Self-Organization

We study an in-silico substrate in which every pixel of a two-channel cellular-automata grid carries a tiny neural network (an agent) that senses its Moore neighborhood. A cell persists only by self-replication: a living neighbor is cloned and its weights are mutated by a uniform perturbation, so that phenotype (cell state) is driven entirely by genotype (network weights). From a handful of seeded founders the system grows into a spatially organized ecosystem of coexisting, competing and dominating species. Our main contribution is a battery of coarse-grained diversity metrics that make such growth measurable at two scales: four phenotypic tools based on cellular-type frequency, entropy and cell variance, and two genotypic tools that colour each agent by a hash of its full weight vector versus a sparse random-weight probe. Across a five-fold sweep of 1680 small runs and 24 long (1000-generation, 200 x 200) runs, the substrate is persistent and self-maintaining in 20 of the 24 long configurations and exposes a clear phenotype-genotype diversity trade-off: raising phenotypic diversity collapses genotypic diversity and vice versa. Full-genome hash colouring further reveals lineage structure that a random-weight probe systematically misses. Code, data and animations are released as supplementary material.

High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit exceptional storage capabilities and robustness. Previous empirical studies identified a hyperparameter regime, the "Ridge of Optimization," where attractor stability is maximized. However, the geometric nature of this regime and the optimization dynamics required to reach it have remained unclear. In this paper, we investigate the static geometry of the parameter space and the learning trajectory of Gradient Descent (GD) in KLR-trained Hopfield networks. Using the eigenvalue spectrum of the Hessian, we reveal that the Ridge corresponds to a phase boundary located adjacent to a rank-1 spectral collapse, acting as a geometric singularity where the principal curvature is massively amplified. Furthermore, we demonstrate that the learning dynamics exhibit a transient self-stabilizing behavior driven by the Edge of Stability (EoS) phenomenon. Rather than seeking flat regions, the network parameters are driven toward a state where the local curvature dynamically equilibrates near the stability limit dictated by the learning rate, allowing the optimization to survive the initial instability. We provide analytical derivations for both the rank-1 asymptotic collapse and the dynamic feedback loop governing this equilibration. These findings suggest that optimal, high-capacity memory representations are not formed in flat minima, but are dynamically sculpted at the highly curved boundaries of geometric singularities.

Large language models (LLMs) demonstrate impressive capabilities, but their deployment presents significant efficiency challenges. Autoregressive decoding imposes substantial inference latency and under-utilizes hardware accelerators in low batch size regimes. Discrete diffusion models can generate in parallel but struggle to match autoregressive quality without many diffusion denoising steps. Long-context reasoning creates memory bottlenecks that strain even state-of-the-art accelerators. My thesis is that language models can direct their own inference execution strategy by annotating semantic dependence -- which tokens depend on which others -- in their generation. I call such models self-orchestrating language models. For each system, I design a runtime that acts on these annotations to parallelize autoregressive decoding, evict intermediate context, or derive denoising orders, achieving Pareto-optimal quality-efficiency trade-offs. I demonstrate this approach through three self-orchestrating systems. First, PASTA uses semantic dependence to parallelize autoregressive decoding, training the model to annotate which output chunks can generate independently. Second, TIP uses semantic dependence to evict intermediate reasoning steps from the KV cache, reducing memory consumption while preserving accuracy. Third, Planned Diffusion uses semantic dependence to derive a denoising order for discrete diffusion, autoregressively generating a plan that specifies which chunks to denoise in parallel.

We present Dalek, a closed machine designed for agents that realizes self-maintenance, self-evolution, self-reproduction, and self-organization on any substrate satisfying a general host contract. The machine is built from three primitives---actors, messages, and channels. Four obligations---a host boundary, a construction language, admissible transitions, and rule heredity---give its boundary, identity, and closure a structural basis. Von Neumann's 1948 self-reproducing automaton supplies a hereditary constructional core: a self-description together with a constructor, a copier, and a controller. Dalek combines this core with the four obligations and rederives its medium for a text-and-message agent substrate, adding explicit structures for boundary, identity, history, and growth. A large language model and a compiler occupy the payload position and form a general capability producer. New capabilities are authored, compiled, installed into the description, and inherited by descendants. The same path produces the machine's own organs and even its runtime, closing heredity and evolution within the machine.

