Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations

TL;DR

This work tackles the representation bottleneck and scalability of implicit neural representations by relocating complexity from the decoder to a learned, hierarchical coordinate transformation. It introduces HC-INR, which uses a hierarchy of hypernetworks to produce multiscale, locally conditioned coordinate warps $T_\phi(x)$ that feed a compact implicit field network $f_\theta$, yielding $y = f_\theta(T_\phi(x))$. Theoretical results establish that adaptive warping expands the effective bandwidth via $\Omega_{\mathrm{eff}} = \|J_{T^{-1}}^T\|_2 \; \Omega_s$ and that the system remains Lipschitz stable under Jacobian regularization, with stability bounds under composition. Empirically, HC-INR achieves 2–4× fidelity improvements with 30–60% fewer parameters across image fitting, 3D SDF reconstruction, and NeRF approximation, highlighting its potential for scalable, high-fidelity implicit representations.

Abstract

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields. While significant progress has been made in architecture design (e.g., SIREN, FFC, KAN-based INRs) and optimization strategies (meta-learning, amortization, distillation), existing approaches still suffer from two core limitations: (1) a representation bottleneck that forces a single MLP to uniformly model heterogeneous local structures, and (2) limited scalability due to the absence of a hierarchical mechanism that dynamically adapts to signal complexity. This work introduces Hyper-Coordinate Implicit Neural Representations (HC-INR), a new class of INRs that break the representational bottleneck by learning signal-adaptive coordinate transformations using a hypernetwork. HC-INR decomposes the representation task into two components: (i) a learned multiscale coordinate transformation module that warps the input domain into a disentangled latent space, and (ii) a compact implicit field network that models the transformed signal with significantly reduced complexity. The proposed model introduces a hierarchical hypernetwork architecture that conditions coordinate transformations on local signal features, enabling dynamic allocation of representation capacity. We theoretically show that HC-INR strictly increases the upper bound of representable frequency bands while maintaining Lipschitz stability. Extensive experiments across image fitting, shape reconstruction, and neural radiance field approximation demonstrate that HC-INR achieves up to 4 times higher reconstruction fidelity than strong INR baselines while using 30--60\% fewer parameters.