We consider a wireless network where each user/sensor wishes to communicate an image to a central base station for the purpose of classifying images with intrinsic class imbalance. We introduce a new framework for encoding images where a single neural network is used to perform joint source coding and channel coding for the purpose of classification. The main novelty in the proposed approach is that all users simultaneously transmit features extracted from their image over the air, and inference is performed directly on the received signal (noisy sum of the transmitted signals) using neural group testing. We show that our framework can achieve significantly lower communication and computational costs than traditional communication schemes while offering privacy and better classification performance.