SNN-Genesis v18: Stochastic Resonance in LLM Reasoning — Aha! Steering, Cross-Architecture Universality, and Causal Proof of Reasoning Directionality

SNN-Genesis v18 provides the first causal existence proof of a reasoning direction in LLM hidden states via "Aha! Steering," demonstrates cross-architecture universality of discriminant axes, and achieves 46.7% solve rate on Mistral through direction+noise combination. NEW in v18 (Season 19, Phases 91, 92, 93, 94, 95): • Aha! Steering — Causal Proof of Reasoning Directionality (Phase 92): Anti-Aha steering on Qwen reduces solve rate from 56.7% to 23.3% (−33.4pp), causally proving that the differential vector encodes the reasoning direction. This is the first causal existence proof of a reasoning direction in LLM hidden states. • Aha! + Noise Achieves 46.7% on Mistral (Phase 95): Direction alone = baseline (3.3%), but Aha! + stochastic noise = 46.7% (matching the all-time record). Anti-Aha collapses to 0%. Mistral requires both direction and stochastic exploration; Qwen requires only direction. • Cross-Architecture Universality of Discriminant Axes (Phase 94): Both Qwen (3584-D) and Mistral (4096-D) concentrate their differential vectors in the same PCA bands: top-64 carries 40–49%, mid-band (65–256) carries ~38%. Verdict: universal_top_pcs — reasoning directions are universally encoded in variance-dominant subspaces. • Differential PCA Extends to Mistral (Phase 91): diff_pca_bottom = random (26.7%) on Mistral, confirming the discriminant axis is in top PCs. The method generalizes across architectures but the optimal noise direction differs: Qwen benefits from top-discriminant targeting, Mistral from off-axis noise. • Blue Noise — Honest Null Completing Temporal Characterization (Phase 93): Temporally anti-correlated noise (ρ<0, "blue noise") achieves 13.3%, below IID's 20.0%. Combined with Phase 90's positive-correlation result: IID noise is optimal; any temporal structure — positive or negative — degrades stochastic resonance. 104 page paper. Full experimental code and data included. Code: https://github.com/hafufu-stack/snn-genesis