Research on emergent communication between deep-learning-based agents has received extensive attention due to its inspiration for linguistics and artificial intelligence. However, previous attempts have hovered around emerging communication under perception-oriented environmental settings, that forces agents to describe low-level perceptual features intra image or symbol contexts. In this work, inspired by the classic human reasoning test (namely Raven's Progressive Matrix), we propose the Reasoning Game, a cognition-oriented environment that encourages agents to reason and communicate high-level rules, rather than perceived low-level contexts. Moreover, we propose 1) an unbiased dataset (namely rule-RAVEN) as a benchmark to avoid overfitting, 2) and a two-stage curriculum agent training method as a baseline for more stable convergence in the Reasoning Game, where contexts and semantics are bilaterally drifting. Experimental results show that, in the Reasoning Game, a semantically stable and compositional language emerges to solve reasoning problems. The emerged language helps agents apply the extracted rules to the generalization of unseen context attributes, and to the transfer between different context attributes or even tasks.

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