Unverified50% confidenceFactExact time
The instability of primal-dual methods stems from a mismatch between the constraint estimate used in the primal update and the measurement used in the dual update, and this mismatch triggers parametric resonance at twice the paired natural frequency.
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50%
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Long-term
Relevance
10/19/2026
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Related Claims
UnverifiedChoosing the two-timescale ratio requires trading off the amplitude of dual oscillations against convergence speed; ensuring that the primal and dual updates use a consistent constraint estimate can avoid resonance, but the estimation bias must be handled.78% similarUnverifiedWhen automatic tuning relies on generative models that have stochasticity, it may instead become a source of instability, leading to a vicious cycle of ever-increasing variability.70% similarUnverifiedOn common heavy-tailed target classes, the initialization error decays exponentially with the forward time window, a property that holds for both α-stable dynamics and Brownian dynamics.70% similarUnverifiedIn the parametric channel, when the constraint sensitivity oscillates, the stiffness modulation of the dual update and the damping modulation of the primal update cancel each other, producing no resonant excitation, and the system has no resonant forcing at any depth.70% similarUnverifiedResearch reveals that LLMs do not reliably weight and update based on evidence reliability like an ideal Bayesian agent, but instead exhibit behavioral patterns close to distributional skew, with their influence being less correlated with the true reliability of evidence than the Bayesian framework would predict.70% similar
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