SNN-Synthesis v4: Noisy Beam Search Scales from 63K CNNs to 7B LLMs—100% Solve Rate via Architecture-Invariant Stochastic Resonance

SNN-Synthesis v4 extends the investigation of stochastic resonance in neural networks from scale-invariant enhancement and autonomous self-evolution (v1–v3) to architecture-invariant validation across CNNs and LLMs. v4 Headline Result Mistral-7B achieves 100% solve rate with Noisy Beam Search (K=11), up from 16% baseline (p < 10−10). The K scaling is strictly monotonic: K=1: 24%, K=3: 72%, K=5: 74%, K=7: 96%, K=11: 100%. This demonstrates that trajectory ensemble is architecture-invariant across five orders of magnitude (63K CNN → 7B LLM), and the effect is amplified at larger scale (+76pp on LLM vs. +66pp on CNN). Four New Experiments (Phases 27–30) (IV) LLM Noisy Beam Search (Phase 29): The decisive experiment. Noisy Beam Search on Mistral-7B-Instruct-v0.3 achieves perfect solve rate on Modified Hanoi, matching the logarithmic K scaling observed in 63K-parameter CNNs. (V) Frame Stacking and Learnability Threshold (Phase 27): Adding 3-frame temporal memory to TR87 raises train accuracy from chance (25%) to 34.5%, but ExIt clear rate remains at 2–4%. Learnability is a continuous property with a threshold effect—partial improvement is insufficient. (VI) Extended Two-Condition Map (Phase 28): Testing ExIt on 4 additional ARC-AGI-3 games (FT09, G50T, WA30, SB26) reveals all have zero miracle rate. The first condition (activation energy) is the primary bottleneck—4 of 7 games fail here. (VII) Dynamic K Scheduling (Phase 30): Comparing fixed (K=11), decreasing (21→7), and increasing (5→15) K schedules shows fixed K is optimal (99%), confirming that K scheduling adds no value. v3 Foundations (Phases 1–26) (I) Noisy Beam Search: Running K independent noisy trajectories in parallel and selecting the best outcome. Achieves 78% clear rate (from 12%) on ARC-AGI-3 with strict monotonic K scaling. Validated at N=1000 with a definitive inverse-U resonance curve (peak 24.1% at σ=0.05, p<10−50). (II) SNN-ExIt (Expert Iteration): An Oracle-free self-evolution pipeline bootstrapping from zero human knowledge. Achieves 99% clear rate on LS20 in 5 iterations—surpassing the Oracle-trained CNN (78%) by 21 percentage points. No human-crafted solver, no game rules, no reward shaping. (III) Two-Condition Theory of ExIt: Systematic ablation (Phases 24–26) identifies two necessary and sufficient conditions for autonomous self-evolution: Activation Energy: Bootstrap miracle rate must be positive (always achievable with sufficient K) State-Action Learnability: The game's state→action mapping must be generalizably learnable by the policy network Key Findings Architecture invariance: Noisy Beam Search works identically on 63K CNNs and 7B Transformers Scale amplification: The effect is stronger on larger models (+76pp on 7B vs. +66pp on 63K) Static noise is optimal: 5 dynamic strategies (temporal scheduling, confidence gating, bandit, PPO-SNN, 3-expert MoA router) all fail to outperform constant σ Fixed K is optimal: Dynamic K scheduling provides no advantage over fixed K=11 Learnability threshold: Partial train accuracy improvement (25%→34.5%) is insufficient for ExIt convergence ExIt is self-healing: Removing 75% of seed miracles paradoxically improves final performance (57% vs. 44%) 30 experiments spanning 63K–7B parameters, CNNs to Transformers, and 7 ARC-AGI-3 interactive environments. Code and data: https://github.com/hafufu-stack/SNN-Synthesis Acknowledgments This research was conducted entirely independently, without institutional affiliation or corporate funding. The author currently faces financial constraints that make it increasingly difficult to maintain subscriptions to AI services essential for this line of research. To sustain and improve the quality of future work, the author is actively seeking community sponsorship. Details are available at https://github.com/sponsors/hafufu-stack.