  Traditional deep learning relies on end-to-end backpropagation for training,
but it suffers from drawbacks such as high memory consumption and not aligning
with biological neural networks. Recent advancements have introduced locally
supervised learning, which divides networks into modules with isolated
gradients and trains them locally. However, this approach can lead to
performance lag due to limited interaction between these modules, and the
design of auxiliary networks occupies a certain amount of GPU memory. To
overcome these limitations, we propose a novel model called HPFF that performs
hierarchical locally supervised learning and patch-level feature computation on
the auxiliary networks. Hierarchical Locally Supervised Learning (HiLo) enables
the network to learn features at different granularity levels along their
respective local paths. Specifically, the network is divided into two-level
local modules: independent local modules and cascade local modules. The cascade
local modules combine two adjacent independent local modules, incorporating
both updates within the modules themselves and information exchange between
adjacent modules. Patch Feature Fusion (PFF) reduces GPU memory usage by
splitting the input features of the auxiliary networks into patches for
computation. By averaging these patch-level features, it enhances the network's
ability to focus more on those patterns that are prevalent across multiple
patches. Furthermore, our method exhibits strong generalization capabilities
and can be seamlessly integrated with existing techniques. We conduct
experiments on CIFAR-10, STL-10, SVHN, and ImageNet datasets, and the results
demonstrate that our proposed HPFF significantly outperforms previous
approaches, consistently achieving state-of-the-art performance across
different datasets. Our code is available at: https://github.com/Zeudfish/HPFF.
