Traditional end-to-end (E2E) training of deep networks necessitates storing intermediate activations for back-propagation, resulting in a large memory footprint on GPUs and restricted model parallelization. As an alternative, greedy local learning partitions the network into gradient-isolated modules and trains supervisely based on local preliminary losses, thereby providing asynchronous and parallel training methods that substantially reduce memory cost. However, empirical experiments reveal that as the number of segmentations of the gradient-isolated module increases, the performance of the local learning scheme degrades substantially, severely limiting its expansibility. To avoid this issue, we theoretically analyze the greedy local learning from the standpoint of information theory and propose a ContSup scheme, which incorporates context supply between isolated modules to compensate for information loss. CIFAR, SVHN, STL-10) achieve SOTA results and indicate that our proposed method can significantly improve the performance of greedy local learning with minimal memory and computational overhead, allowing for the boost of the number of isolated modules. Our codes are available at https://github.com/Tabct/ContSup. End-to-end (E2E) back-propagation, a standard training paradigm for deep neural networks, enables deep neural networks to solve complex tasks and cognitive applications with great success (Szegedy et al., 2015; He et al., 2016; Huang et al., 2016). As shown in Figure 1a, an E2E training loss is calculated at the final layer, and the error is propagated backward layer-by-layer for weights update. In this case, the E2E is caught in the well-known backward-locking problem (Jaderberg et al., 2017; Frenkel et al., 2021; Duan & Principe, 2022), which prohibits module updates until all dependent modules have completed forward and backward passes, and restricts the network from performing training in a sequential manner (Jaderberg et al., 2017).

Due to the need to store the intermediate activations for back-propagation, end-to-end (E2E) training of deep networks usually suffers from high GPUs memory footprint. This paper aims to address this problem by revisiting the locally supervised learning, where a network is split into gradient-isolated modules and trained with local supervision. We experimentally show that simply training local modules with E2E loss tends to collapse task-relevant information at early layers, and hence hurts the performance of the full model. To avoid this issue, we propose an information propagation (InfoPro) loss, which encourages local modules to preserve as much useful information as possible, while progressively discard task-irrelevant information. As InfoPro loss is difficult to compute in its original form, we derive a feasible upper bound as a surrogate optimization objective, yielding a simple but effective algorithm. In fact, we show that the proposed method boils down to minimizing the combination of a reconstruction loss and a normal cross-entropy/contrastive term. Extensive empirical results on five datasets (i.e., CIFAR, SVHN, STL-10, ImageNet and Cityscapes) validate that InfoPro is capable of achieving competitive performance with less than 40% memory footprint compared to E2E training, while allowing using training data with higher-resolution or larger batch sizes under the same GPU memory constraint. Our method also enables training local modules asynchronously for potential training acceleration. Code is available at: https://github.com/blackfeather-wang/InfoPro-Pytorch.