  Relieving the reliance of neural network training on a global
back-propagation (BP) has emerged as a notable research topic due to the
biological implausibility and huge memory consumption caused by BP. Among the
existing solutions, local learning optimizes gradient-isolated modules of a
neural network with local errors and has been proved to be effective even on
large-scale datasets. However, the reconciliation among local errors has never
been investigated. In this paper, we first theoretically study non-greedy
layer-wise training and show that the convergence cannot be assured when the
local gradient in a module w.r.t. its input is not reconciled with the local
gradient in the previous module w.r.t. its output. Inspired by the theoretical
result, we further propose a local training strategy that successively
regularizes the gradient reconciliation between neighboring modules without
breaking gradient isolation or introducing any learnable parameters. Our method
can be integrated into both local-BP and BP-free settings. In experiments, we
achieve significant performance improvements compared to previous methods.
Particularly, our method for CNN and Transformer architectures on ImageNet is
able to attain a competitive performance with global BP, saving more than 40%
memory consumption.
