In modern neural networks like Transformers, linear layers require
significant memory to store activations during backward pass. This study
proposes a memory reduction approach to perform backpropagation through linear
layers. Since the gradients of linear layers are computed by matrix
multiplications, we consider methods for randomized matrix multiplications and
demonstrate that they require less memory with a moderate decrease of the test
accuracy. Also, we investigate the variance of the gradient estimate induced by
the randomized matrix multiplication. We compare this variance with the
variance coming from gradient estimation based on the batch of samples. We
demonstrate the benefits of the proposed method on the fine-tuning of the
pre-trained RoBERTa model on GLUE tasks.

该研究提出了一种将随机矩阵乘法用于梯度反向传播的方法，并证明该方法可以通过降低所需内存容量，从而更加有效地处理神经网络中的线性层。通过在语义理解任务中对 RoBERTa 模型进行测试，结果表明，该方法即使降低了测试准确度，但仍能实现显著的内存消耗优化。