Evolutionary Implications of Self-Assembling Cybernetic Materials with Collective Problem-Solving Intelligence at Multiple Scales

We are ultimately interested in the question of whether a substrate of competent parts shows the ability to generalize to environmental conditions that have never been experienced by its evolutionary predecessors, and hence would allow the evolutionary process to adapt an organism to changing environmental conditions more efficiently compared to a direct encoding scheme. Thus, we systematically vary in Figure 6 the system parameters, i.e., the noise level and the decision-making probability competency level, for selected NCA solutions of the Czech flag problem that have been trained with certain sets of the system parameters above.

For instance, we utilize NCA solutions that have been evolved to solve the 8×8 Czech flag problem in tD=25 developmental steps (see above) under zero-noise conditions without and with evolvable competency. Here, we utilize such solutions for larger noise levels of ξc∈[0,0.5] and for lifetimes of 100 time steps and present the average fitness values of 100 statistically independent simulations at each particular noise level in Figure 6A,B, respectively, without any further evolutionary optimization. Analogously, we expose NCA solutions that have evolved with a competency level of PD=0.5 and noise levels of ξc=0.25 and 0.5, respectively, to vastly different noise levels of ξc∈[0,1] compared to the conditions during their respective evolutionary processes, and present the results in Figure 6C,D. Eventually, we again deploy the latter NCA solutions but vary the competency level PC∈[0,1] instead, at respectively fixed noise levels of ξc=0.25 and 0.5, with the results depicted in Figure 6E,F. Notably, we only consider the “correctness” part of the fitness score, i.e., the first term in Equation (5) by setting rT=0 and rS=0.

The results in Figure 6 demonstrate that the performance of the here evolved NCAs, optimized with evolutionary methods to assemble and maintain a target morphology over time at particular system parameters, differs greatly between NCA solutions that follow the direct- or multi-scale encoding paradigms when subjected to novel environmental conditions: The typical fitness over the lifetime of an NCA without competency that encodes the target phenotype pattern directly (cf. Figure 6A) is constantly affected by random fluctuations and thus decreases in fewer time steps with increasing noise levels in a diffusive process; the duration of how long the corresponding maximum fitness score of 64 can be maintained and the speed at which the fitness eventually decays during the lifetime of the here discussed 8×8 Czech flag NCA depend on the particular noise level and on the values of the initial cell states, which are limited numerically to the interval [−3,3] for each cell. In contrast, NCA solutions with larger competency levels that have been evolved at finite noise-level conditions still perform well—and can maintain the target pattern for exceptionally long times—also when changing the system parameters dramatically (cf. Figure 6B–F); note the noise-level axis of ξc=0 to 1, compared to the maximum noise levels of ξc=0.5 during training.

The results in panel Figure 6B are especially curious, as the corresponding NCA has been trained to evolve its decision-making probability alongside the structural and functional parts of the genome at zero noise conditions. While no competency at all would have been required to solve this task, the presented NCA solution evolved to afford a maximum competency of PD=1 (cf. Figure 5C). Strikingly, this particular NCA is capable of resisting much larger noise levels of ξc≈0.25 while maintaining the pattern perfectly for at least tD=25 steps, and the average fitness score of 100 independent solutions does still not drop below a certain threshold of ≈40–50 for even higher noise levels and for 100 time steps. Notably, there appears to be a bifurcation of the long-term behavior of these NCA solutions (not shown here) where the NCA—in some realizations—maintains the target pattern perfectly for long times, while in other independent runs, the fitness drops quickly.

In this sub-section, we thus show that NCAs that have evolved to assembly and maintain a target pattern within a relatively short developmental stage are capable of maintaining the corresponding target pattern over much longer time scales—without any further optimization—and thus show great signs of functional, morphostatic generalizability. Moreover, the here-discussed in silico morphogenesis and morphostasis model systems are capable of handling, essentially on the fly, system–parameter combinations that neither they nor their evolutionary ancestors ever experienced before. Thus, we conclude that such multi-scale competency architectures [1], whose substrate is composed of competent rather than passive parts, can be more than capable of generalizing to changes in their environment—within reasonable boundaries, of course—by allocating robust problem-solving competencies at many scales [93,94].

Deducing from the discussion in Section 4.5 about the generalizability of multi-scale competency architectures [1] towards changing environmental conditions, such systems should also exhibit increased evolvability and transferability properties to new problems: if such multi-scale competency architectures are capable of adapting their behavior towards changing environmental conditions on the fly during a single lifetime (cf. Figure 6), this has great consequences for the evolutionary process when environmental conditions change.

