What question did this study set out to answer?

This research aims to validate the existence of a reasoning direction within LLM hidden states and explore universal discriminant features across different architectures.

March 25, 2026Open Access

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

Key Points

This research aims to validate the existence of a reasoning direction within LLM hidden states and explore universal discriminant features across different architectures.
Implemented the Aha! Steering technique in LLMs to observe reasoning directionality.
Compared performance metrics of Mistral and Qwen architectures using directional and stochastic noise combinations.
Utilized PCA analysis to assess the concentration of differential vectors among architectures.
Tested various noise structures to evaluate their impact on stochastic resonance.
Achieved a solve rate of 46.7% on Mistral using Aha! and stochastic noise, a significant improvement over baseline.
Causal proof demonstrated that differential vectors encode reasoning direction, with a substantial drop in solve rate upon anti-Aha steering.
Both Qwen and Mistral displayed concentration of their differential vectors in shared PCA bands, establishing a universal trait.
Differential PCA confirmed that the optimal noise direction varies, with each architecture benefiting from different approaches.

Abstract

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: universalₜopₚcs — reasoning directions are universally encoded in variance-dominant subspaces. • Differential PCA Extends to Mistral (Phase 91): diffₚcabottom = 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

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