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

TL;DR

The paper reframes embodiment as an information-theoretic problem, treating the body as a physical channel through which sensorimotor information flows and is encoded. It leverages entropy maximization and Shannon theory to argue that efficient, often low-precision codes—often random or dispersive—can achieve near-optimal information transfer and robustness, enabling accurate perception and control with unreliable hardware. By introducing Informational Embodiment, the authors connect motor synergies, morphological computation, and reservoir/physical reservoir computing as mechanisms to maximize information throughput within bodily constraints, and they illustrate this with examples of motor-sensor equivalence, random coding, and developmental dynamics. The work suggests practical pathways for designing soft, bio-inspired, and reservoir-based systems that maintain high functional performance despite noise and material limits, with potential implications for robotics and AI theory.

Abstract

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 PME, 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.

Figures (6)

• Figure 1: Different strategies of information transfert in robotic and biological agents. a) rigid robots use very precise motors and sensors for perception and motion control. The accuracy of the motion behavior, $\bf R_{out}$ is related directly to the precision of the precision of the devices $\bf R_{in}$ so that $\bf R_{in} \approx R_{out}$. Gigantic models in current Artificial Intellgience (AI) uses the same strategy to obtain high performance. b) digital processing, instead, uses a different strategy with very raw binary codes to encode high resolution signals so that $\bf R_{in} \ll R_{out}$. Novel techniques from Information theory, such as compressive sensing, turbo-codes, or low density parity check, uses random matrices (high entropic codes) to achieve near Shannon limits in terms of information compression and robustness against noise. c) similarly, the human body and brain possess low precision muscles and neurons but achieve high performance so that we have also $\bf R_{in} \ll R_{out}$. d) Biologically-inspired robotics and AI systems may achieve high accuracy from low precision neurons and body by using similar techniques from Information Theory and observed in biology.
• Figure 2: Information structure for different types of codes. a) Digital encoding represents directly a high resolution input $\bf X$ with orthogonal and low resolution (binary) codes $\bf Y$ so that the number $\bf k$ of codes is the shortest, with $\bf R_Y \ll R_X$. b) random codes used in Telecom and signal exploit a similar strategy to digital processing by creating orthogonal embeddings of low resolution on the fly so that $\bf R_Y \ll R_X$. The number of codes $k$ is small so that $\bf \log R_X \approx k \log R_Y$. c) Besides, highly redundant codes require high resolution devices to approximate the input values with same resolution, so that $\bf R_Y \approx R_X$.
• Figure 3: Efficient coding in random matrices in Compressive sensing, application to sensing and control in robotics. a) Compressive methods in Telecom and signal have delivered efficient methods for compression and redundancy reduction using random matrices $\bf W$ to collect and compress at the same time high dimensional signals $\bf X$ into only few codes $\bf Y$ so that $\bf k \log Y \approx \log X$, with $\bf k$ the number of units. b) Random projections of one original signal --, and also permutations,-- don't destroy information but create orthogonal embeddings readily. Information is compactly preserved into few codes that can reconstruct back information by inference (decoding); results taken from pitti_digital_2022. c) efficient codes can serve to compactly regenerate high dimensional signals into a lower dimensional space. d-e) In motor domain, they represent then motor primitives or motor synergies.
• Figure 4: Information equivalence of different embodied systems. One motor device $X$ of high precision within $R_X$ is equivalent in term of information to the combination of multiple actuators $Y$ in series of lower dimensions, say $R_Y$, resp. a) and b). In the case where $R_X=1024$ and $R_Y=2$ (on-off actuators), one equivalence exists in terms of information between the two systems for a minimum number of $k= \log R_X / \log R_Y = 10$ units. c) same equivalence for a hand-like five-link parallel robot with $4$ possible motor states. The combinatorics is also $1024$. Image credit upklyak, ddraw.
• Figure 5: Combinatorics of one hand motion, quantification of contacts and constraints. a) Free hand motions are the most entropic ones $H_{free}$ as they are also the most unconstrainted ones. This state corresponds to the complete repertoire of actions. Besides, constrained actions occuring when touching soft and rigid objects can be quantified by the number of possible configurations $H_{soft} > H_{rigid}$. The full grasp of one object is paradoxally the most minimal and the less entropic one, as it corresponds to only one possible configuration of the hands b-c) same explanation for a more simplistic robotic hand with 2 DoFs and 9 possibles actions. The grasping of one object represents to a lower entropic state than one of a free-hand motion, and thus, to a more stable state. Image credit ddraw.