Quantization Robustness of Monotone Operator Equilibrium Networks

Abstract:Monotone operator equilibrium networks are implicit-layer models whose output is the unique equilibrium of a monotone operator, guaranteeing existence, uniqueness, and convergence. When deployed on low-precision hardware, weights are quantized, potentially destroying these guarantees. We analyze weight quantization as a spectral perturbation of the underlying monotone inclusion. Convergence of the quantized solver is guaranteed whenever the spectral-norm weight perturbation is smaller than the monotonicity margin; the displacement between quantized and full-precision equilibria is bounded in terms of the perturbation size and margin; and a condition number characterizing the ratio of the operator norm to the margin links quantization precision to forward error. MNIST experiments confirm a phase transition at the predicted threshold: three- and four-bit post-training quantization diverge, while five-bit and above converge. The backward-pass guarantee enables quantization-aware training, which recovers provable convergence at four bits.

6 pages, 4 figures. Accepted for publication in IEEE Control Systems Letters (L-CSS)

Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY)

arXiv:2603.10562 [math.OC]

(or arXiv:2603.10562v2 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2603.10562 Focus to learn more arXiv-issued DOI via DataCite

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