SNN-Synthesis v3: Noisy Beam Search and Oracle-Free Self-Evolution—Scaling Stochastic Resonance from 63K-Parameter CNNs to 7B LLMs

SNN-Synthesis v3 extends the investigation of stochastic resonance in neural networks from scale-invariant enhancement (v1–v2) to a complete autonomous learning paradigm. Three Major Advances (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 learnable by the policy network TR87 fails despite 72% miracle rate at K=1000 because its state-action mapping is structurally unlearnable. Conversely, LS20 succeeds even with 75% of miracles removed—ExIt self-generates sufficient training data within 3 iterations. Additional Findings Static noise is optimal: 5 dynamic strategies (temporal scheduling, confidence gating, bandit, PPO-SNN, 3-expert MoA router) all fail to outperform constant σ Scale invariance: Optimal σ*≈0.05–0.20 is consistent from 63K-parameter CNNs to 7B-parameter Transformers ExIt is self-healing: Removing 75% of seed miracles paradoxically improves final performance (57% vs 44%) 26 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.