Self-Communicating Deep Reinforcement Learning Agents Develop External Number Representations


  • Silvester Sabathiel NTNU Trondheim
  • Trygve Solstad Department of Teacher Education, NTNU, NO-7491 Trondheim, Norway
  • Alberto Testolin Department of Information Engineering, University of Padova, Italy
  • Flavio Petruzzellis



deep learning, reinforcement learning, self-communication, neural networks, numerical cognition, mathematical cognition, external representations


Symbolic numbers are a remarkable product of human cultural development. The developmental process involved the creation and progressive refinement of material representational tools, such as notched tallies, knotted strings, and counting boards. In this paper, we introduce a computational framework that allows the investigation of how material representations might support number processing in a deep reinforcement learning scenario. In this framework, agents can use an external, discrete state to communicate information to solve a simple numerical estimation task. We find that different perceptual and processing constraints result in different emergent representations, whose specific characteristics can facilitate the learning and communication of numbers.


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