论文用560个模型实测了4比特量化在S&P 500波动率预测上的效果，发现校准方式能决定性能好坏，做量化部署的可以看看。
该论文系统研究了后训练量化（PTQ）中激活值校准对S&P 500横截面波动率预测的影响，涵盖7种神经网络架构、8个walk-forward测试年（2018-2025）和560个训练模型。结果显示，8比特下校准影响很小，但4比特时校准成为预测性能的主要决定因素。在默认abs-max校准下，静态4比特量化权重和激活值会使受影响架构的全精度平均信息系数损失11-62%。改用百分位校准可恢复四种受影响最严重架构中53-94%的退化。论文指出激活值校准是金融预测中可靠4比特PTQ的一级部署决策，剩余退化严重时可选用8比特激活值或仅权重4比特量化。
Calibration Bets on the Past: Post-Training Quantization for Financial Time-Series Forecasting
Financial forecasting models are typically developed in full precision, yet production deployment often requires low-precision inference to reduce memory and computational cost. Post-training quantization (PTQ) enables such deployment without retraining. However, reliable activation quantization requires calibration: activation ranges are estimated from historical data before deployment and then remain fixed during future inference. The importance of this deployment choice for financial forecasting remains poorly understood. We present a systematic study of activation calibration for PTQ in cross-sectional volatility forecasting on the S&P 500. Our evaluation covers seven representative neural architectures, eight walk-forward test years (2018-2025), and 560 trained models. We find that activation calibration has little effect at 8 bits but becomes the primary determinant of predictive performance at 4 bits. Under default absolute-maximum (abs-max) calibration, static 4-bit quantization of both weights and activations removes 11-62% of the full-precision mean information coefficient in affected architectures. Replacing abs-max with percentile calibration recovers 53-94% of this degradation in the four most affected architectures. The preferred activation range also varies across market periods. Narrow ranges improve resolution under typical market conditions but lose part of their advantage when test-period market dispersion exceeds the calibration history. These findings show that activation calibration is a first-class deployment decision for reliable 4-bit PTQ in financial forecasting. When substantial degradation remains, 8-bit activations or weight-only 4-bit quantization provide more robust deployment choices.