# Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations

arXiv: https://arxiv.org/abs/2511.18387 · HTML: https://mlsanity.com/paper/2511.18387/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 22 references that are in the map.
- First posted on arXiv 23 Nov 2025.

## Builds on (most cited first, 17 of 17)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles](https://mlsanity.com/paper/2505.19914/) (2025)
- [FLEX: Continuous Agent Evolution via Forward Learning from Experience](https://mlsanity.com/paper/2511.06449/) (2025)
- [RefConv: Re-parameterized Refocusing Convolution for Powerful ConvNets](https://mlsanity.com/paper/2310.10563/) (2023)
- [FalconNet: Factorization for the Light-weight ConvNets](https://mlsanity.com/paper/2306.06365/) (2023)
- [X-MLP: A Patch Embedding-Free MLP Architecture for Vision](https://mlsanity.com/paper/2307.00592/) (2023)
- [SA-GD: Improved Gradient Descent Learning Strategy with Simulated Annealing](https://mlsanity.com/paper/2107.07558/) (2021)
- [Jitter: Random Jittering Loss Function](https://mlsanity.com/paper/2106.13749/) (2021)
- [Encoding Semantic Priors into the Weights of Implicit Neural Representation](https://mlsanity.com/paper/2406.04178/) (2024)
- [Reborn Mechanism: Rethinking the Negative Phase Information Flow in Convolutional Neural Network](https://mlsanity.com/paper/2106.07026/) (2021)
- [Interflow: Aggregating Multi-layer Feature Mappings with Attention Mechanism](https://mlsanity.com/paper/2106.14073/) (2021)
- [Evolution: A Unified Formula for Feature Operators from a High-level Perspective](https://mlsanity.com/paper/2305.14409/) (2023)
- [Learn to Enhance the Negative Information in Convolutional Neural Network](https://mlsanity.com/paper/2306.10536/) (2023)
- [Conv-INR: Convolutional Implicit Neural Representation for Multimodal Visual Signals](https://mlsanity.com/paper/2406.04249/) (2024)
- [Split-Layer: Enhancing Implicit Neural Representation by Maximizing the Dimensionality of Feature Space](https://mlsanity.com/paper/2511.10142/) (2025)

## Abstract (arXiv)

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.