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

2026-01-30

AI Summary

This work addresses the lack of rigorous theoretical understanding regarding how weights in implicit neural representations (INRs) encode data semantics. By leveraging the implicit function theorem, the authors establish a differentiable mapping between the data space and the INR weight space for the first time. They further introduce a shared hypernetwork that maps instance embeddings to INR weights, thereby enabling semantic-preserving weight learning. This approach provides theoretical guarantees for semantic encoding within INRs and constructs an interpretable framework for learning in weight space. Experiments on 2D and 3D datasets demonstrate that the proposed method achieves competitive performance on downstream classification tasks compared to existing baselines, validating both its effectiveness and theoretical advantages.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Implicit Neural Representations
• Weight Space Learning
• Semantics Encoding
• Implicit Function Theorem
• Neural Network Weights

Innovation

• Implicit Function Theorem
• Implicit Neural Representations
• Weight Space Learning
• Hypernetwork
• Semantic Encoding