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An artificial neural network (ANN) is a graphical
(signal-flow) representation of a hypothesis that maps the
features of a data point at its input to a
prediction for the label at its output. Its
computational unit is the artificial neuron, which applies an
activation function to the weighted sum of its inputs; the
edge weights are the tunable model parameters. An ANN can
be represented as a directed acyclic graph, and its connectivity
structure — the architecture — is a central design choice.
Deep nets arrange neurons in consecutive
layers; varying the connectivity yields feedforward
networks, convolutional neural networks (CNNs), recurrent networks, and
transformer-based architectures.
Definition
The face
recognition of a smartphone camera and the speech transcription of
a voice assistant are both computed by networks of simple
computing units with tuned connection strengths. Such a network is
an ANN: a graphical (signal-flow)
representation of a hypothesis that maps features of a
data point at its input to a prediction for the corresponding
label at its output.
B-layersThe fundamental computational unit
of an ANN is the artificial neuron, which applies an activation function
$\actfun(\cdot)$ to the weighted sum of its inputs plus an offset
term (Fig. 1); the
edge weights of the network are its tunable
model parameters.
Figure 1: A single artificial neuron: it applies an
activation function $\actfun(\cdot)$ to the weighted sum
$w_{1} \feature_1 + w_{2} \feature_2$ of its inputs plus an
offset term $b$, and delivers the output $a_{1}$. The
weights $w_{1}$, $w_{2}$ and the offset $b$ are tunable
model parameters. This neuron appears as node $a_{1}$ of
the ANN in Fig. 2, which does not draw
the offset terms
The output
of a neuron can be used either as the final output of the
ANN or as an input to other neurons. One important design aspect
of an ANN is its connectivity structure (or architecture), i.e., which
outputs are connected to which downstream neuron's inputs
(Goodfellow et al., 2016).
As illustrated in Fig. 2, an
ANN can be represented as a directed acyclic graph (DAG).
Figure 2: ANN represented as a weighted DAG with nodes
corresponding to neurons or features of
a data point. Feature nodes $\feature_1$,
$\feature_2$ have a fixed output given by the
feature value, with no input. Each of the neuron
nodes $a_{1}$, $a_{2}$ applies an activation function to the weighted
sum of its inputs (Fig. 1). The
weighted directed edges indicate how
node outputs are used as inputs to downstream neurons.
The edge weights are tunable model parameters and are
used to scale the inputs to the neurons. The prediction $\hypothesis^{(\weights)}(\featurevec)$ is the output
computed from the inputs $\feature_1$, $a_1$, and $a_2$
One widely used type of ANN is deep nets
where neurons form consecutive layers
(Fig. 3). In a deep net, the
outputs of neurons in a given layer are typically only connected
to the inputs of the neurons in a consecutive layer.
Each layer $l$ then applies a feature transformation
$\featuretrafovec^{(l)}$ whose components are computed by the
neurons of that layer (each as in
Fig. 1), and the deep net computes
the concatenation of these layer-wise maps. The network
of Fig. 3, with its dashed edge removed,
delivers the prediction
\[\hypothesis^{(\weights)}(\featurevec)
= \featuretrafovec^{(3)}\Big(\featuretrafovec^{(2)}
\big(\featuretrafovec^{(1)}(\featurevec)\big)\Big)
\text{,}\]
starting from the input feature vector
$\featurevec = (\feature_1, \feature_2, \feature_3)^{\top}$:
the two hidden layers compute
$\featuretrafovec^{(1)}, \featuretrafovec^{(2)}:
\reals^{3} \rightarrow \reals^{3}$ and the output layer
computes $\featuretrafovec^{(3)}: \reals^{3} \rightarrow
\reals$.
Sometimes it
is useful to add shortcut or skip connections that directly connect the outputs of
neurons in one layer to the inputs of neurons in a nonconsecutive layer
(Goodfellow et al., 2016; He et al., 2016).
Figure 3: A deep net: the neurons form consecutive
layers, and each neuron receives only the
outputs of the preceding layer. Every solid
edge carries a tunable edge weight (not drawn). The
dashed edge is a skip connection, directly connecting
two nonconsecutive layers
Varying the connectivity pattern yields different ANN
architectures: feedforward networks connect layers
strictly in sequence, convolutional neural networks (CNNs) share weights across
spatial positions, recurrent networks include feedback
connections for sequence processing, and
transformer-based architectures underlie modern
large language models (LLMs).
See also:label, artificial neuron, activation function,
deep net, layer, convolutional neural network, transformer.
References
Goodfellow et al. (2016). Deep Learning. MIT Press.
He et al. (2016). Deep Residual Learning for Image Recognition. 2016 IEEE Conf. Comput. Vis. Pattern Recognit.. doi.org/10.1109/CVPR.2016.90
Cite this entry
@misc{dictml_ann,
author = {Jung, Alexander and Olioumtsevits, Konstantina and Schnoor, Ekkehard},
title = {artificial neural network},
howpublished = {Dictionary of Applied Machine Learning (course edition)},
year = {2026},
doi = {10.5281/zenodo.21569296},
note = {ISBN 978-952-64-3013-3, CC BY 4.0, retrieved 2026-09-11},
url = {https://dictionaryofml.org/terms/ann.html}
}
