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arXiv · 2601.23181

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

Tianming Qiu·Christos Sonis·Hao Shen
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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.

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Tianming Qiu, Christos Sonis, Hao Shen. 2026-01-30. Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem. https://arxiv.org/abs/2601.23181

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