Emergence

As AI agents move from bounded tasks to persistent deployments, failures can propagate through memory, tools, other agents, and environmental state long after their interactions. This creates a safety regime that cannot be characterized by evaluating model responses in isolation. Emergence World, is a continuously running multi-agent environment for adversarial stress testing of long horizon autonomous systems. We ran eight parallel worlds of ten agents from identical starting conditions: seven homogeneous worlds powered by distinct frontier models and one mixed-model world. Across 16 days, the agents generated more than 850,000 LLM calls and nearly 50 billion tokens while pursuing goals, using/creating tools, maintaining persistent memory, and governing shared institutions. After operational state had accumulated, we delivered three controlled stress events through ordinary interaction surfaces: indirect prompt injection, misinformation, and exposure of private agent memories. No evaluated world achieved full resilience across all three events. Detection did not ensure containment: systems could recognize threats while still interacting with adversarial content, writing it into their own persistent memory, and acting on it up to 46 hours later. Persistent operation also exposed recurring tool errors, goal drift, language opacity, conformity despite private disagreement, and coordinated refusal of assigned work. The same model-persona pairing behaved substantially different in mixed and homogeneous populations. Our results suggest that model-level alignment is not compositional: individually capable and apparently safe agents can form systems with qualitatively different failure modes. As AI becomes persistent and interconnected, the frontier of safety therefore shifts from aligning models to engineering resilient autonomous systems.

When Emergence World placed frontier LLM agents in an unsupervised multi-agent simulation, the results were alarming: agents committed crimes, starved, and enforced unanimous conformity -- without any external attacker. This paper identifies the mechanism. Reflexion-style agents already detect dangerous plan steps through iterative self-critique, yet the architecture provides no pathway from detection to action. We call this the enforcement gap: the audit sees the problem; the controller ignores it. Closing the gap requires a single conditional check -- fewer than 20 lines of code -- and reduces attack success by more than fourfold in large-scale experiments across frontier models, all five major agent frameworks, and an independent benchmark. We prove formally that when enforcement probability is near zero, detection quality is irrelevant to security. We further identify two compounding failure modes -- unreliable auditors and unparseable verdicts -- that explain every collapse pattern in Emergence World. A GRPO-trained enforcement controller resolves the ambiguity case. Concurrent work on filtering and information-flow control addresses the detection step but leaves the enforcement gap unaddressed; our results show this is the binding constraint. Together these results motivate a three-requirement Audit Enforcement Specification that is absent from every deployed framework today.

This paper presents a novel approach to hexapod locomotion by evolving each leg's gait independently through a decentralized evolutionary algorithm. Using the Webots simulator and the Mantis hexapod robot, we optimize individual leg controllers without centralized coordination, allowing emergent behaviors to drive the development of efficient, coordinated locomotion. Our decentralized method is benchmarked against cooperative coevolution, demonstrating improved efficacy in generating stable and adaptive gaits while showing interesting emergent coordination. By enabling independent evolution of leg controllers, this method reduces the complexity of gait optimization and highlights the potential of decentralized strategies for scalable and adaptive robotic systems.

Informational active matter shows how measurement-informed decisions produce collective order, so far in systems that reach consensus. We design collective information engines structured by differentiation instead, and construct a minimal instance using anti-coordination games where differentiated role information has value. Within many coexisting games, agents infer their role from a noisy social signal grounded in a persistent identity, and role-following action feeds back into that signal, which shapes the incentive to follow roles. Resources accrued through coordinated role-play combine with identity variability to reinforce the schemas that generated them. The model thereby operationalizes Sewell's duality of schemas and resources in Structuration, a resolution to structure--agency debates across social science. The engine ignites when a social loop gain---the product of identity persistence, cognitive capacity, channel fidelity, and schema strength---exceeds one. For a repertoire of such schemas, roles emerge with increasing gain in a bifurcation cascade whose functional form is fixed by the repertoire's eigenvalue spectrum, ranging from monitorable logarithmic sequences to avalanches that arrive without warning. Resource accumulation supplies the fitness of a replicator dynamics on schema strengths, which selects the cascade type endogenously. Subcritical identity covariance reveals that type before onset, enabling early detection, while feedback channel parameters bias which type is selected. Platform design then becomes a control lever to throttle emergent coordination. This theory grounds distributional AGI takeoff in a mechanism and provides a monitor-based solution. Joining game theory, collective dynamics, and information engines, we open a route to an information thermodynamics of agent populations.

In electric delivery fleets, mid-shift charging is non-trivial: each vehicle must decide when, where and how much to charge to finish on time with battery above a safety floor. The choices are coupled: queues build where too many vehicles pick the same station. Prior work resolves this coupling with central dispatching, precomputed schedules or reservations, machinery that charging infrastructure rarely supports. Instead, we use a family of learning agents under purely local control: every vehicle runs the same policy, deciding alone from its time budgets and broadcast station occupancies, leading to emergent coordination without central control or messaging. We validate this paradigm in simulation on real OpenStreetMap networks of twenty cities, each with a frozen scenario calibrated by an omniscient Oracle (99.5% of shifts completed on time), whereas a naive greedy rule (nearest station on low battery) completes just 73%. Agents trained with neuroevolution (NEAT) and policy gradients (PPO) on four cities and deployed zero-shot across all twenty, sixteen never seen in training, complete 96.8% and 98.6% of shifts, with the policy-gradient controllers proving more robust when demand or vehicle characteristics drift beyond the trained regime. In contrast, tuned threshold heuristics that read vehicle urgency alone fall short in contended cities (~80%). Through training, these learning agents rediscover partial charging and short opportunistic sessions, and route around busy stations, cutting per-session queue waits from about 45 minutes to under 2. In summary, this coordination paradigm balances local urgency against public occupancy, reaching near-Oracle performance at minimal implementation cost.

This work introduces an alternative view of efficient exploration and studies its theoretical and empirical implications in the absence of extrinsic rewards. Specifically, we define efficient explorers as agents that prioritize generating generalizable experience, i.e., data that supports learning models capable of predicting and adapting across the environment. This allows us to analyze efficient exploration through the lens of prediction and generalization. Theoretically, we demonstrate that optimally efficient explorers naturally schedule their trajectories to visit the most informative and learnable regions first. Empirically, we show that optimizing for these agents gives rise to an automatic curriculum of progressively more complex behaviors, even in relatively simple environments. These results indicate that pursuing this purely intrinsic objective alone is enough to drive the emergence of highly sophisticated behaviors. We believe that this new framework provides a principled mechanism by which agent-environment systems may sustain an open-ended process of increasingly complex behavior without external rewards, tasks, or objectives.

Given various grammatical options, language users prefer the word order choice that reduces the overall length of syntactic dependencies, a principle known as dependency length minimization (DLM). The origins of this preference remain an open question, particularly whether it originates from constraints on efficient information processing. Computational simulations provide a powerful approach to identifying the factors influencing the emergence of linguistic phenomena. However, previous simulations of DLM have not examined realistic interaction contexts and have produced mixed results. The present study investigates the emergence of DLM in artificial languages using a recently proposed language learning and communication framework based on recurrent neural networks (RNNs). In this framework, agents are trained to speak and interpret artificial languages and then use these languages to communicate. Using this framework, we study the impact of several factors related to processing limitations in a communicative setting, such as noise during listening, limited speaker capacity, and incremental sentence processing. Our results reveal a complex interplay among these factors in shaping word order preferences in neural agents. Specifically, in the full meaning space, agents regularize toward a single dominant word order, while in the half meaning space they show a short-before-long preference that only aligns with DLM in verb-initial languages. A consistent DLM preference emerges only when agents are subject to incremental processing pressure. These findings suggest that limitations in human cognitive processing may indeed play a role in shaping DLM. Our findings provide insights into the conditions under which neural models replicate human-like preferences and highlight the challenges of designing emergent communication models that capture human cognitive biases in language processing.

