# The Inlet Rank Collapse in Implicit Neural Representations: Diagnosis and Unified Remedy

arXiv: https://arxiv.org/abs/2602.01526 · HTML: https://mlsanity.com/paper/2602.01526/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 19 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Rethinking Positional Encoding](https://mlsanity.com/paper/2107.02561/) (2021)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)
- [H-SIREN: Improving implicit neural representations with hyperbolic periodic functions](https://mlsanity.com/paper/2410.04716/) (2024)

## Abstract (arXiv)

Implicit Neural Representations (INRs) have revolutionized continuous signal modeling, yet they struggle to recover fine-grained details within finite training budgets. While empirical techniques, such as positional encoding (PE), sinusoidal activations (SIREN), and batch normalization (BN), effectively mitigate this, their theoretical justifications are predominantly post hoc, focusing on the global NTK spectrum only after modifications are applied. In this work, we reverse this paradigm by introducing a structural diagnostic framework. By performing a layer-wise decomposition of the NTK, we mathematically identify the ``Inlet Rank Collapse'': a phenomenon where the low-dimensional input coordinates fail to span the high-dimensional embedding space, creating a fundamental rank deficiency at the first layer that acts as an expressive bottleneck for the entire network. This framework provides a unified perspective to re-interpret PE, SIREN, and BN as different forms of rank restoration. Guided by this diagnosis, we derive a Rank-Expanding Initialization, a minimalist remedy that ensures the representation rank scales with the layer width without architectural modifications or computational overhead. Our results demonstrate that this principled remedy enables standard MLPs to achieve high-fidelity reconstructions, proving that the key to empowering INRs lies in the structural optimization of the initial rank propagation to effectively populate the latent space.