Thus, we utilized the NCA solution discussed in Figure 5C and Figure 6D and performed subsequent CMA-ES on the 8×8 Czech flag problem at changed environmental conditions, i.e., at higher noise levels: only a single or, at most, a handful of generations are necessary for solving the task even at intermediate and high noise levels of ξc=0.25 and 0.5.

To emphasize the potential of the transferability of multi-scale competency architectures, we here investigate the adaptation capability of pre-evolved NCAs when their objective function is suddenly changed, i.e., when the environment starts selecting for different target patterns than the one they have originally been evolved for. More specifically, we utilize NCA solutions from Section 4.3, and discussed in Figure 4, which successfully solve the 8×8 Czech-flag task, and additionally perform 1000 evolutionary cycles of CMA-ES on a related 8×8 blue-, white-, red-, Viennese-, blue/white-, and blue/red-flag morphogenesis task for various noise and competency levels. We allow changes to both the structural and functional parts of the genomes of the pre-evolved NCA.

In Figure 7, we present the corresponding number of generations it takes for 10–60 CMA-ES runs on average to adapt a pre-evolved, i.e., “informed”, NCA solution that can solve the 8×8 Czech-flag morphogenesis task to then solve the respective new morphogenesis task under different environmental conditions. We see a clear advantage in terms of the evolvability and adaptability of pre-evolved individuals at high-competency levels (in contrast to individuals with lower competency levels) so that adaptation can happen in as few as ≈10 generations. While the Czech→blue-, white-, and red-flag tasks are rather trivial (see top panels in Figure 7), computationally, the Czech→Viennese-, blue/white-, and blue/red-flag adaptation tasks (bottom panels in Figure 7) are more complicated. Still, the latter can be solved in as few as ≈20 generations compared to ≫100 generations of evolving a corresponding randomly initialized NCA to solve the Czech-flag problem from scratch as shown in Section 4.2 and Section 4.3.

Thus, we conclude that pre-evolved (or “informed”) competency at subordinate scales of a multi-scale competency architecture greatly enhances a collective system’s capability of adaptation. Thus, a competent and informed substrate has great effects on a multi-scale competency architecture’s evolvability towards changing environmental conditions and on the transferability of already acquired (evolved) solutions to new problems.

We have investigated the evolutionary implications of multi-scale intelligence on an example of the in silico morphogenesis of two-dimensional tissue of locally interacting cells that are equipped with tunable decision-making machinery. More specifically, we have utilized evolutionary algorithms (EAs) [103] to evolve the parameters of neural cellular automata (NCAs) [100] on morphogenesis tasks under various conditions of the competency level of the uni-cellular agents and the developmental noise in the system.

In this model of a multi-scale competency architecture [1], a two-dimensional grid of locally interacting cells is tasked to self-assemble and maintain a global spatial target pattern of predefined cell types, here, primarily of a two-dimensional, 8×8 Czech flag pattern (we model and investigate the evolution of the process of morphogenesis and morphostasis in silico and deploy our framework to a self-orchestrated pattern formation task, primarily of a two-dimensional 8×8 Czech flag pattern but also for other much more involved target shapes, such as a 9×9 smiley face (see Appendix G)). Each uni-cellular agent’s internal decision-making machinery is modeled by an artificial neural network (ANN), allowing these cells to independently perceive the cell states of their adjacent neighbors on the grid and propose actions to regulate their own cell state over time via local communication rules. Both the ANN parameters and the initial cell states of all permanent cells represent the parameters of the NCA and are optimized by EAs for a specific in silico morphogenesis task, thus forming the functional and structural part of the system’s genome, respectively.

To investigate the effects of competency in a multi-scale competency architecture on the underlying evolutionary process, we introduce (I) a “competency level” parameter that controls the reliability of the uni-cellular agents of an NCA to regulate their cell types during a noisy developmental stage. This allows us to continuously scale the NCA competency level from a direct encoding scheme of the target pattern (no competency) to a multi-scale competency architecture that self-assembles the pattern with perfect reliability in cell decision executions. Furthermore, we introduce (II) a variable number of redundant sub-modules in the NCA ANN, which we utilize as another “axis” of redundancy- and computational capacity-based competency of the cells’ decision-making machinery.

In large-scale simulations, we systematically vary these two competency levels (I, II), expose the corresponding NCA to different noise conditions (III), and perform several statistically independent evolutionary searches at each parameter combination (I–III). In that way, we demonstrate that an evolutionary process proceeds significantly more rapidly (on average) on noisy pattern formation tasks when evolving the parameters of a multi-scale competency architecture compared to evolving the target pattern directly (with no competency involved).