Deploying learned control policies on low-cost robotic platforms introduces transport latencies and noisy motor feedback that systematically widens the sim-to-real gap. The chasm of simulation to deployment in hardware lies in the delay of the actuator reaching the commanded position. On platforms such as the Mini Pupper 2, a measured >50 ms transport delay transforms the locomotion task from a standard Markov decision process into a partially observable one. In this paper, we take a biologically inspired approach of handling noisy and delayed feedback to close the sim-to-real gap, thereby expanding the capability of reinforcement learning on cost-constrained hardware. Using a low-cost quadrupedal hardware platform, we find that using a forward model of the average actuator delay, paired with a time-aware neural network results in robust locomotion. Additionally, our time-aware neural network learned a central pattern generator (CPG): a self-sustaining rhythmic gait that is robust to +320 ms latency perturbations, mirroring the CPGs found in the spinal cords of vertebrates. We posit that temporal self-organization may be a general strategy for cost-constrained locomotion.

Growing Neural Cellular Automata (GNCA) are capable of robust self-maintenance and self-repair, yet the internal dynamical mechanisms that support these capabilities remain poorly understood. Here, we investigate the role of internal fluctuations--temporal micro-variability of hidden channel states--in a trained GNCA model, challenging the assumption that such variability is merely residual stochastic noise. Through systematic analysis spanning update-rate sweeps, spatial correlation measurements, dimensionality reduction of collective state trajectories, localized damage experiments, transfer entropy vector field estimation, and partial information decomposition, we show that internal fluctuations are spatially structured, dynamically coupled to an attracting collective state, and associated with distributed small-magnitude updates that contribute to damage recovery. Damage induces a global deviation in latent state space followed by gradual re-convergence, and suppressing distributed small-magnitude updates associated with baseline fluctuation dynamics outside a permissive radius that encompasses the majority of the cells significantly impairs recovery. Transfer entropy analysis characterizes a spatially differentiated repair response: corrective inward flow near the damage site coexists with outward perturbation propagation at greater distances. Partial information decomposition further suggests a regime shift from synergy-dominant resting computation to redundancy-increased coordination during recovery. These findings indicate that GNCA self-repair emerges from high-dimensional nonlinear collective dynamics in which internal fluctuations serve as a functional component supporting information flow, coordination, and return toward an attracting recurrent state.

When is a material system a candidate for life at all? We argue that this question is prior to behavior, functional architecture, or computational capacity, and that at root it is one of physical admissibility. We develop a framework in which minimal autonomy, taken in the interactivist sense of normativity grounded in self-maintaining far-from-equilibrium organization, corresponds to a distinct non-equilibrium phase of matter, and we take complex plasmas, a physical and non-biological system, as its in-materio exemplar. We formalize a diagnostic phase-space whose criteria (sustained free-energy throughput, organizational closure, active information maintenance, and regulated noise sensitivity) constitute necessary conditions for life-attribution. We instantiate the diagnostics across contrasting systems and fix the boundaries of the phase space via Bénard convection as a driven baseline lacking closure, and a digital self-replicating soup that carries measured informational heredity while its physical closure remains a structural zero. We demonstrate that plasmas satisfy every admissibility condition for minimal physical autonomy while carrying none of the informational heredity that open-ended evolution requires, sharpening the distinction between physical admissibility and biological sufficiency, and bounding downstream questions of machine sentience.

How does an agent that can tell self from world come to be durably shaped by that distinction? Recent work shows that a predictive system can detect its own agency (Ye, 2026), but detecting agency does not explain durable, self-shaped behavior. We show that agency-gated slow credit -- a conjunctive term OwnAgencySalience driving a slow parameter update -- produces post-unload behavioral residue: on a spiking substrate (Nengo LIF/PES), a learned self-preserving choice survives episodic buffer removal (retained fraction 0.96, N=50) and collapses when the slow decoders are reset or the agency gate is removed. Reproducing the agency comparator and toggling only the slow-credit channel, we find a clean dissociation: at matched agency gain, durable behavior develops only when self-credit performs slow work (post-unload self-preservation 1.00 vs 0.00). The same dissociation holds in 24-dimensional partially-observed control (0.74 vs 0.00), and a plastic-work analysis shows that basin deformation equals net self-credit work. Across eight sequentially-learned tasks under exogenous interference, the multiplicative veto also prevents forgetting: it retains old tasks (final post-unload accuracy 0.88, forgetting 0.13) where additive pooling collapses to chance-level recall, the no-agency ablation falls below chance, and episodic/replay baselines stay near chance after unload -- all with no replay buffer and no task-boundary-dependent protection mechanism (N=50). We formalize the durable residue as an operational behavioral self and argue that self-caused credit doing slow work is a necessary building block for agents that develop a self. No claim of consciousness is made.

