Toward INT4 Fixed-Point Training via Exploring Quantization Error for Gradients

Network quantization generally converts full-precision weights and/or activations into low-bit fixed-point values in order to accelerate an inference process. Recent approaches to network quantization further discretize the gradients into low-bit fixed-point values, enabling an efficient training. They typically set a quantization interval using a min-max range of the gradients or adjust the interval such that the quantization error for entire gradients is minimized. In this paper, we analyze the quantization error of gradients for the low-bit fixed-point training, and show that lowering the error for large-magnitude gradients boosts the quantization performance significantly. Based on this, we derive an upper bound of quantization error for the large gradients in terms of the quantization interval, and obtain an optimal condition for the interval minimizing the quantization error for large gradients. We also introduce an interval update algorithm that adjusts the quantization interval adaptively to maintain a small quantization error for large gradients. Experimental results demonstrate the effectiveness of our quantization method for various combinations of network architectures and bit-widths on various tasks, including image classification, object detection, and super-resolution.

Transition Rate Scheduling for Quantization-Aware Training

Quantization-aware training (QAT) simulates a quantization process during training to lower bit-precision of weights/activations. It learns quantized weights indirectly by updating latent weights, i.e., full-precision inputs to a quantizer, using gradient-based optimizers. We claim that coupling a user-defined learning rate (LR) with these optimizers is sub-optimal for QAT. Quantized weights transit discrete levels of a quantizer, only if corresponding latent weights pass transition points, where the quantizer changes discrete states. This suggests that the changes of quantized weights are affected by both the LR for latent weights and their distributions. It is thus difficult to control the degree of changes for quantized weights by scheduling the LR manually. We conjecture that the degree of parameter changes in QAT is related to the number of quantized weights transiting discrete levels. Based on this, we introduce a transition rate (TR) scheduling technique that controls the number of transitions of quantized weights explicitly. Instead of scheduling a LR for latent weights, we schedule a target TR of quantized weights, and update the latent weights with a novel transition-adaptive LR (TALR), enabling considering the degree of changes for the quantized weights during QAT. Experimental results demonstrate the effectiveness of our approach on standard benchmarks.