Training convolutional neural network models is memory intensive since back-propagation requires storing activations of all intermediate layers. This presents a practical concern when seeking to deploy very deep architectures in production, especially when models need to be frequently re-trained on updated datasets. In this paper, we propose a new implementation for back-propagation that significantly reduces memory usage, by enabling the use of approximations with negligible computational cost and minimal effect on training performance. The algorithm reuses common buffers to temporarily store full activations and compute the forward pass exactly. It also stores approximate per-layer copies of activations, at significant memory savings, that are used in the backward pass. Compared to simply approximating activations within standard back-propagation, our method limits accumulation of errors across layers. This allows the use of much lower-precision approximations without affecting training accuracy.

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice.The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root.

I haven't seen papers that propose to do a simple uniform quantization in the preactivations just to save memory during training. But I could be over looking some of the network quantization literature. It shows that the proposed method is able to save memory while maintaining the same accuracy on a selection of networks on CIFAR and ImageNet. I was able to understand the core contribution and Figure 2 is very nicely designed. I think it would make it clearer, if the text can explain Eq. 9 better.

This paper proposes the elegant and obvious-in-retrospect idea of using exact activations for the forward pass and low-precision activations for the backward pass, thereby achieving nearly the full memory savings of low-precision activations. It shows that this scheme nearly matches the exact training curves while allowing 4-bit precision. Overall, the paper is well-executed. The writing is clear, references to related work are pretty complete, and the experiments seem sensible and convincing. The reviewers feel like the paper could have been more ambitious in certain respects (e.g.

Training convolutional neural network models is memory intensive since back-propagation requires storing activations of all intermediate layers. This presents a practical concern when seeking to deploy very deep architectures in production, especially when models need to be frequently re-trained on updated datasets. In this paper, we propose a new implementation for back-propagation that significantly reduces memory usage, by enabling the use of approximations with negligible computational cost and minimal effect on training performance. The algorithm reuses common buffers to temporarily store full activations and compute the forward pass exactly. It also stores approximate per-layer copies of activations, at significant memory savings, that are used in the backward pass.

Training convolutional neural network models is memory intensive since back-propagation requires storing activations of all intermediate layers. This presents a practical concern when seeking to deploy very deep architectures in production, especially when models need to be frequently re-trained on updated datasets. In this paper, we propose a new implementation for back-propagation that significantly reduces memory usage, by enabling the use of approximations with negligible computational cost and minimal effect on training performance. The algorithm reuses common buffers to temporarily store full activations and compute the forward pass exactly. It also stores approximate per-layer copies of activations, at significant memory savings, that are used in the backward pass.