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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.23181 |
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| _version_ | 1866911411732480000 |
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| author | Qiu, Tianming Sonis, Christos Shen, Hao |
| author_facet | Qiu, Tianming Sonis, Christos Shen, Hao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23181 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem Qiu, Tianming Sonis, Christos Shen, Hao Machine Learning 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. |
| title | Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.23181 |