INR
Implicit Neural Representation

A continuous, coordinate-based neural function that encodes signals (e.g., images, 3D geometry, radiance fields, or audio) by mapping input coordinates to signal values, providing a compact, differentiable alternative to discrete grids.

Implicit Neural Representations are neural networks—typically multilayer perceptrons (MLPs)—that learn to represent a signal as a continuous function fθ(x) that maps coordinates x (spatial positions, spatial+view directions, time, etc.) to signal attributes (color, density, occupancy, signed distance, amplitude). This paradigm contrasts with explicit discrete representations (voxels, meshes, point clouds) by storing information in network weights and optionally low-dimensional latent codes, yielding continuous, resolution-agnostic outputs, smooth differentiability for gradient-based optimization, and strong compression properties. Key technical advances that made INRs practical include positional encodings and Fourier features (to overcome spectral bias), periodic activations (SIREN) to better capture high-frequency detail, conditioned latent decoders (DeepSDF, Occupancy Networks) for multi-instance models, and efficient encodings/hashes (Instant-NGP) for real-time queries. INRs underpin many modern applications in ML (Machine Learning) and AI: neural rendering and novel-view synthesis (NeRF), shape representation and reconstruction (DeepSDF, Occupancy Networks), differentiable simulation and inverse problems, compression of high-dimensional signals, and physics-informed solvers; they also raise distinct challenges in scaling, generalization across scenes, and fast inference/query performance—areas addressed by hybrid approaches combining learned feature grids, sparse structures, or explicit primitives.

First uses of neural implicit ideas trace to research on coordinate-based function approximation and early learned signed-distance/occupancy concepts in the late 2010s; the term and concept coalesced around 2019 (DeepSDF, Occupancy Networks) and gained widespread popularity in 2020 with NeRF, with further mainstreaming and real-time scaling arriving in 2022 (Instant-NGP).

Key contributors include Jeong Joon Park et al. (DeepSDF, 2019) and Martin Mescheder et al. (Occupancy Networks, 2019) who developed neural shape/occupancy formulations; Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron and colleagues (NeRF, 2020) who popularized neural radiance fields for view synthesis; Vincent Sitzmann et al. (SIREN) and Matthew Tancik for positional/Fourier encoding work addressing spectral bias; and Thomas Müller, Alex Evans, Christoph Schied, Alexander Keller (Instant-NGP, 2022) for practical, high-performance encodings—alongside a broad community across academic labs and industry (Google Research, NVIDIA, academic vision/graphics groups) that has driven rapid development and applications.