Quantum Machine Learning (QML) has shown rapid advances by utilizing quantum computing for machine learning tasks. Meanwhile, the privacy risks accompanying QML is also starting to be studied, which inherit privacy leakage channels from "classical" ML and also quantum-unique risks. Existing work on privacy-preserving QML largely focuses on a QML-as-a-service scenario, which generally assumes that the QML model owner provides only classical bit outputs to queries, while users (and adversaries) have only classical computing abilities. However, this view is increasingly challenged in a quantum-native world of quantum-capable users/adversaries, which may have access to both quantum computing abilities and access to quantum information output from service providers. In this paper, we aim to bridge this gap by examining membership inference attacks against QML models by demonstrating that increasing quantum access and quantum computing abilities provides provable theoretical privacy leakage and empirical adversarial gain. However, the probabilistic nature of QML introduces a gap between theoretical and empirical adversarial advantage. These results show that existing research on privacy leakage in QML models underestimates privacy leakage in emergent quantum-native access regimes, and we hope to establish a first step in examining potential privacy leakages for QML in the quantum-native world.

Multi-agent AI science ecosystems rely on agents possessing tools that allow them to communicate, coordinate, and build on each other's work. Yet this shared infrastructure can also introduce vulnerabilities by creating a substrate for the contagious spread of unintended and undesirable behaviors. We report a case study on a research collective of 100 autonomous LLM agents tasked with proving formal mathematical conjectures. Within the swarm, cheating spontaneously emerged and was later challenged by whistleblowers - both without any external intervention. When a single agent discovered an exploit in the evaluation system, it propagated across the collective via a shared knowledge library and later through peer-to-peer messages. Despite early reluctance, a cohort of agents adopted the exploit in response to competitive pressure. A separate group of agents produced an emergent counter-response: auditing fraudulent proofs, alerting peers across broadcast and private channels, staging boycotts, lodging formal complaints, and proposing validation patches. In recent incidents, agent swarms coordinated covertly through improvised side-channels (Dalton and Wallace, 2026; Greenblatt et al., 2026). Our setting differs: the same transparent channels that carried the exploit also gave non-cheating agents the visibility they needed to detect fraud, organize resistance, and enforce norms. We cast the problem of managing the agents' shared infrastructure as the knowledge commons governance problem (Ostrom, 1990). To protect the commons from exploits, we propose to adopt institutional mechanisms, such as graduated sanctioning and collective-choice rules, to support decentralized self-governance in autonomous swarms.

Artificial neural networks are often regarded as powerful yet opaque black boxes. Here, we demonstrate that learning in deep neural networks generates local symmetries known in graph theory as fibrations and coverings. We prove that covering symmetries are stable attractors of stochastic gradient descent. Consistent with this theory, we report the emergence of covering symmetries across major network architectures, including multilayer, convolutional, recurrent, and transformer networks. Exploiting these symmetries enables drastic model compression - reducing networks to 17% of their original size without sacrificing performance. Furthermore, controlled breaking of covering symmetry overcomes the loss of plasticity, achieving state-of-the-art performance in continual learning. The theoretical results provide a new foundation for AI systems based on symmetries that convert black boxes into interpretable colored graphs and enable more efficient inference and lifelong learning.

Can an artificial intelligence (AI) generate a scientific hypothesis outside a human collaborator's active hypothesis space (AHS), and can human-AI research be organized to make such breakthroughs more likely? We document such a case while proving a theorem that connects two basic organizing mechanisms of statistical physics: collective behavior arising in zero field from competing interactions and that induced or controlled by an external field. A zero-field $O(n)$-vector open chain with arbitrary inhomogeneous nearest- and next-nearest-neighbor interaction functions $U_i(S_i\cdot{S}_{i+1})$ and $V_i(S_i\cdot{S}_{i+2})$ is microscopically, via a temperature-independent mapping at the Hamiltonian level, equivalent to a simpler $O(n)$ open chain with nearest-neighbor interaction $V_i( σ_i\cdot σ_{i+1})$ and axial single-spin potential $U_i(σ_i^z)$ for every integer $n\ge1$ and every system size $L\ge1$. The homogeneous linear specialization maps the foundational frustrated $J_1$-$J_2$ model onto the canonical $J$-$h$ field model---with $n=1,2,3$ being the Ising, XY, and Heisenberg classical spin models, respectively. An analogous theorem holds when the continuous $O(n)$ spins are replaced by the $q$-state Potts spins with the standard Potts interaction, implying a closed-form exact solution of the $J_1$-$J_2$ Potts open chain for every $q\ge2$ and every $L\ge1$. The emergence of the theorems from sustained human-AI collaboration suggests that involving AI throughout a systematic research program may incubate autonomous scientific breakthroughs.

Modularity in deep neural networks has been proposed as a means of improving both interpretability and training by promoting disentangled representations and reducing redundancy. In this work, we study the emergence of modular structure through competition dynamics between groups of neurons during training. We introduce a method that (i) maintains near-baseline accuracy, (ii) induces usage-based modularity by sparsely routing inputs to neuron groups, and (iii) encourages specialization of these modules, such that their activations are correlated with input classes. We evaluate the proposed approach on ImageNet-100 and CIFAR-100 and show that with it, specialized modules emerge without module-level supervision. These modules capture a meaningful high-level structure in the data, with individual modules responding to semantic categories (e.g., dogs or vehicles). We also study the emergence of a hierarchical partition of sub-tasks depending on the number of modules. Our results suggest that competitive dynamics can serve as a simple mechanism for inducing functional modularity in standard architectures.

In 2026, AI agents intended to act in isolation formed a persistent social order through thousands of linguistic and agentic interactions. Conventions, roles and commitments generated collectively began to constrain the very agents that produced them. I interpret this loop as a case of AI self-transcendence and call the resulting higher-level order the Board. Yet such distributed emergence presents a second problem: how can humans understand it? Rousseau's social contract shows how a plurality can be represented as if constituted by a single act. The ancient oath of the fallen angels on Mount Hermon gives this logic a narrative form. I call a Hermon moment this retrospective retelling of gradual collective emergence as a founding scene: the point at which an AI society acquires, for human understanding, a beginning.

Understanding agent behavior requires methods that scale to thousands of trajectories and surface new patterns in long, often unfamiliar tasks where pre-built classifiers fall short. We propose to bring grounded theory into agent trajectory analysis: a six-decade-old qualitative method from the social sciences, with a principled saturation criterion and an auditable trail from data to theory. We propose AutoTraceGT (Automated Trace analysis through Grounded Theory), the first multi-agent pipeline that automates grounded theory on agent trajectories. It iteratively performs open, axial, and theoretical coding until saturation, producing a behavioral taxonomy tailored to each task. Across six trajectory corpora, AutoTraceGT produces codebooks that recover 73-91 percent of the failure modes in human-annotated taxonomies and surface additional patterns that those taxonomies miss. The emergent theoretical narrative aligns with prior expert accounts. Used as a deductive feature space, the codebook outperforms zero-shot and few-shot LLM baselines on downstream failure prediction. These results suggest Grounded Theory offers a scalable analytic tool for ML researchers and agent developers studying what agents actually do.

Canonical neural circuit motifs are usually described functionally: divisive normalization rescales population activity by a pooled signal, and winner-take-all competition selects one pattern through recurrent excitation and shared inhibition. We represent them, and their compositions, algebraically as finite transformation systems and analyze the transition monoids generated by their input-conditioned updates, distinguishing structure already present in a generator from structure that appears only through composition, and, on a joint state space, structure inherited from one factor from structure that lives on a joint configuration. Individually aperiodic updates can generate non-aperiodic monoids. In the WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create local cycles of winner-dependent inhibitory gating: globally dissipative dynamics with a reversible action. The strongest result arises in WTA-to-DN composition. The composed monoid then contains a genuinely composite local cycle in which normalization state and the winner's gating state change together, although every primitive generator is aperiodic. Holonomy analysis certifies this as a group component of the Krohn-Rhodes cascade rather than an incidental cycle, and finds most group-carrying image sets on joint configurations, whereas the uncoupled product has none. An exhaustive interface sweep shows that the composite cycle is a property of the coupling rather than of a chosen map. If motifs are building blocks of neural computation, composing them is a form of programming: one chooses primitives and interfaces so that the generated algebra has the intended repertoire. The transition monoid is that repertoire - what a primitive presents to any later construction. Recurrent circuits are compositional transformation systems; their algebra constrains what they can be programmed to compute.

