Wave Field LLM: O(n log n) wave attention

• Models tokens as a continuous 1D field where attention simulates damped wave propagation: wave equation form exp(-αt)cos(ωt+φ), solved efficiently with FFT for convolution in O(n log n) time.
• Each multi-head attention layer has heads with specialized roles: low-frequency for long-range, high-frequency/damping for local grammar and medium context.
• 3 learnable parameters per head: ω (frequency), α (damping factor for decay), φ (phase shift), enabling physics-inspired dynamics without full quadratic matrix.
• Physics diagnostics monitor energy dissipation and causality enforcement, contrasting with attention rollout (recursive multiplication) or flow (max-flow paths) for interpretability.
• Scales to long contexts by avoiding KV cache quadratic growth, akin to PagedAttention issues, with 367x speedup at 32K tokens vs. vanilla transformer.

Wave Field LLM's physics-based wave attention could disrupt long-context LLM inference by slashing quadratic bottlenecks to O(n log n), enabling efficient scaling to million-token sequences and reducing KV cache memory pressures in serving. This may accelerate adoption in real-time applications like extended document processing, while head specialization and diagnostics improve model interpretability over black-box transformers.