  The great success neural networks have achieved is inseparable from the
application of gradient-descent (GD) algorithms. Based on GD, many variant
algorithms have emerged to improve the GD optimization process. The gradient
for back-propagation is apparently the most crucial aspect for the training of
a neural network. The quality of the calculated gradient can be affected by
multiple aspects, e.g., noisy data, calculation error, algorithm limitation,
and so on. To reveal gradient information beyond gradient descent, we introduce
a framework (\textbf{GCGD}) to perform gradient correction. GCGD consists of
two plug-in modules: 1) inspired by the idea of gradient prediction, we propose
a \textbf{GC-W} module for weight gradient correction; 2) based on Neural ODE,
we propose a \textbf{GC-ODE} module for hidden states gradient correction.
Experiment results show that our gradient correction framework can effectively
improve the gradient quality to reduce training epochs by $\sim$ 20\% and also
improve the network performance.