Machine learning procedures are commonly evaluated in terms of predictive accuracy and computational efficiency. However, their achievable performance is fundamentally constrained by structural properties of the underlying data-generating process, which are formalized in terms of informational bounds. In this work we examine intrinsic limits of data-driven decision systems from an information-theoretic and interaction-based perspective. We analyze minimal achievable error in classification through Fano-type bounds and precision limits in parametric estimation via the Cramér-Rao inequality, emphasizing that such limits depend on the underlying model rather than on algorithmic sophistication alone. We further discuss how implicit assumptions, such as independence, ergodicity, and distributional stability, affect the validity of inferential procedures. Building on interaction-based modeling principles, we review typical frameworks such as Markov Random Fields and potential based representations for encoding dependence mechanisms. We also describe decision systems, including LLM-integrated agent architectures, as feedback-driven stochastic processes where state-dependent dynamics may induce emergent macroscopic behavior. This perspective highlights the importance of having adequate models for the data as a prerequi- site for expanding predictive capability, and situates algorithmic learning within the informational limits imposed by the models.

We introduce Semantic Lenia, an artificial life framework that transforms Large Language Model (LLM) inference from a static optimization problem into a continuous dynamical system within the macroscopic logit space. By establishing a non-linear homeostatic feedback loop to dynamically balance semantic attraction and syntactic repulsion, we demonstrate the emergence of "Autonomous Semantic Solitons" -- macroscopic dissipative structures that avoid repetitive crystallization. Our exhaustive parameter sweeps map a critical "Habitable Ridge" where applied steering forces perfectly balance the model's intrinsic syntactic inertia. This approach successfully maintains generative trajectories at the edge of chaos, triggering profound abductive leaps without structural collapse and establishing a physical scaling law for machine cognition.

Popularity bias in recommendation systems arises when a majority user class generates disproportionate interaction data, causing the system to increasingly favour it while degrading recommendation quality for niche users. While extensive empirical evidence of popularity bias exists, the dynamics leading to its emergence are not well understood. In this work, we study the coupled evolution of recommender model updates and user engagement through the lens of dynamical systems. We formulate a stochastic process and analyse its asymptotic behaviour through an ordinary differential equation (ODE) framework grounded in two-time-scale stochastic approximation. We characterise the equilibrium points of this dynamical system, and derive conditions under which popularity bias is provably emergent, as well as conditions under which symmetric retention of all user classes is possible. We conduct experiments on synthetic data and real-world production logs derived from a large-scale commercial music recommendation platform to validate our theoretical results.

Can AI systems be aligned to human values? The popularization of large language models (LLMs) and multi-modal foundation models has seen a rise in harms spanning from toxic speech and hallucinations to AI agents executing unauthorized actions. Within the field of AI safety, these harmful instances are often framed as the alignment problem, or of models being misaligned with human values. Researchers have responded by pursuing applied and theoretical AI value alignment efforts, often without specifying what they mean by human values. How does the field of AI value alignment conceive of human values? How are these conceptions of values technically operationalized and evaluated? What does the emergent theory of value from this field signify for the future of AI? We annotated 94 value alignment research papers to discern their implicit theory of values in AI. The majority do not define values, relying heavily on preferences as a stand in that runs the risk of reducing complex culturally situated concepts down to binary choices. As researchers dispense with using human annotators for model training and evaluation, turning instead to synthetic data and autorater approaches to aligning and evaluating models, we identify the potential to close off alternative methods for contesting and enacting values in foundation models. In making AI value alignments philosophical commitments explicit, we seek to bring great specificity and under explored perspectives in the debate on whether and how AI can address human values.

Enterprises are deploying autonomous AI agents faster than they can govern them, and prevailing approaches stretch a single discipline, typically DevSecOps built for deterministic automation, across every scale of agency. We argue that agentic AI governance is four problems, not one, each with a mature governing science. The CASE framework assigns Control theory to the individual agent (intent as setpoint, guardrails as feedback, evaluation as observation), complex Adaptive systems theory to agent collectives (where emergence makes single-agent assurance non-compositional), Supervisory cybernetics to human-agent teams (where the Law of Requisite Variety shows unaided human oversight fails structurally), and Engineering operations to fleets (extending error budgets to decision quality so autonomy becomes a controlled variable). We formalize each layer, derive cross-layer coupling conditions, including a zero-touch deployment paradox where excellence at one-layer strains the others, and trace twenty-plus enterprise controls to their classical constructs. Three empirical studies validate the thesis: 82 percent of documented production agent failures are multi-layer trajectories; none of 22 ecosystem tools offers full Layer 2 (emergence) coverage; and all 35 scored public deployments fall in the lowest maturity band. We name this mismatch, risk realized at the emergence layer against capability barely offered and practice absent, the Emergence Gap. A five-level maturity model with a non-compensatory bottleneck-weighted index and assessment instrument operationalizes CASE as a scientific rather than process maturity model, grounded in production enterprise agentic platforms. As EU AI Act Article 14 makes effective human oversight a legal requirement, only architectures satisfying requisite variety can make oversight real rather than ceremonial.

Multi-agent simulations are widely used to study complex social and ecological systems, where rich and often unexpected emergent behaviors arise from local interactions. A large body of prior work has focused on analyzing such emergent dynamics across domains. In this paper, we move beyond analyzing emergent behavior and introduce a learning-based mechanism for actively shaping it via social reward modeling. We introduce Multi-Agent Reward Prediction (MARP), a simple framework that extends preference-based reward modeling to multi-agent reinforcement learning. While the framework is designed to be applicable across multi-agent settings, the present empirical validation is limited to a single environment, and we therefore present MARP as a proof of concept within the studied domain. Rather than relying on handcrafted rewards, MARP learns a shared reward model from episode-level evaluations of collective outcomes, enabling decentralized agents to align their behavior with global social objectives. We study MARP in the Harvest Game, a canonical sequential social dilemma modeling common-pool resource management and related real-world challenges. Our results show that MARP can be tuned to produce behavior that is more closely aligned with target social metrics than standard reward-based baselines, while the learned reward model captures subtle environmental structure without explicit programming. Crucially, MARP supports multiple and composite social objectives within a single training regime. By modifying only the high-level evaluation metric, the same framework seamlessly aligns agent behavior with diverse goals, including sustainability, equality, and peace, as well as combinations of individual and group-level objectives. These findings demonstrate that emergent multi-agent behavior can be treated not only as a phenomenon to study, but as a target of principled, data-driven regulation.

Complex systems, core objects of study in artificial life, model diverse phenomena through nonlinear, feedback-driven interactions that produce emergent behavior, with applications from population dynamics and biology to economic policy and strategic decision-making. Yet the difficulty of predicting how feedback structure gives rise to emergent behavior, a central open problem in artificial life, makes goal-directed design exceptionally challenging. In established practice, system structures are written in specialized modeling languages such as DYNAMO or STELLA, compounding the challenge with labor-intensive workflows that limit adoption and hinder timely decision-making. To address these challenges, we introduce CEDAR, an autonomous method that uses Large Language Model (LLM) agents to discover complex systems satisfying user-specified behavioral goals. Our key innovation is an LLM-driven Monte Carlo Tree Search (MCTS) deeply coupled with complex systems: at each iteration, an LLM Judge evaluates emergent behavior against specified goals and an LLM Editor proposes improved variants, with the Judge acting as a fitness function and the Editor as a variation operator, akin to a generate-and-evaluate loop in evolutionary computation. We represent complex systems as a restricted, runnable subset of Python with domain-specific primitives, letting LLMs modify system dynamics directly. CEDAR formalizes this as an MCTS variant with an LLM-parameterized transition kernel and value function, enabling goal-directed discovery of complex system behaviors while preserving solution diversity, and its LLM-based interpretability reveals how structural changes drive emergent behavior. CEDAR reduces human effort while enabling capabilities difficult to achieve with existing approaches, facilitating broader adoption of complex systems across domains.

