Ensuring Semantics in Weights of Implicit Neural Representations through the Implicit Function Theorem
This provides a theoretical foundation for understanding weight semantics in neural networks, which is incremental but useful for researchers in meta-learning and transfer learning.
The paper tackled the lack of a theoretical explanation for how semantics are encoded into neural network weights in Weight Space Learning, using the Implicit Function Theorem to establish a rigorous mapping between data and weight spaces, achieving competitive performance on classification tasks with 2D and 3D datasets.
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.