Leaky Integration as Safe Edge Regulation: A Layer-9 Control Mechanism in Safe Attractor Architecture

This technical report presents two paired-design experiments (L2 and L2b)investigating leaky integration as a structural noise mechanism within the SafeAttractor Architecture (SAA) framework. Previous experiments established thatamplitude-modulated noise (β(t) modulation) is structurally safe but producesno measurable improvement in safe-edge occupancy. We demonstrate that leakyintegration, parameterized by a mixing coefficient λ controlling the blend betweenthe current hidden state and the attention update, produces a qualitatively differentand strongly positive effect.In Test L2 (Npairs = 30, paired design), all five λ < 1.0 conditions showedsubstantial improvement in pedge (Δpedge > 0.35), substantial reduction in pchaos,and no MSE degradation relative to the static λ = 1.0 baseline. In Test L2b(Npairs = 30), a full λ sweep from 1.0 to 0.2 revealed three distinct operating regimes:a chaos-prone regime (λ = 0.8–1.0), a safe edge zone (λ = 0.5–0.7), and a freeze zone(λ = 0.2–0.4). The optimal operating point is λ = 0.5, maximizing pedge = 0.640,while the balanced operating point considering freeze risk is λ = 0.6 (pedge = 0.614,pchaos = 0.110, freeze rate = 0.20).These findings suggest that leaky integration is a viable candidate for Layer-9structural noise implementation in transformer-based dynamical systems, providinga tunable mechanism to maintain safe-edge dynamics without architecturalmodifications.