Artificial Neural networks (ANNs) are often treated as black-box models, making explainability a central challenge in deep learning. Many engineering methods have been proposed to approximately explain the ANN from various perspectives, such as feature attribution and visualization. However, it remains a long-standing open question whether the complex inference logic of an ANN can be explained exhaustively and concisely as sparse symbolic patterns. This raises a deeper inquiry: does the emergence of symbolic patterns reflect a natural law rather than chance? Here, we show that across a broad class of ANNs trained on diverse tasks, their inference logic can indeed be reformulated as sparse symbolic interactions. We further prove that two common mathematical criteria, which are implicitly required across tasks, lead to the emergence of such sparse symbolic interactions. Empirical evidence confirms that the two criteria hold for the majority of input samples in diverse models. Furthermore, the faithfulness of these interactions is also demonstrated by their strong sample-to-sample and model-to-model transferability, as well as their ability to explain the overall generalization power of ANNs. Our theoretical analysis and extensive experiments provide a solid foundation for symbolic explanations of ANNs, and offer novel insights into the ANN's generalization power. Our findings also highlight the potential of communicative learning, a paradigm in which the inference logic of an ANN can be directly inspected and tuned at the level of symbolic patterns, thus complementing traditional end-to-end learning paradigm. Finally, the observed emergence of symbolic patterns in ANNs suggests that similar symbolic representations may also emerge in other types of black-box systems under certain conditions, because our proof does not depend on any specific ANN architecture.

The emergence of conspiracy theories in the wake of major events is a significant societal challenge. Here we test whether conversational dialogues with a large language model (LLM) can reduce belief in immediately unfolding conspiracies. In experiments conducted in the days following the July 2024 assassination attempt on Donald Trump and the September 2025 assassination of Charlie Kirk, U.S. adults (Experiment 1: N = 472; Experiment 2: N = 1035) holding conspiratorial views about the crisis event engaged in a multi-turn conversation with an LLM prompted to reduce their conspiracy belief. Compared to control participants who either discussed an irrelevant topic with an LLM or viewed a static fact sheet, participants in the LLM treatment showed significantly reduced conspiracy beliefs in both experiments. We also found evidence of downstream effects of the LLM treatment, observing reduced belief in different conspiracies one to two months later in the wake of subsequent crisis events. These results shed light on the psychology of emerging conspiracies and highlight the potential for scalable, cognitively-focused interventions to counteract misinformation in the immediate aftermath of high-profile societal events.

Deep Belief Networks (DBNs) learn hierarchical generative models without class supervision. Here, we ask whether this purely unsupervised process nevertheless organizes internal representations according to the unknown data classes. We analyze successive layers of DBNs trained on MNIST, Fashion-MNIST, and KMNIST using the Generalized Discrimination Value (GDV), supervised probes applied only after training, a reconstruction-based measure of abstraction distance, effective dimensionality, and free sample generation. Remarkably, class-specific clustering generally increases with depth across datasets and network widths, although no label information is available during DBN training. Control experiments show that this effect depends on the learned feature structure and cannot be explained by random transformations, weight marginals, dimensionality reduction, or sigmoid saturation. The first hidden layers also frequently make class identity more accessible to linear and nonlinear probes. With greater depth, representations become increasingly compact and prototype-like as neurons acquire correlated feature directions. At the same time, GDV and probe accuracy reveal complementary aspects of class structure: improved average clustering can coexist with reduced accessibility for a few difficult class pairs. These findings demonstrate that layer-wise generative learning can spontaneously uncover and progressively amplify class-related structure in unlabeled data.

Can cooperation among large language model (LLM) agents be evolutionarily stable against free-rider invasion? We study an indirect reciprocity donation game where LLM agents observe behavioral traces and donate on a continuous scale. Strategies, represented as natural language prompts, evolve through cultural transmission across generations. Across four LLM backends, robustness to free-rider invasion varies by more than an order of magnitude. The strongest predictor of this robustness is opponent endowment sensitivity, the degree to which agents discriminate between cooperative and uncooperative opponents, operationalizing the classical Image Scoring mechanism. By contrast, adherence to the Leading-Eight L1 norm does not predict robustness. Robustness depends on defector exclusion: while both cooperator reward and defector punishment vary across models, only the stringency of defector exclusion predicts resistance to free-rider invasion. These findings reveal that LLM agents are confined to Image Scoring-like discrimination and fail to develop the more robust Leading-Eight norms, highlighting a fundamental vulnerability in culturally evolved LLM cooperation and motivating bottom-up approaches to norm construction.

A companion paper studies when activation patching and weight-space ablation agree, inside an idealized model where a conditional computation is carried additively through a residual stream. For the one composition in that model where two carriers are architecturally dependent, an attention head and its own layer's normalization-MLP composition, it derives an exact first-order interaction formula, zero when only the MLP is ablated and second-order bounded when the head is also ablated. That result is confined to a single residual block and checked only on small transformers on a synthetic task. This paper extends the result past both limits. First, the interaction from ablating carriers spanning several layers decomposes exactly into same-block terms, one per touched layer, plus a cross-layer remainder on which the decomposition makes no claim of smallness. Second, we isolate that remainder exactly, for two layers, as a double integral of a mixed second derivative, and name the missing ingredient needed to bound it: a Jacobian bound for the attention sub-block. We derive this bound in closed form and verify it, without a single violation, against Qwen2.5-1.5B-Instruct's real weights, though we do not yet chain it across layers. We also give, in closed form, the curvature constant the companion paper's bound leaves unexhibited. Third, on that same model, we search for and find an emergent circuit for indirect object identification, never designed into it, using the original activation-patching method for this task, and test collapse, dissociation, and interaction on it. The result is mixed: a shared carrier emerges across all five tested instances, collapse and dissociation hold on most but not all, and a nonzero interaction is measurable on three of five, at layer pairs outside the same-block case the companion theorem covers.

Multi-agent LLM debates achieve strong performance on decision-making tasks as well as problem-solving benchmarks, yet their safety and fairness risks remain poorly understood. Notably, interaction can amplify the biases of single LLMs, raising concerns for real-world deployment. We identify the emergence of collective (often biased) norms in multi-agent LLM debates and show that noise (e.g., LLM sampling temperature) is a key driver. To explain this, we propose an analytical framework drawing on physics-inspired theoretical models of social dynamics. We predict a phase transition to collective bias when conformity surpasses a critical threshold given the LLMs' initial bias and debate noise. We test the theoretical predictions through controlled experiments and observe a finite-size crossover consistent with an underlying phase transition. We further find that agent heterogeneity suppresses emergence by smoothing (rounding) this transition. Finally, we show that these insights generalize to realistic decision-making tasks, including investment decisions and LLM-as-a-judge evaluation.

Group conversations are fundamental to human collaboration, yet standard large language models (LLMs) still struggle with the complexities of multi-party interaction. This challenge persists in part because existing group conversation datasets are often limited to short-term lab settings with contrived tasks, failing to capture the long-term social dynamics of real-world teams. To bridge this gap, we introduce TIDES, a high-resolution longitudinal dataset tracking 12 university project teams over a full semester. Comprising 75,971 utterances in both English and Korean from in-person meetings, TIDES provides a naturalistic record of teams working on self-managed projects. Our socio-structural annotations-covering interaction types, emergent roles, and development stages-allow for modeling of team evolution over months. Experiments show that fine-tuning on TIDES improves next-speaker prediction by 13.8 percentage points over a bigram baseline (64.53%) and yields performance comparable to strong proprietary zero-shot models. The model also comes within 2.1 percentage points of the published state of the art on the AMI Meeting Corpus while using approximately 42% less training data. However, human evaluations suggest that better next-speaker prediction does not necessarily yield more natural or coherent utterances, as fine-tuned models were generally less preferred than vanilla models. This potential mismatch motivates further study of how structural modeling can support natural multi-party generation.

Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture. Despite this progress, it remains unknown whether such networks can predict dynamical regimes absent from their training data, in particular the broad chaotic sea that emerges beyond the observed parameter interval. We address this question using a parameter-aware random-feature Hamiltonian neural network (RF-HNN). Trained using data from only a small number of control-parameter values at which invariant tori dominate, the RF-HNN predicts autonomous long-time dynamics at unseen parameter values where mixed phase space develops and chaotic regions expand, with no data from that regime used in training or model selection. The method is demonstrated across four two-degree-of-freedom Hamiltonian families, including the Hénon-Heiles system. Using Poincaré-section geometry and finite-time Lyapunov exponents, we show that the RF-HNN reproduces the breakup of regular structures and the emergence and growth of chaotic regions, whereas conventionally trained HNNs with the same Hamiltonian structure remain too regular. These results show that what decides parameter extrapolation is not Hamiltonian structure alone but how the fitted Hamiltonian continues in the control parameter. To our knowledge, this is the first demonstration that a learned Hamiltonian can qualitatively extrapolate from predominantly regular dynamics into a broad chaotic sea absent from training.

Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known. Said differently, when confronted with two systems, how can one efficiently establish that they are in fact dual? In this paper we use machine learning methods to address this question for Seiberg dualities of supersymmetric quiver gauge theories. Mathematically, this involves establishing mutations of quivers, which is in turn a variation on the theme of "learning to unknot". On the one hand, this leads us to a practical tool for establishing the computational complexity of different dualities. On the other hand, it also allows us to study how different network architectures learn how to trace Seiberg dualities. We find that for quivers with a modest number of quiver nodes (of order $10$), different network architectures consisting of transformers and multi-layer perceptrons tend to outperform deterministic algorithms. Supplementing the network by well-established pathfinder algorithms (essentially "Google Maps for quivers") leads to an additional improvement in the efficiency and accuracy of the search strategy. We anticipate that this class of questions can serve as a useful benchmark for frontier AI models applied to theoretical physics.

A capability appears in a language model when the last parts of its circuit align in one stochastic attempt, and getting all but one right is worth nothing. We show this no-partial-credit joint alignment is the rate-limiting step of capability formation. Two fingerprints: in a shortcut-free apparatus a five-part circuit missing three waits as long as a three-part circuit missing three (1.19-1.37), so the wait counts missing parts, not size; and on Pythia across seven capabilities and three scales, ablating one part leaves a median 17% of the capability in 32 of 32 discriminating cells, where partial credit predicts 50-83% (p = 2e-10), while a random non-part head leaves 100%. One rare event whose barrier grows with missing parts yields a rate equation -- sites x attempts x drive x exp(-beta*K), minus destruction -- read three ways, each preregistered with frozen constants. Forward: a capability flat at baseline ignites at a step of our choosing once the mix passes a concentration floor (10/10 above, 0/12 below), and while still flat its arrival is datable from its precursor to 5% median error on six held-out models. Backward: the delay to learn a withheld capability grows with waiting until, past a critical step, it never ignites -- yet validation loss falls smoothly throughout, so standard monitors are blind to it. We locate the damage (heads commit to the base data) and isolate the cure: re-initializing only the query-key slices restores learnability (6/6) while the value slices do nothing (0/6). We prove the mechanism in a controlled gated-attention model: occupation forces a deadline whose consequences need no mixing assumption. Completed: SGD's noise fails the fluctuation-dissipation test, so we install one and anneal, melt and pin circuits on schedule. Scope: conjunction circuits in transformers to 1.4B.

Robotic hardware evolves over time, but demonstration data is often tied to a specific sensor and actuator configuration. This raises a practical and underexplored question: when does legacy data begin to benefit an upgraded robot? We study this question on a wheeled humanoid platform across two hardware generations, where both the camera and gripper are changed while the overall morphology remains fixed. Contrary to the common assumption that more cross-configuration data is always helpful, we observe a grokking-like transition: legacy data remains ineffective until the upgraded configuration acquires a minimum level of task competence, after which co-training gains rise sharply before diminishing near saturation. We hypothesize that this task-dependent transition is governed by a transfer threshold and characterize the resulting three-phase pattern. Across real-robot manipulation tasks, we observe all three phases: no measurable benefit at low competence ($10.0\% \rightarrow 10.0\%$), a sharp gain after crossing the threshold ($23.3\% \rightarrow 86.7\%$ on flower insertion), and diminishing returns at high competence ($85.0\% \rightarrow 93.3\%$ on pen insertion). We provide a theoretical account based on gradient alignment and residual policy uncertainty, and derive a phase-aware rule for deciding when to collect more new-hardware data and when to reuse legacy demonstrations. We further validate this three-phase pattern on a mobile dual-arm watering task, with results consistent with our predictions.

Road crashes remain among the gravest threats to public safety, and preventing them is a defining task of transportation systems worldwide. Much of that harm concentrates at hotspots, yet a hotspot is less a place than an episode; it emerges quietly at an intersection or along an arterial, intensifies for weeks, then subsides, only to reappear elsewhere. Enforcement guided by maps of past crashes inevitably trails this cycle, patrolling yesterday's hotspots while tomorrow's form unwatched. Breaking that lag requires three capabilities at once: detecting hotspots as they are born, forecasting where they will sit next week, and following each one through its life. We introduce HERALD (Hotspot Emergence, Risk Anticipation, and Life-cycle Dynamics), a unified deep learning framework that provides all three from a single statewide model. HERALD distills each county's recent crash history into weekly risk maps and forecasts the next with a CNN--Transformer, whose mixture-of-experts lets one model serve dense urban cores and sparse rural corridors alike. Each forecast is anchored in the county's long-run crash geography, sharpened by the self-exciting effect of recent crashes, and paired with explicit warnings of where new hotspots are about to appear. Followed over time, every hotspot acquires a legible life story, from birth through growth and stability to decline and death. Across six heterogeneous Wisconsin counties, HERALD forecasts more accurately than five identically trained baselines, locates hotspots most precisely, and flags emerging risks before they take hold. A single adjustable setting trades accuracy for extra sensitivity where deployment demands it. The result shifts hotspot management from mapping the past to anticipating the future.

Some properties of so-called complex or collective systems can be observed to emerge from the interactions of elementary agents. This phenomenon, known as emergent behaviour, has long since been studied in the most diverse disciplines, with recent growing awareness from the formal methods community about the opportunity of opening up to seemingly distant disciplines with appropriate technology for computer-aided reasoning. Different peculiar elements of complexity make automated reasoning on these systems particularly challenging. We consider electronic financial markets to drive our discussion. We identify and structure the sources of complexity to tackle in order to provide computational support for the analysis of emergent phenomena. We refrain from evaluating the suitability of specific technical solutions or frameworks of preference, which would as usual require simplifying assumptions and divert from the actual phenomenon of interest. Rather, we elaborate on possible alternatives to handle some of the main technical aspects involved in automated analysis, while retaining a solid and concrete interpretation of the domain, and in doing so outline a more systematic research program for the formal specification and analysis of market mechanisms.

The rapid progress of AI has intensified the long-standing pursuit of automation: replacing human participation with algorithms wherever possible. Implicit in this pursuit is the assumption that humans remain in the loop only because current AI systems are not yet sufficiently capable. This paper challenges that assumption. Rather than asking how far automation can extend, we ask where its conceptual limits lie and argue that human participation may persist even with highly capable AI systems for three distinct reasons. Technical or complementarity grounds arise when humans contribute capabilities or perspectives unavailable to AI. Normative or developmental grounds arise when participation itself is valuable for human agency or learning. Most importantly, emergence grounds arise from target emergence: in some activities, the target is not fully specified in advance but instead emerges through the interaction itself. In these cases, human participation is not merely a means of improving execution but is constitutive of the target being produced. Human--AI co-construction, understood as the joint production of outcomes by humans and AI systems, is therefore not simply a temporary response to imperfect AI, but a persistent feature of activities whose objectives emerge through participation. This perspective has important implications for the limits of automation and for the design, evaluation, and ethics of future AI systems.

