Abstract
Effective communication in multi-agent reinforcement learning (MARL) is critical for success but constrained by bandwidth, yet past approaches have been limited to complex gating mechanisms that only decide \textit\{whether\} to communicate, not \textit\{how precisely\}. Learning to optimize message precision at the bit-level is fundamentally harder, as the required discretization step breaks gradient flow. We address this by generalizing Differentiable Discrete Communication Learning (DDCL), a framework for end-to-end optimization of discrete messages. Our primary contribution is an extension of DDCL to support unbounded signals, transforming it into a universal, plug-and-play layer for any MARL architecture. We verify our approach with three key results. First, through a qualitative analysis in a controlled environment, we demonstrate \textit\{how\} agents learn to dynamically modulate message precision according to the informational needs of the task. Second, we integrate our varian