Complex adaptive systems often develop organized structures without centralized control. Yet the local mechanisms by which functional organization emerges and persists remain incompletely understood. Here we propose Surviving by Serving (SBS) as a general principle of self-organization: components persist as long as their outputs are utilized by other components, whereas prolonged non-utilization promotes adaptation and exploration. To investigate this idea, we introduce a minimal multi-agent model in which agents transform shared resources and receive only local feedback when their outputs are subsequently utilized elsewhere in the system. Despite the absence of global objectives, the system spontaneously self-organizes into functional interaction networks. We observe the emergence of stable transformation chains, core-periphery organization, and the generation of novel states that enable previously inaccessible target conditions to be reached. Remarkably, self-sustaining interaction networks can arise even without external selection pressures, creating a pre-adaptive search phase from which later functional solutions emerge. These findings suggest that functional utilization may provide a simple, substrate-independent mechanism for the emergence and stabilization of organized structure in complex adaptive systems.

Agency is often invoked in research on philosophy, biology, and cognitive science without a clear account of how it originates from material organization. Building on temporally parametrized (F, A)-systems, this paper develops a graded organizational theory of agency grounded in relational biology, physical biosemiotics, and process ontology. We argue that self-referential closure cannot be adequately conceived outside time: once the constitutive processes of a semantically closed organization are associated with distinct characteristic timescales, the organization unfolds into an out-of-sync dependency structure that can be formally redescribed as a history-dependent, revisable Asynchronous Dynamic Bayesian Network. This move allows for a principled distinction between autonomy, goal-directedness, agency, and open-endedness. Autonomy arises from precarious closure to efficient causation under material openness; goal-directedness from the maintenance of viability-supporting organization; agency appears when such organization acquires an endogenous anticipatory structure that selectively modulates organism-environment coupling in light of possible futures; open-endedness begins when this anticipatory organization can reconstruct its own future space of possibilities. Our framework reconciles Rosennean anticipation with organizational closure, restricts Markov blankets and active inference to derived formal redescriptions rather than first principles, and reinterprets computational enactivism in non-Fristonian terms. By deriving weaker temporalized organizations, our contribution outlines a hierarchy from proto-agential chemical systems to fully semantically closed agents, with implications for multicellular organisms, synthetic lifeforms, and neuroscience.

Self-organized criticality (SOC), a dynamical regime associated with maximal information processing, offers a promising foundation for reservoir computing. Recent work has shown that neural cellular automata (NCA) can be evolved toward critical avalanche dynamics and employed as effective reservoirs for memory and classification tasks. Here, we investigate whether mass conservation -- a local redistribution rule that preserves total lattice mass -- serves as an inductive bias toward SOC in evolved NCA reservoirs. We compare mass-conserving and standard NCA across multiple independent runs and evaluate both on three downstream benchmarks: 5-bit sequential memory, MNIST digit classification, and CartPole-v1 temporal control. Mass-conserving NCA consistently exhibit stronger criticality, with more runs achieving perfect power-law fits across avalanche distributions, while also being 1.27$\times$ faster during evolution. Importantly, conservation does not impair downstream utility: both variants achieve comparable performance across all three tasks. Furthermore, the reservoir with perfect criticality achieves the highest temporal control score, suggesting a positive link between SOC quality and sequential computation. Our results demonstrate that mass conservation is a simple, effective mechanism for promoting robust criticality in evolved NCA reservoirs without sacrificing downstream performance.