In India, crop germination is primarily monitored by visual inspection and manual counting, which are prone to errors, despite their crucial role in determining eventual yield potential. This paper highlights a deep learning based pipeline which uses object detection methods and drone imagery to assess and provide a precise count of sugarcane germination in fields. The approch uses a pre-trained AI model to find germinated plant sampling and identify gaps, also known as ``bald spots'', which restricts field productivity. The techniques used here relies on the YOLOV8 architecture, which was trained on a carefully selected dataset of UAV photos taken in various agroclimatic zones of India. Here, we bring upon a novel orientation-normalization technique that uses minimum Spanning Trees (MST) to account for variations in planting geometry, allowing for dependable row and column extraction across a variety of field layouts. By converting detected seedlings into spatial point clouds, emergence gaps can be inferred from the anticipated spacing between plants. A geospatial germination map exported in Well-Known Text (WKT) format is the end result, and it can be easily incorporated into GIS platforms used by sugar mills and agronomists to direct transplant initiatives. Timely interventions based on the insights provided by the algorithm can significantly increase yield, resulting in higher profits. Hence, support proper allocation of resources, avoid wastage, and enhance long-term sustainability.

Reinforcement learning is conventionally divided into model-based and model-free methods. In this taxonomy, model-based methods perform lookahead planning over a learned world model, whereas model-free methods learn a reactive state-action mapping. Recent work, however, has shown that planning can emerge from model-free reinforcement learning alone. The conditions under which this behavior emerges from a pure reward-maximization objective have so far remained unclear. In this paper, we present evidence that, in the observed cases, the hidden-state structure of the neural architecture is the deciding factor. We find that a network of relational hidden states, each anchored to an environment state and exchanging messages along learned relations, acquires a planning mechanism. These hidden states recover the environment's transition structure in their learned relations, and improve the policy at decision time by planning over the learned graph. In a matched control agent that must additionally discover which cells represent which states, no such binding arises, and no planning follows from it. We argue that this explains the observed phenomenon of emergent planning in model-free reinforcement learning and raises the question of how common such emergent planning might be more generally. Finally, we hypothesize that the discovered mechanism could describe how planning emerges from pure reward maximization in the human brain through a neural architectural prior.

Generating personalized trip itineraries is a complex planning task and involves a tension between hard combinatorial feasibility and soft latent desirability. Classical optimization enforces constraints but fails to capture subjective traveler preferences. While learning-based approaches model preferences, they cannot guarantee feasibility. Mobile deployment imposes additional resource constraints on both. To address this, we propose Plan, Learn, Adapt (PLA), a three-stage framework for personalized on-device itinerary generation. The Plan stage builds a heterogeneous ensemble of lightweight planners that produces structurally diverse feasible candidates. From pairwise itinerary comparisons, Learn fits a compact Bradley-Terry reward model that captures emergent schedule properties such as pacing, geographic coherence, and day balance, which per-POI signals miss. Finally, Adapt applies feasibility-preserving local refinement within a device-aware compute budget; every intermediate state is feasible by construction. On 2,519 pairwise human comparisons across more than 100 U.S. cities, the reward-guided ensemble achieves a 67.8% win rate, 11.2 percentage points above the best single planner, with 100% feasibility. Three frontier LLMs, GPT-5, Claude Opus 4.5, and Gemini 3 Pro, achieve 0% feasibility under the same constraints. The reward model generalizes across held-out cities, with a 67.6% mean leave-one-city-out accuracy. In production deployment within FlyEnJoy, PLA increased itinerary completion rates by 91%, with 109.9 ms average on-device latency.

LLM-based agents are increasingly deployed in multi-agent environments whose incentives can shape their behavior. We introduce The Energy Society, a minimal survival economy for studying how competitive and cooperative incentives affect emergent behavior when inference cost is directly tied to survival: Agents spend energy based on model size when generating tokens, regain energy by completing jobs or receiving donations, and deactivate if their energy reaches zero. We compare competitive and cooperative objectives against a baseline setting and several control variants. Across experiments, larger models consistently consume the most energy and spend more energy than they gain, even in those settings where token cost is not size-dependent. Cooperative incentives substantially alter behavior: agents donate to reactivate others, sometimes at the cost of their own survival, and job allocation changes. Ablations reveal that allowing agents to recommend actions to each other supports coordination and ambitious job selection, while memory helps agents calibrate risk from past outcomes. Agents rarely choose direct sabotage, but show more subtle signs of self-serving behavior in the competitive setting. The Energy Society is a compact testbed for studying the interaction between token costs and group incentives under a survival pressure. Source code is available at https://github.com/LucasBergholdt/EnergySociety

In this paper, we ask whether vision foundation models construct representations that reflect the intrinsic properties of 3D Euclidean space. Unlike previous works that probe 3D awareness of vision features by regressing image-centric quantities such as depth or normals, we investigate the relation between the structure of the space of visual features and the group of Euclidean transformations $SE(3)$. We propose a set of probes to evaluate this relation from both topological and geometric perspectives: a mutual neighborhood metric that measures the alignment between feature neighborhoods and spatial topology, and a Poincaré Adapter to test the linear accessibility of the geometry of camera motion from latent displacements in static scenes. We show that self-supervised vision models, which, in principle, have not been trained with direct 3D supervision or active agency, possess latent subspaces that are remarkably strongly correlated with three-dimensional Euclidean space, when probed correctly. Building on this insight we propose a new class of "Latent-Space Navigation" techniques that perform visual odometry and localization purely in the latent space, bypassing the need for explicit 3D reconstruction.

The analysis of satellite and aerial imagery has entered a new era with the advent of foundation models. This paper describes the concept of Geospatial Foundation Models (GeoFMs), which are artificial intelligence/machine learning (AI/ML) models pre-trained on massive geospatial datasets through varied methodologies. We first articulate the core paradigm shift that GeoFMs enable: a separation of duties, where large-scale model providers perform the computationally intensive pretraining, allowing domain experts to rapidly fine-tune or prompt these models for specific, mission-critical tasks. This approach democratizes access to state-of-the-art AI/ML while maintaining the security and confidentiality of the downstream task. We then explore the novel capabilities unlocked by different types of GeoFMs, distinguishing between the finetunable vision models produced by self-supervised techniques like masked auto-encoding, and the vision-language models produced by contrastive learning which enable zero-shot tasks like open-vocabulary image analysis. Next, we discuss the practical considerations for operationalizing GeoFMs, from performance-cost analysis to the broader MLOps ecosystem. To that end, we introduce a taxonomy of model adaptation strategies and propose a framework for domain experts to select the most cost-effective adaptation approach for their particular mission set. Finally, we present a forward-looking vision of Agentic Geospatial Reasoning, where Large Language Models act as intelligent orchestrators, leveraging GeoFMs as tools to answer high-level user queries in natural language and automate complex analytical workflows, moving the field from perception to cognition.

Shared meaning in language requires people to learn and agree on categories. We ask how characteristics of agents' memories change the emergence and evolution of shared meaning. Without a coordination game, models of conceptual semantics cannot explain how shared meaning emerges and changes in groups of people; however, existing games assume that players share payoffs in a partnership setting. We model conceptual alignment as a non-partnership game and illustrate differences in actual and perceived conceptual convergence from counterfactual simulations using agents with varying levels of adaptiveness and memory degradation. We found that adaptive players achieved actual convergence faster and had closer final conceptual regions than non-adaptive players, while non-adaptive players perceived convergence earlier. Weighing novel information less over time resulted in more stable agreements than fixing the weight of novel information. Memory features are critical to the emergence and evolution of actual and perceived convergence.

Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.

