This paper studies Implicit Neural Representations (INRs) and Neural Fields, novel paradigms for representing signals such as images, audio, 3D scenes, and video. We present a novel analysis of neural image compression, considering neural images, which are 2D images represented by neural networks. Specifically, we introduce Adaptive Neural Images (ANI), an efficient neural representation that can adapt to various inference or transmission requirements. The proposed method can reduce the pixels-per-bit (bpp) of neural images by up to eight times without losing sensitive details or compromising fidelity. This study provides a novel framework for developing compressed neural fields and achieves a new state-of-the-art performance in terms of the PSNR/bpp tradeoff through the successful implementation of a 4-bit neural representation.