Informational embodiment: Computational role of information structure in codes and robots

The body morphology plays an important role in the way information is perceived and processed by an agent. We address an information theory (IT) account on how the precision of sensors, the accuracy of motors, their placement, the body geometry, shape the information structure in robots and computational codes. As an original idea, we envision the robot's body as a physical communication channel through which information is conveyed, in and out, despite intrinsic noise and material limitations. Following this, entropy, a measure of information and uncertainty, can be used to maximize the efficiency of robot design and of algorithmic codes per se. This is known as the principle of Entropy Maximization (PEM) introduced in biology by Barlow in 1969. The Shannon's source coding theorem provides then a framework to compare different types of bodies in terms of sensorimotor information. In line with the PEM, we introduce a special class of efficient codes used in IT that reached the Shannon limits in terms of information capacity for error correction and robustness against noise, and parsimony. These efficient codes, which exploit insightfully quantization and randomness, permit to deal with uncertainty, redundancy and compacity. These features can be used for perception and control in intelligent systems. In various examples and closing discussions, we reflect on the broader implications of our framework that we called Informational Embodiment to motor theory and bio-inspired robotics, touching upon concepts like motor synergies, reservoir computing, and morphological computation. These insights can contribute to a deeper understanding of how information theory intersects with the embodiment of intelligence in both natural and artificial systems.