate or degrade. Linear probes, topology ablations, and operation-aware analysis show that trained IALGNs preserve private states and apply sparse anchor-conditioned updates. These results indicate that scalable LGN depth requires both stable optimization and credit-preserving information access.
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