Gate-level boolean evolutionary geometric attention neural networks

2025-11-11

AI Summary

This work addresses the challenge of simultaneously achieving model interpretability and hardware efficiency in image processing. We propose a fully Boolean-domain neural network: images are modeled as Boolean fields on a 2D geometric manifold, with pixels treated as Boolean variables; XNOR-based Boolean self-attention and Boolean rotary position encoding (RoPE) are introduced, integrated with a Boolean reaction–diffusion mechanism and trainable gate-level logic kernels for information propagation and update; continuous relaxation enables end-to-end differentiable training. The architecture retains the expressive power of convolutional and attention-based models while operating entirely in the Boolean domain, significantly enhancing digital circuit compatibility and inference speed. Experiments demonstrate high interpretability, ultra-low power consumption, and exceptional hardware acceleration potential—achieving a unified balance between theoretical rigor and practical deployment efficiency.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Modeling images as Boolean fields using logic gates
• Implementing Boolean self-attention via XNOR-based diffusion modulation
• Achieving hardware efficiency through discrete Boolean domain operations

Innovation

• Boolean evolutionary geometric attention neural networks
• Boolean reaction-diffusion mechanism with logic gates
• XNOR-based Boolean self-attention with Rotary Position Embedding