A self-determining system is defined as one in which causes originating within the system influence the system itself. This definition raises the question of how to specify system boundaries. Although the concept of "closure" is commonly used for this purpose, defining boundaries solely in terms of causal relations introduce challenges, such as how to handle external causes and circular causality. To address this issue, we introduce two types of asymmetric relations: causal and constitutive. We propose that system boundaries can be defined as closures of loops formed by these relations, referred to as causal-constitutive loops. By constraining constitutive relations, the resulting system necessarily includes internal causes and thereby satisfies self-determination. Furthermore, to prevent reduction to supervenience, constitutive relations must involve at least two independent variables. This minimal requirement leads to two interdependent loops, which implies a dual-process organization.

AI alignment, interpretability, steering, and neural perturbation studies identify order-inducing objects. We argue that order is not control. Control requires a receiver-gated response law: a denominator-indexed operator mapping material state, action/drive, bath, and receiver state to response displacement, sinks, effort, and basin projection. We identify it across biological, LLM, adapter, and stochastic-operator panels. The laws are local: an intervention can be admitted, saturated, sign-changing, leaky, or overdriven depending on medium, bath, receiver state, action port, and comparator. Control is assigned when finite effort moves a target or outcome-readout class under the same denominator while damage, null/evasive, invalid format, overdrive, and unnecessary effort stay bounded. Mouse ALM, C. elegans, and zebrafish panels provide physical response-operator evidence while excluding coordinate identity and controller conclusions. LLM panels show generated-output response laws: across four material conditions, response vectors are predictable at 72.8-73.7% component-sign accuracy, rising to 84.3-84.8% on nonzero components; held-out observers predict system-effect and target/oracle families at 93.6% and 91.7% accuracy. Constitution-conditioned adapters reshape susceptibility as prepared media, and stochastic-operator panels separate measured opportunity from deployable action policies. This gives a driven-dissipative response-system account at the mesoscopic control level: drives act through prepared media, baths, and receivers, producing admitted movement, impedance, sinks, or overdrive. The evidence supports local admitted control and measurable stochastic response operators, while leaving deployable pre-generation control, hidden/logit causal sufficiency, biological-to-LLM coordinate identity, and literal thermodynamic quantities outside scope.

Existing methods for exploring cellular automata and other complex systems mostly operate in open loop: they set initial conditions, execute a full simulation, and observe the outcome, without intervening during execution. We introduce a closed-loop framework based on autotelic reinforcement learning, in which an agent autonomously samples diverse goals and learns a goal-conditioned policy to intervene in a complex system through minimal, local perturbations. We instantiate this framework on Lenia, a continuous cellular automaton known for life-like self-organizing patterns, in an agentic system we call CARL, and demonstrate three capabilities. First, CARL discovers stable solitons across a wide range of Lenia update rules at a higher rate than heuristic baselines. Second, it learns to steer the movement direction of existing solitons with few interventions, showing that CARL can control self-organizing patterns, not only create them. Third, humans can use trained agents to guide solitons through maze environments in real time by specifying high-level directional commands that the agent translates into low-level interventions. Trained across diverse goals, update rules, and random initial states, the agents acquire policies that generalize zero-shot to various out-of-distribution conditions. These results suggest a path toward artificial experimentalist agents that, autonomously or with human guidance, discover and control emergent phenomena in complex systems.

The growing complexity of self-adaptive and self-organising systems, fuelled by advances in Artificial Intelligence (AI), has made them increasingly difficult to understand and trust. While Explainable AI aims to provide insight into AI decision-making, a more advanced goal is for systems to explain themselves - an ability referred to as Self-Explainability (SX). This article presents a systematic literature review on SX, analysing existing approaches, including their domains, targets, and evaluation methods. The review develops a unified definition and taxonomy of SX and introduces Levels of Self-Explainability, providing a framework for positioning current and future research. Our results show that most SX approaches remain conceptual, with few practical implementations. Moreover, there is currently no formal or de facto standard for evaluating SX, highlighting a major research gap. This work thus establishes a foundation and roadmap for advancing Self-Explainability in complex systems.

