Title: End-to-end Invariance Learning with Relational Inductive Biases in Multi-Object Robotic Manipulation. Abstract: Although reinforcement learning has seen remarkable progress over the last years, solving robust dexterous object-manipulation tasks in multi-object settings remains a challenge. In this paper, we focus on models that can learn manipulation tasks in fixed multi-object settings \emph{and} extrapolate this skill zero-shot without any drop in performance when the number of objects changes. We consider the generic task of moving a single cube out of a set to a goal position. We find that previous approaches, which primarily leverage attention and graph neural network-based architectures, do not exhibit this invariance when the number of input objects changes while scaling as $K^2$. We analyse effects on generalization of different relational inductive biases and then propose an efficient plug-and-play module that overcomes these limitations. Besides exceeding performances in their training environment, we show that our approach, which scales linearly in $K$, allows agents to extrapolate and generalize zero-shot to any new object number.