RIM-Hash: Retrievable Information Maximization Based Multiresolution Hash Encoding for Parameter-Efficient Signal Fitting

Multiresolution hash encodings, popularized by Instant-NGP, provide fast and compact implicit neural representations. However, their layout is data-agnostic, level resolutions follow a fixed geometric schedule, and every spatial location accesses the hash tables identically. This uniform capacity allocation is mismatched to natural signals, whose information varies sharply across space and frequency. Consequently, it wastes capacity on low-information regions while inducing hash collisions in information-dense ones. To improve the efficiency of the multiresolution hash encoding, we recast its layout design as a Retrievable Information Maximization (RIM) problem. Specifically, for a given hash-table size, RIM selects the layout that maximizes the information that remains retrievable after hash collisions. The resulting encoder, RIM-Hash, routes low-information blocks to lightweight fallback features and concentrates hash capacity where information is both present and recoverable. Across benchmarks involving 2D images and 3D signed-distance fields, RIM-Hash consistently achieves a better parameter–fidelity trade-off than strong hash-grid baselines. On Tokyo, RIM-Hash achieves fidelity comparable to the prior state-of-the-art method using only 11.43% of its parameters, while on Girl it improves PSNR by 12.43 dB at a comparable parameter scale. Code is available in the https://anonymous.4open.science/r/Retrievable-Information-Maximization-FCCD.