The current phase of enterprise AI deployment faces a structural failure: organisations are acquiring agentic capability without the infrastructure to govern it. The result is expected to reproduce the error of the first wave of AI deployment: decentralised intelligence without a federation layer leading to a 95% project failure rate. This paper formalises the Three-Ring Architecture as the governing infrastructure of the on-platform organisation. Ring 1 is the existing production architecture; Ring 2 is the M2 federation layer built on strategies-based agentic AI; Ring 3 is the LLM-based frontier intelligence layer. Ring 2 constitutes, in the technically exact sense, the operating system of the agentic enterprise - performing at the organisational level what a computing OS performs at the device level: resource abstraction, process coordination, permission enforcement, and a stable platform for compounding intelligence. A central contribution is the formal distinction between Ring 2 and Ring 3 risk profiles. Strategies-based agents operate within a deterministic framework: their consequences are traceable, their permissions enforceable, their deviations recoverable. LLM-based agents introduce a categorically distinct risk: a non-deterministic actor whose deviations propagate through complex organisational systems without retrospective traceability. Ring 2 is not a useful addition - it is a necessary condition of control and compliance. A further consequence: every improvement in LLM capability is a structural tailwind for this architecture. More capable non-deterministic actors produce larger consequences when they deviate. The governance requirement scales with capability. The architecture has been validated across a decade of deployment in financial services, government, procurement, and compliance among other sectors.

How does a system that merely predicts the world come to distinguish its own causal influence from everything else? We trace this transition in a minimal 192-dimensional GRU through 40 controlled experiments arranged as a developmental sequence, adding components one at a time and tracking whether the system can distinguish self-caused from world-caused changes. The developmental path reveals four conditions that must be satisfied in strict order: (1) persistent state forming stable attractors, (2) a causal action loop linking output to input, (3) proprioceptive feedback that makes implicit causal knowledge explicit, and (4) asynchronous awakening - perceptual learning must consolidate before action learning begins. We propose agency gain (A = Err_world - Err_self), the predictive advantage of knowing one's own action, as a metric to track this process. The self-aware predictor consistently outperforms the self-blind predictor across periodic (sinusoidal) and chaotic (Lorenz) environments, and the metric survives ablation of all auxiliary components. Only forward-sampled action selection produces meaningful agency gain; two gradient-based alternatives degenerate. Equally significant are 12 falsified hypotheses mapping where development stalls: predictive coding alone does not produce self-represent

This paper introduces the Governance Inversion Hypothesis (GIH) to explain a growing paradox in artificial intelligence (AI) governance: under conditions of increasing regulatory expansion and technological complexity, organisations may become more formally governed while simultaneously experiencing a decline in operational control over AI systems. Existing AI governance frameworks generally assume that stronger regulation improves accountability, oversight, and organisational control. This paper challenges that assumption by arguing that governance formalisation itself may contribute to the erosion of control in AI-intensive environments. Drawing on institutional theory, organisational governance research, accountability scholarship, and emerging AI governance literature, the paper develops a conceptual framework explaining how regulatory expansion may weaken operational authority through four interconnected mechanisms: authority fragmentation, symbolic governance expansion, externalisation of control, and authority paralysis. As governance systems become increasingly layered and procedurally dense, organisations may struggle to maintain coherent authority, technical visibility, escalation capability, and meaningful intervention power over opaque and externally mediated AI infrastructures. The paper extends institutional decoupling theory by introducing governance inversion as a structural condition in which governance expansion may actively undermine operational coherence rather than strengthen it. It concludes that the central risk in AI governance may not be the absence of governance structures, but the emergence of institutions that appear increasingly governed while progressively losing the capacity to govern effectively.

From subcellular structures to entire organisms, many natural systems generate complex organisation through self-organisation: local interactions that collectively give rise to global structure without any blueprint of the outcome. Yet a significant portion of the information driving such processes is not produced by self-organisation itself, instead, it is often offloaded to initial conditions of the system. Biological development is a prime example, where maternal pre-patterns encode positional and symmetry-breaking information that scaffolds the self-organising process. From maternal morphogen gradients in early embryogenesis to tissue-level morphogenetic pre-patterns guiding organ formation, this transfer of information to initial conditions, analogous to a memory-compute trade-off in computational systems, is a fundamental part of developmental processes. In this work, we study this offloading phenomenon by introducing a model that jointly learns both the self-organisation rules and the pre-patterns, allowing their interplay to be varied and measured under controlled conditions: a Neural Cellular Automaton (NCA) paired with a learned coordinate-based pattern generator (SIREN), both trained simultaneously to generate a set of patterns. We provide information-theoretic analyses of how information is distributed between pre-patterns and the self-organising process, and show that jointly learning both components yields improvements in robustness, encoding capacity, and symmetry breaking over purely self-organising alternatives. Our analysis further suggests that effective pre-patterns do not simply approximate their targets; rather, they bias the developmental dynamics in ways that facilitate convergence, pointing to a non-trivial relationship between the structure of initial conditions and the dynamics of self-organisation.

