SNN-Synthesis v6: Knowledge Multiplexing, σ-Diverse Beam Search, and Universal Stochastic Resonance from 63K to 7B Parameters

SNN-Synthesis v6 extends the investigation of stochastic resonance in neural networks from architecture-invariant validation (v5) to knowledge multiplexing, hyperparameter-free exploration, and multi-model universality. v6 New Results (Phases 33–38) (I) Knowledge Multiplexing via ID Gating (Phase 35c): A single 115K-parameter CNN stores distinct knowledge for multiple games without interference, using discrete condition-ID gating (h ← h ⊙ σ(Embed(id))). Knowledge separation score reaches +0.572. Four alternative approaches (noise modulation, SNN chaotic noise, continuous-wave gating, pink noise) all fail—only discrete gating succeeds, mirroring biological neurotransmitter-based mode switching. (II) σ-Diverse NBS (Phase 37a): Assigning different σ values to each of K=11 beams eliminates the need for task-specific σ* tuning. Performance matches the best individually-tuned fixed σ across all tested difficulty levels, providing a hyperparameter-free exploration strategy. (III) Capacity Scaling (Phase 38a): ID gating requires ≥2.7K parameters for effective knowledge separation. At 115K parameters, gated models surpass ungated models (0.706 > 0.625), demonstrating that gating acts as positive regularization. (IV) Multi-Model NBS (Phase 38): Qwen2.5-7B-Instruct achieves 100% solve rate at K=11 on Modified Hanoi, matching Mistral-7B and confirming cross-model universality. (V) GSM8K LLM-ExIt (Phase 33): Extending LLM-ExIt to math reasoning: Mistral-7B K1 accuracy improves from 56.5% to 58.0% over 3 iterations. The modest gain confirms ExIt functions on open-ended tasks but reveals that high-baseline tasks limit self-improvement headroom. (VI) σ* Prediction (Phase 34): TruthfulQA MC1 achieves 100% accuracy at σ*=0.2 with K=11, extending the σ* map to four tasks: GSM8K (0.01), TruthfulQA (0.2), Hanoi (0.15), ARC-AGI (0.2). v5 Headline Results GSM8K Multi-Task NBS (Phase 31/31b): Noisy Beam Search on Mistral-7B with GSM8K math reasoning achieves 89.5% accuracy at K=11 (from 53% baseline, +36.5pp). The optimal noise is σ*=0.01—an order of magnitude smaller than Hanoi (σ*=0.15)—revealing that σ* scales inversely with task complexity. LLM-ExIt (Phase 32b): Combining NBS miracle collection with QLoRA fine-tuning, Mistral-7B achieves 100% solve rate in 3 iterations (16% → 94% → 96% → 100%) on Modified Hanoi—without any Oracle, reward shaping, or human demonstrations. This completes the pipeline from CNN ExIt (v3) to full Oracle-free LLM self-evolution. Key Findings (v6) Discrete ID gating enables knowledge multiplexing: Only categorical signals work; 4 continuous alternatives fail σ-diverse NBS eliminates hyperparameter tuning: No per-task σ* calibration needed Gating acts as regularization: At sufficient capacity, gated > ungated (0.706 > 0.625) NBS is model-invariant: Qwen2.5-7B matches Mistral-7B at K=11 σ* map extended to 4 tasks: GSM8K (0.01), TruthfulQA (0.2), Hanoi (0.15), ARC-AGI (0.2) 5 honest null results: Explain why only discrete gating succeeds 38 experiments spanning 63K–7B parameters, CNNs to Transformers, 9 task domains, and 2 model families (Mistral, Qwen). 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.