  Deep learning is often criticized by two serious issues which rarely exist in
natural nervous systems: overfitting and catastrophic forgetting. It can even
memorize randomly labelled data, which has little knowledge behind the
instance-label pairs. When a deep network continually learns over time by
accommodating new tasks, it usually quickly overwrites the knowledge learned
from previous tasks. Referred to as the {\it neural variability}, it is
well-known in neuroscience that human brain reactions exhibit substantial
variability even in response to the same stimulus. This mechanism balances
accuracy and plasticity/flexibility in the motor learning of natural nervous
systems. Thus it motivates us to design a similar mechanism named {\it
artificial neural variability} (ANV), which helps artificial neural networks
learn some advantages from ``natural'' neural networks. We rigorously prove
that ANV plays as an implicit regularizer of the mutual information between the
training data and the learned model. This result theoretically guarantees ANV a
strictly improved generalizability, robustness to label noise, and robustness
to catastrophic forgetting. We then devise a {\it neural variable risk
minimization} (NVRM) framework and {\it neural variable optimizers} to achieve
ANV for conventional network architectures in practice. The empirical studies
demonstrate that NVRM can effectively relieve overfitting, label noise
memorization, and catastrophic forgetting at negligible costs. \footnote{Code:
\url{https://github.com/zeke-xie/artificial-neural-variability-for-deep-learning}.
