Abstract: Coordinate network or implicit neural representation (INR) is a fast-emerging method for encoding natural signals (such as images and videos) with the benefits of a compact neural representation. While numerous methods have been proposed to increase the encoding capabilities of an INR, an often overlooked aspect is the inference efficiency, usually measured in multiply-accumulate (MAC) count. This is particularly critical in use cases where inference bandwidth is greatly limited by hardware constraints. To this end, we propose the Activation-Sharing Multi-Resolution (ASMR) coordinate network that combines multi-resolution coordinate decomposition with hierarchical modulations. Specifically, an ASMR model enables the sharing of activations across grids of the data. This largely decouples its inference cost from its depth which is directly correlated to its reconstruction capability, and renders a near $O(1)$ inference complexity irrespective of the number of layers. Experiments show that ASMR can reduce the MAC of a vanilla SIREN model by up to 350$\times$ while achieving an even higher reconstruction quality than its SIREN baseline.