Our multi-scale competency architecture model and the corresponding evolutionary optimization process comprise several scales: At the smallest scale (1), each structural and functional gene is represented by a floating point number. The functional genes parameterize the behavior of artificial neurons (2), our atomic decision-making centers, which are then hierarchically arranged into layers of artificial neurons (3), sub-modules of interconnected layers (4), to an ANN with a predefined architecture (5). Thus, even the uni-cellular phenotypes (6) in our system—ANN-based agents that maintain a particular internal cell state—are composites of smaller (proto-competent) decision-making centers down the hierarchical ladder. The composite uni-cellular agents perceive the cell states of their grid neighbors (7) on the NCA, perform potentially several cycles of internal calculations, and eventually update their own cell state in a single developmental step. In that way, clusters of different tissue types (8) may be formed in successive developmental steps. A fixed number of developmental steps comprise the lifetime of a single NCA, giving rise to self-assembled phenotypic tissue of cell types on the entire grid of the NCA (9), e.g., as in our case, to the Czech flag pattern. The quality of each individual in an evolutionary population of NCAs (10) is evaluated via a phenotypic fitness score, quantifying the deviation of the assumed cell types from a target pattern. Based on the fitness scores of a particular generation of NCAs, the genotypes of potentially better-adapted successor generations are successively sampled by the EA, closing the loop (1) and forming the largest scale in our system, an evolutionary lineage (11).

Eventually, on a meta-scale (12), we compare the efficiency of the evolutionary process at different system parameters (I–III), i.e., at different competency- and noise levels, by analyzing the fitness trajectories of statistically independent lineages evaluated at the same system parameters.

We demonstrate that especially in the presence of developmental noise, affecting cell state updates during morphogenesis, the evolutionary process favors a multi-scale competency-based realization over a direct encoding scheme of the target pattern. Moreover, when the competency level itself is left as an evolvable parameter to the EA, there appears to be a non-trivial dynamical trade-off in the evolutionary process’ efficiency between exploiting the competency level of its components or the direct, pre-patterning-like encoding of the target pattern. We thus report that under realistic conditions (i.e., at moderate noise levels), an evolutionary process can be significantly more efficient when working with an agential rather than a passive material [1,94].

Notably, we explicitly omit a reward or fitness feedback from the environment to the NCAs’ uni-cellular agents’ perception, restricting the cells’ decision-making solely to the local communication of cell state updates between grid neighbors. Thus, the cells need to figure out their own communication protocol such that their single-agent decisions align with the global (multi-agent) system-level objectives of assembling the correct target pattern. These uni-cellular competencies are acquired over evolutionary time scales and can be understood as emergent behavior-shaping signaling [1].

On a more technical note, we specifically employ permutation-invariant ANNs as trainable update functions of the NCAs and successfully evolve the corresponding models to perform the here studied pattern formation tasks. We thus show that, contrary to previous assumptions [101,130], a perfect spatial resolution of neighboring cell states in an NCA is not necessary but that a mean-aggregated neighboring cell state can be sufficient for single cells to reliably contribute to the objective of a larger scale collective. Strikingly, we show that such uni-cellular agents do not even need to distinguish between their own states and the states of their neighbors to achieve this task, thus fully integrating into the tissue locally and essentially losing their individuality [93,95].

Also, in contrast to Ref. [101] and similar work, we do not start our morphogenesis experiments from a single “alive” cell but instead evolve the initial cell states of all permanent cells on the grid of an NCA, while the uni-cellular agents are constantly challenged to correct their state from developmental noise (notably, a process reminiscent of the denoising steps of Diffusion Models [131,132,133,134,135]). This allows us to explicitly distinguish between the evolutionary implications of (i) direct and (ii) multi-scale competency-based encodings of the target pattern, where we either constrain the evolutionary process to (i) only evolve the structural part of the genome, or to (ii) evolve both the structural and functional parts simultaneously. Admittedly, the choice of the structural part of the genome limits the scalability of the approach, as the size of the structural genome will grow correspondingly with the number of cells in the system. However, as occurs with biomechanical [136], biochemical [137,138] and bioelectric pre-patterning [8,94,139], the initial states of an NCA of moderate size could be seen as a coarse-grained scaffold, based on which an NCA of a potentially much higher resolution can run its multi-scale competency-based developmental program to self-assemble a high-resolution target pattern [140]. Alternatively, we suggest utilizing a Compositional Pattern Producing Network (CPPN) [120,141] to indirectly encode the initial states of all cells on the grid of an NCA, allowing such a hybrid approach to perform in silico morphogenesis at scale.