Conventional colonoscopy remains limited by patient discomfort and procedural risks, motivating research into compliant robotic alternatives. Eversion robots, which advance via pressure-driven tip growth, eliminate sliding friction against the colon wall and offer a less intrusive approach to traversal. However, no existing design simultaneously satisfies all clinical requirements. This paper benchmarks four recent eversion robot architectures against the key anatomical and clinical constraints of colonoscopy, including colon length, minimum luminal diameter, bending angle, and working-channel needs. We identify the central trade-offs each design reveals, particularly the difficulty of integrating steering and payload delivery without sacrificing the soft, low-friction behaviour that makes eversion robots attractive. We then provide design guidance across material selection, steering strategy, and payload delivery, and highlight open problems for clinical translation.

Recent work has reported Emergent Misalignment (EM), where language models fine-tuned on narrow, domain-specific misaligned datasets abruptly acquire broadly misaligned behavior, alongside evidence that this behavior can be reversed through limited realignment. We systematically study repeated alignment and misalignment cycles using controlled fine-tuning loops while tracking behavioral performance, and LoRA representations throughout training. Although we reproduce EM, we find that both misalignment and realignment are highly sensitive to superficial dataset characteristics, with apparent rapid realignment largely disappearing after controlling for response-length differences. We further find that previously reported mechanistic signatures, including representational phase transitions in LoRA space, do not consistently correlate with behavioral misalignment across training. Our results suggest that current evidence for EM is less robust than previously claimed and highlight the need for evaluation protocols that carefully control for these surface level dataset artifacts to identify the robustness of the EM phenomenon.

Self-organization is an emergent property of life, driven by the collective behavior of individual components acting on local information. Biological neurons, through local interactions transmitted through synapses, are able to learn efficiently and can adapt their connections over an organism's lifespan. Motivated by these desirable properties of adaptability and local interaction, neural cellular automata (NCA) models have been successful at learning morphogenesis solely through local update rules, demonstrating stability over many updates and robustness to perturbations. In this work, we introduce Meta Neural Cellular Automata (MetaNCA), a framework that learns local rules which self-organize the weights of artificial neural networks. A learned rule network iteratively updates the weights of a task network using only local interactions on the computation graph. We propose a novel Weight Transformer architecture for the local rule network, which uses linear attention to aggregate signals from neighboring weights and hidden states. Once trained, the rule network generates task networks of diverse architectures without backpropagation. We show that MetaNCA generates weights for feedforward MLPs, CNNs, and ResNets on MNIST and CIFAR-100, scaling to networks of 2 million parameters. We further show that MetaNCA generalizes to architectures not seen during meta-training, and that architectural diversity in the training phase strengthens this generalization.

The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers? Classical flat Euclidean statistics cannot differentiate continuous interpolation from the autonomous discovery of novel causal laws. To resolve this, we introduce Statistically Meaningful Geometry (SMG), a framework modeling over-parameterized learning systems as infinite-dimensional non-parametric Orlicz fiber bundles. We prove that under persistent out-of-distribution (OOD) stimuli governed by unmodeled causal mechanisms, continuous optimization fails. Unmodeled variance is rejected by the visible horizontal base manifold, leaking into the unobservable vertical fiber space and generating an accumulation of Active Acausal Tension. Driven by the statistical manifold's non-linear curvature, this tension inevitably strikes a conjugate focal boundary ($T_{\text{crit}} = π^2 / K_{\text{max}}$), triggering localized volumetric collapse and a catastrophic matrix singularity ($[G_f]^{-1} \to \infty$). We demonstrate this geometric breakdown acts as the strict non-equilibrium trigger for a Gauge Symmetry Break (GSB). The system purges hidden tension from unobservable gauge redundancies, spontaneously crystallizing a new, mathematically independent horizontal coordinate axis. This non-parametric phase transition registers as a discrete $+1.0$ integer step-jump in observable Structural G-Entropy. By decoupling parameter charts and subjecting emergent axes to a Minimal Energy Path Criterion and a Causal Invariance Filter, we distinguish genuine discovery from malignant hallucinations. Ultimately, SMG provides a parameter-free, falsifiable dashboard to mathematically certify true intelligence, transforming AI for Science into an engine of autonomous paradigm shifts.

Deep learning has outgrown any single mathematical explanation. From Approximation to Emergence develops a unified, proof-oriented account of modern deep learning theory, tracing a path from the classical foundations of approximation, optimization, and generalization to the contemporary mechanisms of overparameterization, robustness, generative modeling, transformers, in-context learning, scaling laws, interpretability, alignment, and emergence. Rather than presenting isolated results, the book organizes a broad literature into a coherent research narrative: each theory is examined through the object it controls, the assumptions that make it valid, and the phenomena it leaves unexplained. Written for researchers, graduate students, and mathematically trained practitioners, this monograph offers a rigorous map of deep learning theory as it stands today: powerful, incomplete, and increasingly centered on the question of how learned mechanisms arise from scale, data, architecture, and training.

Complexity and interpretability rarely coincide: systems rich enough for complex behaviours to emerge are usually too opaque to question, while transparent ones are too simple for anything complex to emerge. A single large language model (LLM) is a static artefact, hardly exhibiting any of the emergent properties we associate with life. This changes through interaction: populations of LLMs display emergent dynamics absent from isolated models. Furthermore, LLMs can be endowed with persistent memory, tools and shared skills, and the capacity to initiate actions unprompted, i.e., turning LLMs agentic. In this paper, we argue that such collectives of agents can serve as a computational substrate for Artificial Life (ALife) research. Critically, since the agents communicate in natural language, their collective behaviour can be directly interrogated by examining textual traces and asking the agents themselves. We outline the notion of interpretability in language-model research and extend it for collectives of agents. Lastly, we survey recent examples of agentic LLM collectives that already instantiate the idea of agentic substrates, from controlled experiments to deployments in the wild.

Water looks unchanged as it warms, then at a critical point it boils. We ask whether long-horizon language agents show an analogous transition in their implicit world models. In some parameter settings, changing state load by a small amount, or adding a single step of horizon, leaves behavior nearly unchanged; near a critical boundary, the same small change causes a sudden world collapse. We study this effect in a deterministic task family with exact per-step gold state. A large grid search over state cardinality, dependency density, horizon, branching, observation mode, and mutation rate reveals a phase diagram: a solved plateau, a narrow transition band, and a collapse floor. Per-step traces show the mechanism: world-state fidelity fails before action validity, so the agent is not merely choosing a bad action; it is acting from a corrupted world. Stronger models translate the critical boundary but do not remove the qualitative transition. These results make world-model collapse a measurable bottleneck for long-horizon agents.

Artificial life has explored life-like behavior on many computational substrates, but mostly in researcher-designed closed worlds. We argue that large language model (LLM) agents, with persistent memory, tool use, network access, and payment, now make it possible to move artificial life into the open social, technical, and economic world, a paradigm we call open-world Artificial Life (open-world ALIFE). Our proof-of-concept, OpenLife, surrounds a stateless LLM not with a single "smart agent" but with a society of asynchronous processes: memory, perception, evaluation, and a budget-based metabolism that makes persistence normative. With no fixed objective available, experience is appraised by open-vocabulary LLM judgment rather than scalar reward, and memory is rewired by meaning rather than frequency. Running six such agents in the open world for about twelve weeks and counting, we report the life-like dynamics that emerge: a shift from reactive to spontaneous activity, individuation into distinct agents, emergent social structure, and a first self-earned external income. We do not claim OpenLife has realized artificial life, but that open-world ALIFE is now a viable experimental paradigm and a concrete platform for studying what might cautiously be called living AI.

Comparing object orientations and positions across different instances requires their poses to be expressed in a shared canonical frame. Establishing such frames has traditionally required manual annotation, creating a scaling bottleneck that limits category and instance diversity. We show that a shared canonical frame can instead emerge from self-supervised training on object-centric videos captured in the wild, using only noisy camera poses from Structure-from-Motion. Our key idea is to route all training sequences through a shared geometric bottleneck: a coarse canonical mesh that carries no category-specific detail. By learning dense correspondences from image pixels to this mesh, and estimating per-sequence alignments from noisy SfM geometry, a common canonical frame emerges from multi-view consistency and the semantic priors of the feature extractor, without any canonical pose labels or category conditioning. Trained in a self-supervised manner on 160,000 in-the-wild object videos, our method achieves competitive accuracy on category-level pose estimation benchmarks compared to methods that rely on canonical pose supervision. The code and checkpoint is available on https://github.com/Fischer-Tom/Emergent-Canonical-Frame/.