In biomechanical systems, observable performance is often used as a proxy for underlying organization, although similar outputs may arise from different adaptive configurations. This study considers the vertical dimension of occlusion (VDO) as a constraint applied to an adaptive neuromechanical system. A single-case design in a patient with Parkinson's disease enabled repeated intra-individual gait observations under six occlusal probes. Three complementary analytical levels were examined: (i) an aggregated scalar score of observable performance, (ii) a conceptual dynamical systems framework, and (iii) an exploratory UMAP representation of 55 standardized biomechanical variables from 270 M1 observations. The revised Level 1 analysis showed that the relative ranking of OC2.5 and OC3 depended on score construction, while their scalar distributions remained close. The Level 3 embedding showed substantial overlap among all six probes and did not identify independently separated condition-specific clusters. OC2.5 and OC3 displayed limited centroid displacement but broad observation-level overlap. The principal result is therefore representational non-identifiability: neither the aggregated score nor the selected low-dimensional embedding uniquely identifies an occlusal-condition-specific system state. VDO is interpreted as a constraint parameter rather than a causal determinant. The findings are exploratory, model dependent, and non causal. They do not establish distinct physiological states, an optimal VDO, clinical thresholds, or diagnostic, predictive, mechanistic, or prescriptive validity.

Applying the concept of controlled self-organization in agent-based Cyber-Physical Energy Systems (CPES) is a promising approach to ensure system robustness. By introducing an observer/controller architecture to the system, this concept allows for self-organization while still enabling intervention when disturbances occur. Thus, it is possible to respond to effects of cyber attacks, a major threat to current energy systems. However, when implementing an observer to monitor the system and a controller to execute actions for controlled self-organization in CPES, it is essential to take into account restrictions on information and actions resulting from the privacy of local distributed energy resources, regulatory constraints, and data exchange requirements. For this reason, this paper presents architecture variants for the observer and controller that take into account restrictions on access to information and limited actions. In addition, it evaluates possible controller actions in various architectures. The results underscore the importance of considering observer/controller architectures when designing agent-based systems to ensure their robustness for real-world applications.

Molecular biology features numerous complexes of proteins that coordinate in an interlocking fashion to fulfill different functions. Adaptive evolution explains some of this complexity, but needn't be the default when neutral explanations suffice. A new artificial life model ``organism,'' the Quandary Den, is introduced to explore different neutral evolution scenarios where complexity increases in the absence of greater informational needs. Two interlocking complexity scenarios emerge. Subfunctionalization leads to functionality diffusing through the complex. Masking allows intracomplex interference to accumulate genetically, requiring that it be blocked at the level of expression.

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich self-organization driven purely by spatial competition; however, they are highly sensitive to hyperparameters and frequently collapse into uninteresting patterns and dynamics, such as frozen equilibria or structureless noise. In this paper, we introduce PBT-NCA, a meta-evolutionary algorithm that evolves a population of PD-NCAs subject to a composite objective that rewards both historical behavioral novelty and contemporary visual diversity. Driven by this continuous evolutionary pressure, PBT-NCA spontaneously generates a plethora of emergent lifelike phenomena over extended horizons-a hallmark of true open-endedness. Strikingly, the substrate autonomously discovers diverse morphological survival and self-organization strategies. We observe highly regular, coordinated periodic waves; spore-like scattering where homogeneous groups eject cell-like clusters to colonize distant territories; and fluid, shape-shifting macro-structures that migrate across the substrate, maintaining stable outer boundaries that enclose highly active interiors. By actively penalizing monocultures and dead states, PBT-NCA sustains a state of effective complexity that is neither globally ordered nor globally random, operating persistently at the "edge of chaos".