MEC-Quant: Maximum Entropy Coding for Extremely Low Bit Quantization-Aware Training

Quantization-Aware Training (QAT) has driven much attention to produce efficient neural networks. Current QAT still obtains inferior performances compared with the Full Precision (FP) counterpart. In this work, we argue that quantization inevitably introduce biases into the learned representation, especially under the extremely low-bit setting. To cope with this issue, we propose Maximum Entropy Coding Quantization (MEC-Quant), a more principled objective that explicitly optimizes on the structure of the representation, so that the learned representation is less biased and thus generalizes better to unseen in-distribution samples. To make the objective end-to-end trainable, we propose to leverage the minimal coding length in lossy data coding as a computationally tractable surrogate for the entropy, and further derive a scalable reformulation of the objective based on Mixture Of Experts (MOE) that not only allows fast computation but also handles the long-tailed distribution for weights or activation values. Extensive experiments on various tasks on computer vision tasks prove its superiority. With MEC-Qaunt, the limit of QAT is pushed to the x-bit activation for the first time and the accuracy of MEC-Quant is comparable to or even surpass the FP counterpart. Without bells and whistles, MEC-Qaunt establishes a new state of the art for QAT.

Stabilizing Quantization-Aware Training by Implicit-Regularization on Hessian Matrix

Quantization-Aware Training (QAT) is one of the prevailing neural network compression solutions. However, its stability has been challenged for yielding deteriorating performances as the quantization error is inevitable. We find that the sharp landscape of loss, which leads to a dramatic performance drop, is an essential factor that causes instability. Theoretically, we have discovered that the perturbations in the feature would bring a flat local minima. However, simply adding perturbations into either weight or feature empirically deteriorates the performance of the Full Precision (FP) model. In this paper, we propose Feature-Perturbed Quantization (FPQ) to stochastically perturb the feature and employ the feature distillation method to the quantized model. Our method generalizes well to different network architectures and various QAT methods. Furthermore, we mathematically show that FPQ implicitly regularizes the Hessian norm, which calibrates the smoothness of a loss landscape. Extensive experiments demonstrate that our approach significantly outperforms the current State-Of-The-Art (SOTA) QAT methods and even the FP counterparts.

Push Quantization-Aware Training Toward Full Precision Performances via Consistency Regularization

Existing Quantization-Aware Training (QAT) methods intensively depend on the complete labeled dataset or knowledge distillation to guarantee the performances toward Full Precision (FP) accuracies. However, empirical results show that QAT still has inferior results compared to its FP counterpart. One question is how to push QAT toward or even surpass FP performances. In this paper, we address this issue from a new perspective by injecting the vicinal data distribution information to improve the generalization performances of QAT effectively. We present a simple, novel, yet powerful method introducing an Consistency Regularization (CR) for QAT. Concretely, CR assumes that augmented samples should be consistent in the latent feature space. Our method generalizes well to different network architectures and various QAT methods. Extensive experiments demonstrate that our approach significantly outperforms the current state-of-the-art QAT methods and even FP counterparts.