Weight-Space Learning Without Weights: Leveraging Neural Operators for Model Editing

Neural networks increasingly serve as representations of continuous signals, from images to dynamical systems. Editing these representations raises a question: should transformations act on discretized signals, network parameters, or the functions they encode? Weight-space learning operates directly on parameters, but neural representations are non-unique, while methods operating on discretized signals can depend strongly on grid resolution. Here, we formulate editing as an operator learning problem and compare our neural operator-based approach to alternatives that operate on discretized signals or weights, using rotating MNIST implicit neural representations and introducing damping into harmonic oscillator neural ODEs as examples. For fixed-angle rotation, our approach, instantiated using Fourier neural operators, performs competitively on the original grid and outperforms weight-space baselines and vision models at intermediate coordinates. Furthermore, angle-conditioned operators generalize to held-out rotations. For oscillator damping, our neural operator-based approach outperforms weight space approaches. These results support model editing as a practical approach to transforming neural representations, with advantages in generalization across sampling grids and families of transformations.