  The input space of a neural network with ReLU-like activations is partitioned
into multiple linear regions, each corresponding to a specific activation
pattern of the included ReLU-like activations. We demonstrate that this
partition exhibits the following encoding properties across a variety of deep
learning models: (1) {\it determinism}: almost every linear region contains at
most one training example. We can therefore represent almost every training
example by a unique activation pattern, which is parameterized by a {\it neural
code}; and (2) {\it categorization}: according to the neural code, simple
algorithms, such as $K$-Means, $K$-NN, and logistic regression, can achieve
fairly good performance on both training and test data. These encoding
properties surprisingly suggest that {\it normal neural networks well-trained
for classification behave as hash encoders without any extra efforts.} In
addition, the encoding properties exhibit variability in different scenarios.
{Further experiments demonstrate that {\it model size}, {\it training time},
{\it training sample size}, {\it regularization}, and {\it label noise}
contribute in shaping the encoding properties, while the impacts of the first
three are dominant.} We then define an {\it activation hash phase chart} to
represent the space expanded by {model size}, training time, training sample
size, and the encoding properties, which is divided into three canonical
regions: {\it under-expressive regime}, {\it critically-expressive regime}, and
{\it sufficiently-expressive regime}. The source code package is available at
\url{https://github.com/LeavesLei/activation-code}.
