通过概率选择最优连接，显著减少逻辑门数量并提升性能。
A Method for Optimizing Connections in Differentiable Logic Gate Networks
- 按门输入的概率分布选择高价值连接，再确定门类型。
- 仅用8000个简单逻辑门即达MNIST超98%准确率，远少于传统方法。
- 连接优化后门数减少24倍，且在多个数据集上表现更优。
我们提出一种针对深度可微逻辑门网络（LGNs）的局部连接优化方法。该训练策略在每个门输入上基于连接概率分布，选择最具优势的连接，随后确定门类型。实验表明，优化连接后的LGN在Yin-Yang、MNIST和Fashion-MNIST基准上优于固定连接的LGN，且所需逻辑门数量大幅减少。当训练所有连接时，仅需8000个简单逻辑门即可在MNIST上实现超过98%的准确率。此外，相比标准全连接LGN，本方法使用24倍更少的逻辑门，同时性能更优。研究展示了通往完全可训练布尔逻辑的一条可行路径。
原文摘要 · Abstract (English)
We introduce a novel method for partial optimization of the connections in Deep Differentiable Logic Gate Networks (LGNs). Our training method utilizes a probability distribution over a subset of connections per gate input, selecting the connection with highest merit, after which the gate-types are selected. We show that the connection-optimized LGNs outperform standard fixed-connection LGNs on the Yin-Yang, MNIST and Fashion-MNIST benchmarks, while requiring only a fraction of the number of logic gates. When training all connections, we demonstrate that 8000 simple logic gates are sufficient to achieve over 98% on the MNIST data set. Additionally, we show that our network has 24 times fewer gates, while performing better on the MNIST data set compared to standard fully connected LGNs. As such, our work shows a pathway towards fully trainable Boolean logic.
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