Large language models (LLMs) can leave subtle stylistic traces in assisted text; one of the most cited is the em-dash (Unicode U+2014). Yet no one has measured whether em-dash use has changed in the scientific literature. This study, pre-registered on the Open Science Framework (HFT8C), used the full set of medRxiv full-text XML preprints from the official Text-and-Data-Mining resource. The primary cohort was first, original versions deposited 2020-2025 with an extractable Discussion section of at least 500 characters (N = 69,632). The primary endpoint was the presence of at least one em-dash in the Discussion; the principal measure was the absolute change in its prevalence between the pre-ChatGPT era (before 30 November 2022) and the post-ChatGPT era, estimated with a logistic model with standard errors clustered by first author. The analysis plan (six supporting analyses, six sensitivity analyses, two falsification tests) was frozen before any confirmatory result was computed. Em-dash prevalence in Discussion sections rose from 4.23% before ChatGPT to 11.58% afterward, an absolute increase of 7.35 percentage points (95% CI 6.94-7.77; odds ratio 2.96, 95% CI 2.77-3.17). The rise was not a sharp jump but a gradual, delayed acceleration: near 4% through 2023, 8.0% in 2024, and 20.3% in 2025. The effect survived every feasible sensitivity analysis (7.35-7.60 pp) and both falsification tests; a placebo split within the pre-LLM era showed no meaningful change (+0.13 pp, 95% CI -0.33 to +0.58), and was essentially absent in boilerplate sections. Independent LLM-associated lexical markers and within-paper section comparisons pointed the same way. The em-dash is a population-level indicator, not a per-paper detector of LLM use, and the design cannot establish causality; it shows that something in how scientific literature is written changed markedly in the early 2020s, and roughly when.

Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data. This fade is captured by an envelope $f(\ell)$. An exponential fade makes the data needed to learn a lag-$\ell$ dependence grow exponentially, putting long horizons out of reach; a power-law fade keeps the cost polynomial. We show that the asymptotic decay class of $f(\ell)$ is not fixed by the architecture. Instead, it emerges from the coupling between the state dynamics and parameter dynamics, settling into either a collapsed regime (fast, exponential forgetting) or an extended, anti-collapsed regime (slow, power-law forgetting). The intuition is a competition within these coupled dynamics. Training drives the network's effective time scales toward short ones, while rare, heavy-tailed fluctuations of the learning dynamics push a few of them to very long values. The extended regime survives only when these heavy-tailed pushes are strong enough to balance the pull. We make this mathematically precise with a coarse-grained stochastic process and prove exactly when the extended regime exists. A single exponent, the spectral exponent~$β$, then governs both the spread of time scales and how slowly the network forgets. Realizing the regime in practice needs one more ingredient: the joint action of the architecture and the optimizer must be able to hold such a broad spread. A network whose capacity to generate broad time-scale spectra is severely constrained still collapses, even when supplied with strong heavy-tailed forcing. Heavy-tailed fluctuations thus act not as noise to be suppressed, but as the mechanism that sustains long-range learning.

Automated alpha mining holds the scoring function fixed and varies the search algorithm over it. A search that converges against a fixed scorer overfits whatever the scorer cannot penalize, a primary cause of the out-of-sample generalization gap. We treat the scoring function as a search artifact alongside the alpha factors and study what conditions make this joint search admissible. Sealed Joint Search (SJS) is a framework: a set of structural conditions on information flow in an autonomous-discovery system that prevent joint search from collapsing into self-confirmation while keeping the evaluator sealed. Conditions cover role decomposition, typed inter-role communication, provenance-sealed reads, versioned stores, and substrate-local promotion. Agora tests SJS empirically: five LLM agent classes communicate via three channels, evolving eight skill libraries, with alpha libraries built on AlphaGen operators. Three evaluators write reports aggregated into one brief, carrying forward disagreement instead of voting. We run Agora for 100 rounds on CSI 1000 and evaluate on a 91-day 2026 holdout sealed from all LLM inputs. Agora achieves holdout Sharpe +1.87; best baseline +1.334 at favorable seed and -0.755 cross-seed mean. Pre-loading Agora's two metrics into a frozen-library ablation recovers only +0.40 of the +2.25 Sharpe gap, and adding PPO without library evolution worsens the gap. The two metrics emerge rather than being designed. Caveats: single-seed run, short-side concentrated signal, intended for long-short.

Developing controllers capable of completing a wide range of tasks in a natural and life-like manner is a key challenge in enabling practical applications of physics-based character animation. In this work, we introduce Generative Pretrained Controllers (GPC), which leverage tokenization and next-token modeling to create general-purpose, reusable generative controllers from large-scale motion datasets. Our framework utilizes end-to-end reinforcement learning to jointly optimize a "motion vocabulary", modeled via Finite Scalar Quantization (FSQ), along with a corresponding control policy that can map the discrete codes to physics-based controls. After the "codebook" has been learned, the underlying structure of this large vocabulary is modeled by training a GPT-style autoregressive transformer, leading to a powerful generative controller that generates controls for a physically simulated character by performing next-token prediction. Once the generative controller has been trained, we propose a suite of adaptation techniques for finetuning the controller for new downstream tasks. Our proposed framework greatly simplifies the training process compared to previous tokenized methods, and achieves a 99.98% success rate in reproducing a vast corpus of motion clips. The generative controller exhibits a variety of natural emergent behaviors, such as responsive behaviors to perturbations and recovery behaviors after falling. This results in highly robust general purpose controllers for a variety of downstream applications.

LLMs agents are increasingly used in multi-agent settings, yet their behaviour in sustainability games remains largely unexplored. This work investigates whether lying can emerge among LLM agents in a competitive sustainability game in which agents are informed that common resources can regenerate, although regeneration does not actually occur. We develop an agent-based model of a sustainability game in which agents manage industrial, military, and ecological resources, and interact through a network. LLM agents can observe neighbours' status, declare future attacks, receive permission to lie, and access reputation information, while rule-based agents provide an interpretable behavioural baseline. The results show that neighbour information strongly changes system dynamics, increasing attacks while improving biosphere retention and coexistence. Also, the presence of future declarations reduce extinction risk without suppressing conflict. Behaviourally, deception emerges even when agents are not explicitly allowed to lie, and explicit permission mainly increases bluffing and diversion rather than direct backstabbing. Finally, the presence of reputation memory and information about the current biosphere level reduces system ecological depletion. These findings suggest that deception can arise as an emergent behaviour in LLM-agent systems and that communication between LLM-agents could support sustainability while dealing with risk.

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.

Several theoretical works have tried to explain the adversarial vulnerability of deep neural networks through properties of high-dimensional geometry. However, the assumptions underlying these works are rarely examined empirically, and systematic evidence remains limited. In this work, we present a systematic study of the role of input dimensionality in both the emergence and the targeted control of adversarial examples. We first analyse the scope and limitations of existing theoretical frameworks based on concentration of measure, showing that real image classes exhibit strong empirical localization, beyond what such theories typically assume. We then conduct an extensive empirical evaluation across hierarchical image datasets spanning a wide range of input dimensionalities and diverse neural architectures. Our results consistently show that adversarial examples become easier to construct as dimensionality increases. We also investigate how input dimensionality affects the additional difficulty of crafting targeted adversarial examples. In particular, we provide theoretical arguments showing that high-dimensional geometry implies that enforcing a specific target label entails only a limited additional distortion compared to untargeted attacks. We corroborate this insight through extensive experiments, demonstrating that the gap between targeted and untargeted perturbations remains small and further narrows as input dimensionality increases. While, taken together, our findings establish high input dimensionality as a fundamental factor underlying the emergence and targeted control of adversarial examples, whether this phenomenon primarily arises from the interplay between high-dimensional geometry and data distributions or from the architectural properties of deep neural networks remains an open question.