Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations

• URL: http://arxiv.org/abs/2511.18387v1
• Date: Sun, 23 Nov 2025 10:27:04 GMT
• Title: Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations
• Authors: Plein Versace,
• Abstract summary: Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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