  This paper presents a new artificial neuron model capable of learning its
receptive field in the topological domain of inputs. The model provides
adaptive and differentiable local connectivity (plasticity) applicable to any
domain. It requires no other tool than the backpropagation algorithm to learn
its parameters which control the receptive field locations and apertures. This
research explores whether this ability makes the neuron focus on informative
inputs and yields any advantage over fully connected neurons. The experiments
include tests of focusing neuron networks of one or two hidden layers on
synthetic and well-known image recognition data sets. The results demonstrated
that the focusing neurons can move their receptive fields towards more
informative inputs. In the simple two-hidden layer networks, the focusing
layers outperformed the dense layers in the classification of the 2D spatial
data sets. Moreover, the focusing networks performed better than the dense
networks even when 70$\%$ of the weights were pruned. The tests on
convolutional networks revealed that using focusing layers instead of dense
layers for the classification of convolutional features may work better in some
data sets.
