Hybrid Digital-Gate Transformer with RC Feedback and Hardware Memory for Bitwise Chaotic Sequence Learning

We introduce a **hybrid digital-analog Transformer** capable of learning and simulating discrete-time chaotic sequences. Unlike conventional floating-point neural networks, all computations—including attention, feed-forward layers, and residual connections—are mapped to **bitwise logical gates** (XOR, AND, OR) augmented by **RC circuit-based feedback and inductive memory (L)**, inspired by digital Lorenz systems. Differentiable approximations of gates enable **bitwise gradient-based training**, while RC circuits and inductors emulate previous-step memory, enabling low-power, hardware-efficient implementation. Experiments demonstrate emergent pseudo-chaotic sequences, and analysis shows superior computational efficiency in hardware relative to software.