This paper presents a gate-level Boolean evolutionary geometric attention neural network that models images as Boolean fields governed by logic gates. Each pixel is a Boolean variable (0 or 1) embedded on a two-dimensional geometric manifold (for example, a discrete toroidal lattice), which defines adjacency and information propagation among pixels. The network updates image states through a Boolean reaction-diffusion mechanism: pixels receive Boolean diffusion from neighboring pixels (diffusion process) and perform local logic updates via trainable gate-level logic kernels (reaction process), forming a reaction-diffusion logic network. A Boolean self-attention mechanism is introduced, using XNOR-based Boolean Query-Key (Q-K) attention to modulate neighborhood diffusion pathways and realize logic attention. We also propose Boolean Rotary Position Embedding (RoPE), which encodes relative distances by parity-bit flipping to simulate Boolean ``phase'' offsets. The overall structure resembles a Transformer but operates entirely in the Boolean domain. Trainable parameters include Q-K pattern bits and gate-level kernel configurations. Because outputs are discrete, continuous relaxation methods (such as sigmoid approximation or soft-logic operators) ensure differentiable training. Theoretical analysis shows that the network achieves universal expressivity, interpretability, and hardware efficiency, capable of reproducing convolutional and attention mechanisms. Applications include high-speed image processing, interpretable artificial intelligence, and digital hardware acceleration, offering promising future research directions.

翻译：本文提出了一种门级布尔演化几何注意力神经网络，该网络将图像建模为由逻辑门控制的布尔场。每个像素是一个嵌入二维几何流形（例如离散环面格点）的布尔变量（0或1），该流形定义了像素间的邻接关系和信息传播。网络通过布尔反应-扩散机制更新图像状态：像素接收来自相邻像素的布尔扩散（扩散过程），并通过可训练的门级逻辑核执行局部逻辑更新（反应过程），从而形成反应-扩散逻辑网络。我们引入了布尔自注意力机制，使用基于XNOR的布尔查询-键（Q-K）注意力来调制邻域扩散路径并实现逻辑注意力。同时，我们提出了布尔旋转位置嵌入（RoPE），通过奇偶位翻转编码相对距离以模拟布尔“相位”偏移。整体结构类似于Transformer，但完全在布尔域中运行。可训练参数包括Q-K模式位和门级核配置。由于输出是离散的，连续松弛方法（如Sigmoid近似或软逻辑算子）确保了可微分训练。理论分析表明，该网络实现了通用表达能力、可解释性和硬件效率，能够复现卷积和注意力机制。应用领域包括高速图像处理、可解释人工智能和数字硬件加速，为未来研究提供了有前景的方向。