Cameras and image-editing software often process images in the wide-gamut ProPhoto color space, encompassing 90% of all visible colors. However, when images are encoded for sharing, this color-rich representation is transformed and clipped to fit within the small-gamut standard RGB (sRGB) color space, representing only 30% of visible colors. Recovering the lost color information is challenging due to the clipping procedure. Inspired by neural implicit representations for 2D images, we propose a method that optimizes a lightweight multi-layer-perceptron (MLP) model during the gamut reduction step to predict the clipped values. GamutMLP takes approximately 2 seconds to optimize and requires only 23 KB of storage. The small memory footprint allows our GamutMLP model to be saved as metadata in the sRGB image—the model can be extracted when needed to restore wide-gamut color values. We demonstrate the effectiveness of our approach for color recovery and compare it with alternative strategies, including pre-trained DNN-based gamut expansion networks and other implicit neural representation methods. As part of this effort, we introduce a new color gamut dataset of 2200 wide-gamut/small-gamut images for training and testing.