SNN-Genesis v19: Stochastic Resonance in LLM Reasoning — Neural Prior Override, 0.5B Scaling, and Task/Architecture Specificity of Reasoning Directions

SNN-Genesis v19 reveals WHY stochastic resonance helps LLM reasoning: the Neural Prior Override mechanism. Noise gain is 4.5× larger when the model must override incorrect prior knowledge (Standard Hanoi +6.7pp vs Modified Hanoi +30.0pp, differential = +23.3pp, p=0.007). Building on v18's Aha! Steering, v19 proves that reasoning directions are both task-specific (cross-task cosine ≈ 0.031) and architecture-specific (cross-architecture transfer = 0%), and demonstrates that the Aha!+noise paradigm scales down to 0.5B models (baseline 0% → 40%). NEW in v19 (Season 20, Phases 96–102): • Cross-Task Specificity (Phase 96): Aha! vectors for different tasks are orthogonal (cosine ≈ 0.031). Matching vector achieves 53.3%, mismatched = 0%. No universal reasoning direction exists. • Cross-Architecture Specificity (Phase 97): Qwen→Mistral transfer = 0% (worse than baseline 3.3%). Native Aha! = 43.3%. Reasoning directions are architecture-specific. • N=100 Validation (Phase 98): v18's 46.7% corrects to 37.0% at N=100 (5.3× baseline). Honest −9.7pp correction. • Architecture Asymmetry (Phase 99): Aha! steering destabilizes Qwen (aha_only = 26.7% < baseline 56.7%). Same intervention produces opposite effects across architectures. • 0.5B Scaling (Phases 100–101): Qwen2.5-0.5B baseline = 0%. Flash σ=0.30 creates reasoning from nothing (10%). Aha!+Flash = 40%. The paradigm scales down. • Neural Prior Override (Phase 102): Standard Hanoi (familiar) gains +6.7pp from noise. Modified Hanoi (unfamiliar, requires prior override) gains +30.0pp. The 4.5× differential (p=0.007) reveals that noise helps most when the model must escape incorrect prior knowledge. 112 page paper. Full experimental code and data included. Code: https://github.com/hafufu-stack/snn-genesis