# Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem

arXiv: https://arxiv.org/abs/2601.23181 · HTML: https://mlsanity.com/paper/2601.23181/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 32)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [HyperDreamBooth: HyperNetworks for Fast Personalization of Text-to-Image Models](https://mlsanity.com/paper/2307.06949/) (2023)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [PointDAN: A Multi-Scale 3D Domain Adaption Network for Point Cloud Representation](https://mlsanity.com/paper/1911.02744/) (2019)
- [Equivariant Architectures for Learning in Deep Weight Spaces](https://mlsanity.com/paper/2301.12780/) (2023)
- [Transformers as Meta-Learners for Implicit Neural Representations](https://mlsanity.com/paper/2208.02801/) (2022)
- [Permutation Equivariant Neural Functionals](https://mlsanity.com/paper/2302.14040/) (2023)
- [Hyper-Representations as Generative Models: Sampling Unseen Neural Network Weights](https://mlsanity.com/paper/2209.14733/) (2022)
- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [Neural Functional Transformers](https://mlsanity.com/paper/2305.13546/) (2023)
- [HyperTuning: Toward Adapting Large Language Models without Back-propagation](https://mlsanity.com/paper/2211.12485/) (2022)
- [Generalizable Implicit Neural Representations via Instance Pattern Composers](https://mlsanity.com/paper/2211.13223/) (2022)
- [Equivariant Deep Weight Space Alignment](https://mlsanity.com/paper/2310.13397/) (2023)
- [We Should Chart an Atlas of All the World's Models](https://mlsanity.com/paper/2503.10633/) (2025)
- [Hypernetwork approach to generating point clouds](https://mlsanity.com/paper/2003.00802/) (2020)
- [Deep Linear Probe Generators for Weight Space Learning](https://mlsanity.com/paper/2410.10811/) (2024)
- [Generalizable Neural Fields as Partially Observed Neural Processes](https://mlsanity.com/paper/2309.06660/) (2023)
- [Foundation Models Secretly Understand Neural Network Weights: Enhancing Hypernetwork Architectures with Foundation Models](https://mlsanity.com/paper/2503.00838/) (2025)

## Built on by (most cited first, 1 of 1)

- [Is Class Signal Clustered or Routed in Task-Induced Implicit Neural Representation Weight Spaces?](https://mlsanity.com/paper/2605.08281/) (2026)

## Abstract (arXiv)

Weight Space Learning (WSL), which frames neural network weights as a data modality, is an emerging field with potential for tasks like meta-learning or transfer learning. Particularly, Implicit Neural Representations (INRs) provide a convenient testbed, where each set of weights determines the corresponding individual data sample as a mapping from coordinates to contextual values. So far, a precise theoretical explanation for the mechanism of encoding semantics of data into network weights is still missing. In this work, we deploy the Implicit Function Theorem (IFT) to establish a rigorous mapping between the data space and its latent weight representation space. We analyze a framework that maps instance-specific embeddings to INR weights via a shared hypernetwork, achieving performance competitive with existing baselines on downstream classification tasks across 2D and 3D datasets. These findings offer a theoretical lens for future investigations into network weights.