From the BitNet paper:

"Straight-through estimator. To train our 1-bit model, we employ the straight-through estimator (STE)[BLC13] to approximate the gradient during backpropagation. This method bypasses the nondifferentiable functions, such as the Sign (Eq. 2) and Clip (Eq. 5) functions, during the backward pass. STE allows gradients to flow through the network without being affected by these non-differentiable functions, making it possible to train our quantized model."

also the author's (@shumingma) answer in the comments: https://huggingface.co/papers/2402.17764#65df17ed4d436404cdc...