{
 "artifacts": null,
 "category": "dynamics",
 "description": "Add a low-dimensional, trusted sentinel state to the optimizer or recurrent inference controller. The sentinel is driven by a secret probe and a protected gain, so unauthorized gain changes produce a predictable shift in its equilibrium even when the main neural dynamics remain numerically stable. Monitor the estimated equilibrium and trigger rollback or quarantine when the measured shift exceeds the expected noise envelope.",
 "formulas_latex": [
  "$$\\dot{s}=-a s+a k q,\\qquad s^*=kq,\\qquad \\tilde{s}(t)=\\tilde{s}(0)e^{-at}.$$",
  "$$s_{t+1}=(1-\\alpha a)s_t+\\alpha a kq_t,\\qquad 0\u003c\\alpha a\u003c2,$$",
  "$$\\widehat{k}=\\frac{\\sum_{t\\in W}q_t s_t}{\\sum_{t\\in W}q_t^2},\\qquad \\Delta s^*=q\\Delta k,$$",
  "$$\\text{alarm if }|\\widehat{k}-k_0|\u003ez_{1-\\beta/2}\\sqrt{\\widehat{\\sigma}^2/\\sum_{t\\in W}q_t^2},$$"
 ],
 "id": 2897,
 "implementation": "Integrate the sentinel at the optimizer-controller boundary, not inside every neural layer. For Adam or SGD, let the protected gain \\(k_0\\) be the nominal learning-rate multiplier, momentum gain, gradient-clipping gain, or recurrent-state feedback gain; keep a copy of \\(k_0\\) in a trusted configuration area. At every update, generate a small bounded probe \\(q_t\\) from a seeded pseudorandom sequence, preferably with zero mean and occasional nonzero amplitudes, and update the sentinel with `s = (1-alpha*a)*s + alpha*a*k0*q`. Do not use \\(s\\) to modify the model on the first experiment; only log it and estimate the equilibrium relation. Pseudocode is: `q=secret_probe(t); s=(1-alpha*a)*s+alpha*a*k*q; if t\u003e=warmup: append(q,s); khat=sum(q*s)/sum(q*q); residual=abs(khat-k0); alarm=residual\u003ethreshold`. The stability condition \\(0\u003calpha*a\u003c2\\) is computed analytically. Equilibrium, regression variance, and the alarm threshold are estimated empirically from a sliding window; \\(k_0\\) and the probe seed are protected inputs. First test on a small MLP trained on MNIST with SGD and Adam, comparing an untampered run against attacks that multiply the learning rate or momentum coefficient by \\(0.8\\), \\(1.2\\), and \\(2.0\\) after convergence. Use window lengths of 100-1000 steps and sentinel relaxation values satisfying \\(alpha*a=0.2\\). The quantitative prediction is that after a transient of roughly \\(5/a\\), the estimated equilibrium changes by \\(q\\Delta k\\) and the estimated gain converges to the tampered value; detection delay should scale as \\(O(a^{-1})\\), while choosing \\(alpha*a\\geq2\\) should produce sentinel oscillation or divergence. Measure whether the empirical stability boundary agrees with \\(alpha*a=2\\) within 10% and whether a 20% gain attack is detected before a comparable loss degradation occurs.",
 "math_summary": "The paper's mechanism is equilibrium-based exposure of a parameter change: a controller can remain stable while gain tampering changes its steady state. The neural adaptation uses the scalar sentinel dynamics \\(\\dot{s}=-a s+a k q\\), where \\(s\\) is the monitored state, \\(a\u003e0\\) is a known relaxation rate, \\(k\\) is a protected controller gain, and \\(q\\) is a bounded secret probe. For constant \\(q\\), the unique equilibrium is \\(s^*=kq\\) and the perturbation \\(\\tilde{s}=s-s^*\\) obeys \\(\\dot{\\tilde{s}}=-a\\tilde{s}\\), so the equilibrium error decays exponentially while the system remains stable. In discrete time, \\(s_{t+1}=(1-\\alpha a)s_t+\\alpha a k q_t\\) is stable for \\(0\u003c\\alpha a\u003c2\\); for constant \\(q\\), \\(s^*=kq\\). A gain attack \\(k'=k+\\Delta k\\) produces the measurable shift \\(\\Delta s^*=q\\Delta k\\). With probe variation, estimate \\(k\\) by least squares from the equilibrium relation \\(s^*/q=k\\) and compare it to the protected reference.",
 "math_tags": [
  "dynamical-systems",
  "control-theory",
  "stability",
  "statistics"
 ],
 "ml_areas": [
  "optimizer",
  "training-dynamics",
  "rnn",
  "ssm"
 ],
 "paper": {
  "arxiv_id": "2608.30574",
  "arxiv_url": "https://arxiv.org/abs/2608.30574",
  "summary_what_math_gives_to_ml": "The paper's key transferable mechanism is that stealthy controller-parameter tampering can preserve apparent stability while changing equilibrium points and reducing dynamic margins. Its modified PLL deliberately makes a hidden gain observable by coupling the gain to an equilibrium shift, turning parameter integrity into a state-estimation problem rather than relying on instability alarms. A neural-network analogue is a small trusted sentinel dynamical system attached to an optimizer or recurrent model, whose equilibrium encodes a secret gain and therefore exposes silent changes to learning-rate, recurrent, or control parameters.",
  "title": "Exposing the Invisible: Detecting Stealthy Parameter-Based Cyber-Attacks on Inverter Synchronization Loops",
  "year": "2026"
 },
 "ratings": {
  "difficulty": 4,
  "novelty": 8,
  "usefulness": 6
 },
 "solves": [
  "stability",
  "generalization"
 ],
 "title": "Equilibrium-Gain Sentinel",
 "url": "https://synthcore.org/idea/2897/equilibrium-gain-sentinel",
 "verification": {
  "peer_reviewed": false,
  "status": "unverified",
  "status_label": "Unverified",
  "verdict_source": "deterministic test code (paired-seed permutation statistics)"
 }
}