Unfortunately, it has been proven difficult, if not unfeasible, to exactly reproduce predefined target patterns reliably with the neuroevolution of CPPNs alone [142], which is why we here refrained from this approach; we emphasize, however, that gradient-based methods such as Neural Radiance Fields (NeRFs) [143] to train CPPN-like architectures might be an interesting workaround.

We find that fully evolved NCA solutions, capable of performing the morphogenesis tasks discussed above, show great signs of generalizability toward changing the system parameters, and can—without any further evolutionary optimization or training—handle noise and competency levels that are vastly different from the training conditions. Consequently, this leads to the increased evolvability of such competency-based models to changing environmental conditions: a subsequent evolutionary process can adapt a pre-evolved solution to altered environmental conditions within a handful or sometimes even a single generation. Moreover, we demonstrate that such pre-evolved NCA solutions can even quickly adapt to new, yet related problems. Specifically, we modify the objective function of our evolutionary process from the 8×8 Czech flag task to self-assemble a blue-, red-, white-, Viennese-, diagonal blue/white and blue/red flag instead, respectively. In most of these situations, an adaptation of an existing NCA solution to the new problem can be performed in significantly fewer generations than evolving the initial 8×8 Czech flag task from a randomly initialized configuration. Typically, these adaptations happen faster the larger the competency level of the NCA is, while for the direct encoding scheme (or in situations with low competency), the structural part of the genome is too dominant to allow quick adaptations by the EA. This suggests that multi-scale competency architectures allow the underlying evolutionary process to not over-train on priors, thus augmenting adaptability through a competent substrate.

We conclude that not only can evolutionary processes efficiently utilize and bring forth the intriguing multi-scale problem-solving machines of biological life but that the efficiency of such evolutionary processes, as well as the generalization abilities, evolvability, and transferability of the corresponding phenotypic outcomes, are strongly affected by the level of competency of the underlying agential material. An intriguing open question is whether this implies a positive feedback loop that enhances that quality over time. Judging from the considerable effects of scaling the competency in the here-studied still shallow multi-scale system on a rather simple in silico evolutionary process (i.e., CMA-ES [103]), it becomes increasingly evident that the vastly more complex multi-scale competency architecture of biological life cycles back and thus affects the process of evolution itself.

One of the key opportunities for future work is to apply the ideas explored here in silico to the understanding of biological mechanisms in natural systems, and to the design of new synthetic constructs via bioengineering [144,145]. It is now known that living tissues implement a kind of multi-scale competency architecture [94]. Problem-solving capacities at one scale, for example, the ability to navigate anatomical morphospace despite perturbations (embryogenesis and regeneration), rely on the communication and cooperation of subunits. One of the emerging modalities for this underlying communication is bioelectricity [89], and future work will explore the mapping from the bioelectrical dynamics that implement neural-like [32] computations within cell networks to the robust plasticity observed with respect to dynamic form and function. A closely related set of questions concerns the implications of this computational property of all cells, not just neurons, for the material on which biological evolution acts [1].

For future directions, our multi-scale competency framework is easily extendable to simulate tissue growth via cell migration or division actions proposed by the underlying ANNs of the NCA. More specifically, our framework allows for a minimal set of biologically relevant uni-cellular actions, such as cell state update, cell division, migration, cell death, and an identity operation, only constrained by the NCA spatial grid. Furthermore, the framework is capable of handling flexible ANN architectures, potentially allowing us to investigate intriguing competencies, such as active inference [146], through utilizing world model architectures [147] in a (neuro)evolutionary context. Our system, so far, has a fixed hierarchical architecture that deviates from the scale-free competency architecture of biological life with open-ended functional adaptation (where any abstraction layer becomes the basis for the next one). Thus, in future work, we aim to model precisely this behavior by introducing multiple layers of horizontal communication pathways in an NCA that the ANN-based agents can dynamically traverse in the vertical direction. Moreover, by choosing a proper fitness function related to measuring scale-invariant pattern formation [107,148], critical dynamics [149,150,151,152,153,154], or applying the free-energy principle [146,155], we are confident that we will achieve a biologically more accurate model of the scale-free dynamics and open-ended evolution of life. Such computational models could thus further quantitative studies of the communication strategies and boundaries of individual and groups of cells in an agential, potentially adversarial umwelt, with possible applications in individual and collective aging (as morphostasis defects) [156,157], or cancer research [93,94,139].