Mixed-Precision Federated Learning via Multi-Precision Over-the-Air Aggregation

Over-the-Air Federated Learning (OTA-FL) is a privacy-preserving distributed learning mechanism, by aggregating updates in the electromagnetic channel rather than at the server. A critical research gap in existing OTA - FL research is the assumption of homogeneous client computational bit precision. While in real world application, clients with varying hardware resources may exploit approximate computing (AxC) to operate at different bit precisions optimized for energy and computational efficiency. Model updates with varying precisions among clients present a significant challenge for OTA - FL, as they are incompatible with the wireless modulation superposition process. Here, we propose an mixed-precision OTA-FL framework of clients with multiple bit precisions, demonstrating the following innovations: (i) the superior trade-off for both server and clients within the constraints of varying edge computing capabilities, energy efficiency, and learning accuracy requirements compared to homogeneous client bit precision, and (ii) a multi-precision gradient modulation scheme to ensure compatibility with OTA aggregation and eliminate the overheads of precision conversion. Through case study with real world data, we validate our modulation scheme that enables AxC based mixed-precision OTA-FL. In comparison to homogeneous standard precision of 32-bit and 16-bit, our framework presents more than 10% in 4-bit ultra low precision client performance and over 65 % and 13 % of energy savings respectively. This demonstrates the great potential of our mixed-precision OTA-FL approach in heterogeneous edge computing environments.