提出量化鲁棒性判据，确保低精度部署时网络仍收敛且解稳定。
Quantization Robustness of Monotone Operator Equilibrium Networks
- 将权重量化视为谱扰动，用单调性裕度判断收敛性
- 三至四比特量化会发散，五比特以上可收敛，实验验证相变阈值
- 支持量化感知训练，四比特也能保证收敛，适合边缘设备部署
单调算子平衡网络是隐层模型，其输出为单调算子的唯一平衡点，保障存在性、唯一性和收敛性。在低精度硬件上部署时，权重需量化，可能破坏上述保证。本文将权重量化视为底层单调包含的谱扰动。当谱范数扰动小于单调性裕度时，量化求解器的收敛性可保证；量化与全精度平衡点间的位移受扰动大小和裕度约束；一个表征算子范数与裕度比的条件数将量化精度与前向误差关联。MNIST实验验证了预测阈值处的相变：三至四比特后训练量化发散，五比特及以上收敛。反向传播保证支持量化感知训练，使四比特下仍能恢复可证明的收敛性。
原文摘要 · Abstract (English)
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.
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