Discovering Sensorimotor Agency in Cellular Automata using Diversity Search

TL;DR

The paper addresses how to engineer functional sensorimotor agency in a bodyless, low-level substrate by evolving environmental rules in Lenia CA via intrinsically motivated goal exploration with curriculum-guided gradient optimization. The authors integrate IMGEP with differentiable Lenia, using a two-channel setup that includes learnable agents and obstacles, enabling automated discovery of robust, moving autopoietic patterns that react to perturbations. They demonstrate strong locomotion, obstacle navigation, and generalization to varied perturbations, including scaling and multi-agent interactions, often surpassing random and handmade baselines. The work provides quantitative and qualitative benchmarks, open-source code, and interactive demos, highlighting potential implications for AI, synthetic biology, and our understanding of open-ended, self-organizing systems.

Abstract

The research field of Artificial Life studies how life-like phenomena such as autopoiesis, agency, or self-regulation can self-organize in computer simulations. In cellular automata (CA), a key open-question has been whether it it is possible to find environment rules that self-organize robust "individuals" from an initial state with no prior existence of things like "bodies", "brain", "perception" or "action". In this paper, we leverage recent advances in machine learning, combining algorithms for diversity search, curriculum learning and gradient descent, to automate the search of such "individuals", i.e. localized structures that move around with the ability to react in a coherent manner to external obstacles and maintain their integrity, hence primitive forms of sensorimotor agency. We show that this approach enables to find systematically environmental conditions in CA leading to self-organization of such basic forms of agency. Through multiple experiments, we show that the discovered agents have surprisingly robust capabilities to move, maintain their body integrity and navigate among various obstacles. They also show strong generalization abilities, with robustness to changes of scale, random updates or perturbations from the environment not seen during training. We discuss how this approach opens new perspectives in AI and synthetic bioengineering.

Figures (16)

• Figure 1: Overview of the scientific question. (A) The enactivist framework: ($t_{i_0}$) In the beginning there is only an environment made of low-level elements (cells) and physical laws (local rules). There is no prior notion of agency, no body, no sensor. ($t_{i_1}$) Agents can come to existence through the coordination of the low-level elements (self-constitution of individuality). ($t_{i_2}$) To maintain their integrity, agents must sense and react to perturbations using only local update rules (self-maintenance of individuality). (B) In cellular automata models like the Game of Life and a more complex continuous extension called Lenia, it was shown that it is possible to self-organize so-called gliders i.e. spatially-localized patterns with directional movement. Directional movement (white arrows) and timesteps are displayed. (Question) In this work, following the enactivist modeling framework, we try to answer the following scientific question: is it possible to find environments in which a subpart could self-organize and be called a "sensorimotor agent"? This would require the existence and emergence of gliders-like structures that not only self-constitute and show motility, but that are also robust to external perturbations and hence must develop some form of sensorimotor apparatus enabling them to make "decision" and "sense" at the macro scale through local interactions only.
• Figure 2: System overview. (top) Illustration of one experimental rollout with automated (i) generation of target goal (green), (ii) generation of environmental obstacles (blue) and (iii) optimization of learnable parameters toward goal (backpropagation shown in orange). The initial state is iteratively updated by the parameterized rule, we then compute the goal conditionned loss from the last state of the rollout and propagate gradient across the steps to the learnable parameters and initialization. (bottom) Detailed view of a step in Lenia with obstacles. A convolution followed by a growth function is applied on each channel, resulting in a growth update which is added to the current state of the learnable channel. Both the convolution and the non-linear growth function in the learnable channel are parameterized (see appendix \ref{['fig:diff_lenia']}).
• Figure 3: Curriculum and performances. a) Schematic view of the curriculum. The curriculum iteratively sample goal positions (yellow disk), further in the grid, starting from very close to the initialization (A) to further away without obstacles (B) to further away in the obstacle area (C, then D). Arrow between reached positions (red square) represent that the parameters leading to a pattern attaining the tip of the arrow position was initialized before training by the parameters reaching the back of the arrow position. b) Examples of patterns obtained along the curriculum as well as their associated goal. We observe patterns going further and further in the same amount of steps (50 steps) and for the latter dealing with obstacles in their way. To display the trajectory of the agent in the learnable channel (yellow) we superposed the frames over all timesteps putting more transparency in earlier timesteps. c) Performances in term of robustness to the basic obstacle test and speed with obstacle perturbations of the moving agent produced by: IMGEP (red), random parameters search with the same computation as our method, i.e. 117 000 parameters tried in total (blue) and handmade agents found in the original Lenia papers (green). d,e) Distribution of the Speed without obstacles perturbation (d) and robustness to moving obstacles (e) of moving agents obtained by the IMGEP along the curriculum. Details on these metrics can be found in Appendix.\ref{['appendix:speed_measure']},\ref{['appendix:generalization_tests']}. We observe that the curriculum is translated in an improvement in the 2 presented quantities.
• Figure 4: Generalization of the discovered sensorimotor agents. (A) We conduct a battery of quantitative tests which we organize in 9 families of parameterized perturbations that test for various (a) obstacle number, size and speed, (b) rate of cell updates, as well as rate and magnitude of noise added to the updates, but also (c) rate and magnitude of noise added to the initial state and (d) scaling factors. For each family, we test for $5$ different parameter values, i.e. perturbation strength, resulting in a total of $9\times 5 = 45$ tests. For each test, the performance of an agent is computed as the average score of survival over 10 random seeds. A score of 1 (dark blue) means that the agent survived all 10 tests whereas a score of 0 (light yellow) means that the agent survived none of the tests. The table reports the mean and standard-deviation performances, over the 10 best agents discovered by our goal-directed curriculum, for all of the 45 tests (one table cell per test), where "best" is determined by the speed/robustness criteria introduced in Figure \ref{['fig:curriculum']}-c. Below each column, we show snapshots of system rollout at test time given the newly introduced perturbations. The shown snapshots are all taken from rollouts of the "best" agents, and from the first seed (out of the 10 tested random seeds). Timesteps are specified under the images, for instance snapshots of the perturbations applied on the initial state are shown at t=1. (B) We also conduct a battery of qualitative tests, where we tested the (best) discovered agents to all sorts of difficult perturbations including (a) freely-drawn obstacles such as walls, mazes or dead-ends (b) freely-drawn initial states such as very big disks (resulting in the emergence of multiple entities) or small disks with gradient asymmetry, (c-d-e) introduction of other agents in the grid (resulting in the emergence of inter-agent interactions such as individuality maintenance, attraction and reproduction), (f) the introduction of novel low-level elements that have an "attractive" effect on the agents (allowing external user to guide the agent trajectory in the grid); and (g) custom mass removal (pixel erasing). Details of the resulting observed behaviors are provided in the text, with videos available on the companion website https://developmentalsystems.org/sensorimotor-lenia-companion/.
• Figure 5: "Phylogeny tree" of one run of IMGEP. The red dot are reached positions (by a step of IMGEP). The blue zone correspond to the zone where obstacles can be placed. Black arrows indicate optimization progress (the point at the end of the arrow was obtained after optimizing the one at the start of the arrow). The path leading to the best agent (reaching the furthest position on the x axis) is highlighted in green. Interestingly we can see that the best path is not necessarily a straight path. For visibility reasons, we put transparency on the optimization steps that led to reached positions far from the reached position of the parameters that was used to initialize the optimization (often due to failing ).