Dynamical Implicit Neural Representations

Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, yet achieving high expressivity with compact architectures remains challenging. We introduce Dynamical Implicit Neural Representations (DINR), a model-agnostic framework that induces richer function classes from existing INRs by changing both what the network learns and how the signal is represented. Rather than directly parameterizing the target function with a static neural network, DINR learns a neural vector field that determines how a latent state evolves, while the target representation is given by the resulting evolution of that state. By augmenting static INRs with latent dynamics, this formulation allows compact neural parameterizations to induce substantially richer mappings without proportionally increasing the number of trainable parameters. We provide theoretical insights into the representational and optimization behavior of DINR through Rademacher complexity and Neural Tangent Kernel analyses. To balance representation capacity and generalization, we further introduce kinetic energy regularization that regulates the complexity of the learned dynamics. Across image representation, 3D field reconstruction, and scientific data compression, DINR consistently improves reconstruction fidelity, parameter efficiency, and robustness over conventional static INRs.