  Multi-layer perceptrons (MLP) have proven to be effective scene encoders when
combined with higher-dimensional projections of the input, commonly referred to
as \textit{positional encoding}. However, scenes with a wide frequency spectrum
remain a challenge: choosing high frequencies for positional encoding
introduces noise in low structure areas, while low frequencies result in poor
fitting of detailed regions. To address this, we propose a progressive
positional encoding, exposing a hierarchical MLP structure to incremental sets
of frequency encodings. Our model accurately reconstructs scenes with wide
frequency bands and learns a scene representation at progressive level of
detail \textit{without explicit per-level supervision}. The architecture is
modular: each level encodes a continuous implicit representation that can be
leveraged separately for its respective resolution, meaning a smaller network
for coarser reconstructions. Experiments on several 2D and 3D datasets show
improvements in reconstruction accuracy, representational capacity and training
speed compared to baselines.
