  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.
