T-MLP: Tailed Multi-Layer Perceptron for Level-of-Detail Signal Representation

Level-of-detail (LoD) representation is critical for efficiently modeling and transmitting various types of signals, such as images and 3D shapes. In this work, we propose a novel network architecture that enables LoD signal representation. Our approach builds on a modified Multi-Layer Perceptron (MLP), which inherently operates at a single scale and thus lacks native LoD support. Specifically, we introduce the Tailed Multi-Layer Perceptron (T -MLP), which extends the MLP by attaching an output branch, also called tail, to each hidden layer. Each tail refines the residual between the current prediction and the ground-truth signal, so that the accumulated outputs across layers correspond to the target signals at different LoDs, enabling multi-scale modeling with supervision from only a single-resolution signal. Extensive experiments demonstrate that our T -MLP outperforms existing neural LoD baselines across diverse signal representation tasks. Representing signals with neural networks is an active research direction, known as implicit neural representation (INR) (Sun et al., 2022; Molaei et al., 2023; Essakine et al., 2024). Unlike traditional discrete signal representation that stores signal values on a fixed-size grid, INR represents a continuous mapping from coordinates to signal values using a neural network, offering a more compact representation than conventional discrete grid-based representations.