  We study the Solid Isotropic Material Penalisation (SIMP) method with a
density field generated by a fully-connected neural network, taking the
coordinates as inputs. In the large width limit, we show that the use of DNNs
leads to a filtering effect similar to traditional filtering techniques for
SIMP, with a filter described by the Neural Tangent Kernel (NTK). This filter
is however not invariant under translation, leading to visual artifacts and
non-optimal shapes. We propose two embeddings of the input coordinates, which
lead to (approximate) spatial invariance of the NTK and of the filter. We
empirically confirm our theoretical observations and study how the filter size
is affected by the architecture of the network. Our solution can easily be
applied to any other coordinates-based generation method.
