Title: Efficient Implicit Neural Surfaces via Multiscale Residuals and Nested Training
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Implicit Neural Representations (INRs), Signed Distance Functions (SDFs), Sinusoidal Input Encoding, Multiscale Neural Networks, Residual MLP Architectures, Sphere Tracing, High-Frequency Detail Modeling, Real-Time Mesh Extraction, Efficient Inference

Abstract: Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. This approach enables the capture of high-frequency detail and supports geometric regularization through MLP derivatives, such as the Eikonal constraint for signed distance function (SDF) fitting. However, existing methods typically rely on a single large MLP to learn the surface across the entire domain — a design that hinders efficient modeling of fine-grained details. Scaling the model may enable enhanced surface modeling, but at the cost of a larger number of MLP parameters and expensive inference, since mesh extraction or sphere tracing requires querying the MLP at many off-surface points. To address these issues, we propose M-plicits (Multiscale Implicit Neural surfaces), a multiscale framework for representing and training INRs to encode surfaces as SDFs, enabling both high-quality reconstruction and efficient inference. To increase representational capacity, we model the INR as a residual sum of MLPs, where each component captures a specific level of detail, modulated by the sinusoidal input encodings. To improve efficiency, a small MLP captures coarse geometry, while finer residual MLPs are trained within a sequence of nested neighborhoods around the zero-level set. This design concentrates modeling capacity near the surface, improving reconstruction and reducing computation by relying on coarse approximations for off-surface points. Experiments show that M-plicits achieve state-of-the-art accuracy in surface reconstruction across standard benchmark datasets, while maintaining a compact representation. Our method also supports real-time sphere tracing and efficient high-resolution mesh extraction. Code and pretrained models will be released.

TL;DR: M-plicits uses residual MLPs in a multiscale SDF framework, restricting fine networks to nested neighborhood for detail and efficiency, enabling compact models, real-time sphere tracing, and fast reconstruction.