Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem
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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.
Key facts. Cited by 1 paper 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.
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32 of 41 references.
References · 32
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20 more
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