A model-based deep learning (DL) architecture is proposed for reconfigurable intelligent surface (RIS)-assisted multi-user communications to reduce the number of bits required for transmitting phase shift information from the access point (AP) to the RIS controller. The AP computes the phase shifts and compresses them into a binary control message that is sent to the RIS controller for element configuration. To help reduce beamformer mismatches caused by phase shift compression errors, the beamformer is updated with the actual (decompressed) RIS phase shifts. By unrolling the iterative weighted minimum mean square error (WMMSE) algorithm within the wireless communication-informed DL architecture, joint phase shift compression and WMMSE beamforming can be trained end-to-end. Simulation results demonstrate that incorporating compression-aware beamforming significantly improves sum-rate performance, even when the number of control bits is lower than the number of RIS elements.