SNN-Genesis v13: Stochastic Resonance in LLM Reasoning — Low-Rank Efficiency, Semantic Phase Decomposition, and Noise Source Invariance

SNN-Genesis v13 decomposes the noise recipe into When, Where, and What — discovering that noise timing and injection site are critical factors while noise source structure is irrelevant.

NEW in v13 (Season 13, Phases 70b, 70c, 76):

• Low-Rank Noise Efficiency (Phase 70b): k=256 matches full-rank performance (26.7%); even k=4 achieves 16.7%. Stochastic resonance operates in a low-dimensional subspace.
• Semantic Phase Decomposition (Phase 76): Reasoning decomposed into Planning/Execution/Recovery phases. Flash Annealing (30.0%) > all-on semantic (23.3%). Recovery-only (+10pp) is the most effective single phase.
• Noise Source Invariance (Phase 70c, honest null result): Gaussian, quasi-periodic, logistic-map chaos, 1/f pink, and uniform noise all fail to outperform baseline. What matters is when and where, not what kind.

From v12 (retained):

• Flash Annealing (Phase 63): First-10 linear decay achieves 46% — all-time record
• 1/√N Dose Law (Phase 68): σ_adj = σ_opt/√N prevents cosine collapse in multi-layer injection
• Correlation Sign Asymmetry: Positive ρ=+1 at σ=0.075 achieves 40% (10× baseline)
• N=100 Replication (Phase 69): 40% confirmed at N=100

73 page paper. Full experimental code and data included.

Code: https://github.com/hafufu-stack/snn-genesis