Pay Attention Later: From Vector Space Diffusion to Linearithmic Spectral Phase-Locking

This version v2 paper will be available on arxiv. Paper is on Arxiv now: https://arxiv.org/abs/2512.01208AbstractStandard Transformers suffer from a “Semantic Alignment Tax”, a prohibitive optimization cost required to organize a chaotic initialization into a coherent geometric map via local gradient diffusion. We hypothesize that this reliance on diffusive learning creates “Catastrophic Rigidity”, rendering models unable to adapt to novel concepts without destroying their pre-trained reasoning capabilities. To isolate this phenomenon, we introduce Iterative Semantic Map Refinement (ISMR), a diagnostic protocol revealing that alignment is a fixed geometric barrier that scaling cannot solve; a 20-layer model overcomes this barrier no faster than a 1-layer model.We introduce the Phase-Resonant Intelligent Spectral Model (PRISM). PRISM encodes semantic identity as resonant frequencies in the complex domain (Cd) and replaces quadratic selfattention with linearithmic O(N log N) Gated Harmonic Convolutions. We validate PRISM on the WMT14 translation task. While the StandardTransformer maintains a slight edge in general competence on static benchmarks (23.88 vs 21.40 BLEU), it fails the “Plasticity-Stability” stress test completely. When injected with novel concepts, the Transformer suffers Catastrophic Forgetting, degrading by -10.55 BLEU points while achieving only 60% acquisition. In contrast, PRISM demonstrates Lossless Plasticity, achieving 96% 5-shot acquisition with negligible degradation (-0.84 BLEU). These results suggest that harmonic representations effectively decouple memory from reasoning, offering a structural solution to the plasticity-stability dilemma in real-time knowledge adaptation.