From Passive Mirrors to Active Agents: Holonic Digital Twins for Physical AI over Networks

The paper addresses the fundamental failure of current AI systems when embedded into physical systems such as robots and vehicles. As the authors state, "today's AI tools, including deep learning and generative AI (e.g., large language models), still fail when embedded into physical systems, such as robots or vehicles that, operate under the physical laws of the real world. This limitation stems from the inability of physical AI systems to maintain reliable world models for long-horizon planning under uncertainty and to generalize to unseen scenarios. The root causes identified include: physical AI systems lack reliable models of themselves and their environment as physical actors; data-driven models learn statistical correlations from training data but have limited ability to reason about the effect of change caused by their own actions and change caused by exogenous disturbances"; physical tasks require long-horizon planning under deep uncertainty that current architectures cannot sustain; and models trained in simulations encounter distribution and domain shift upon real-world deployment.

The paper argues that wireless cellular systems such as 6G have a unique opportunity to act, not only as communication providers, but rather as orchestrators of physical intelligence due to their pervasive deployment. However, "current wireless networks are typically designed as passive data transport layers, and, thus, they still cannot support the real-time inference and collective reasoning that is required to operate and coordinate physical AI at scale. Four specific challenges are identified: (a) transmission decisions are not governed by the cognitive value a packet carries to a receiving agent—defined as how much a transmitted belief improves the receiving agent's world model about causally relevant hidden states; (b) closed-loop physical action requires inference updates perfectly synchronized with real-world dynamics, since any misalignment between communicated beliefs and the physical state of the world can result in hazardous consequences for safe operation; (c) heterogeneous agents encode the world in incompatible representational spaces with no mechanism for aligning or composing these representations while preserving semantic structure; and (d) the network lacks theory of mind capabilities that can allow it to predict how physical AI agents will interpret and act upon transmitted beliefs."

The main contribution is the transformative concept of a networked holonic digital twins (HDTs), called HDT-Nets. The term holonic "captures the defining structural property of our framework, where each twin is simultaneously an autonomous cognitive agent that maintains its own causal world model and reasons independently about its local environment, and a cooperative part of progressively larger cognitive units whose collective intelligence exceeds what any individual achieves alone. The 6G network orchestrates this holonic composition by providing the shared spatiotemporal context, communication resources, and edge computation through which individual HDTs discover coordination partners, exchange beliefs about the world, and compose into collectively intelligent agents at the network level."

Each HDT is "realized as a hierarchical twin spanning both the physical agent and the network edge, where the agent-side twin maintains a causal world model grounded in local sensor observations, while the network-side twin enables real-time distributed inference through collective belief coordination, multi-agent fusion, and resource orchestration across the 6G infrastructure."

The framework rests on four interconnected fundamental pillars that synthesize causal reasoning, compositional structure, adaptive learning, and collective coordination:

1. Causal Markov blankets (MBs): "provide a principled framework for partitioning cyber-physical networks into autonomous AI agents by defining the boundary of each HDT. In particular, MBs identify the minimal set of variables that must be exchanged for coordination while preserving conditional independence from the rest of the system. MBs define boundaries via sensory states (observations flowing in), active states (actions flowing out), and internal states (beliefs), enabling decisions about with whom to coordinate based on causal relevance... when to initiate coordination to meet safety-critical deadlines, and how much information to exchange."

2. Category theory: "provides the mathematical foundation for this compositionality and operates at the interfaces between HDTs. It provides formal guarantees that semantic structure involving the causal relationships, temporal ordering, and geometric structure is preserved when heterogeneous agents coordinate, regardless of their internal implementation differences."

3. Active inference: "provides this unified framework by casting perception, sensing, action selection, and learning as a single optimization objective... formalized through the minimization of expected free energy, which can be interpreted as a combination of 'goal mismatch' (how far outcomes are from desired ones) and 'uncertainty' (how unsure the agent is about the world)."

4. Integrated information theory (IIT): "can address this challenge by deriving a network-level measure called spatiotemporal integrated information Φ computed over the collective state of multiple HDTs. Φ quantifies how much a network of coordinating agents collectively exceeds the sum of what each agent could achieve independently in terms of resolving uncertainty about the shared physical environment and executing coordinated actions toward mission goals."

The authors emphasize that these pillars "form a single computational chain across sensing, communication, computing and control domains rather than independent contributions. MBs determine with whom each HDT must coordinate based on causal relevance to its mission. Active inference determines what to transmit by evaluating the cognitive value of each potential belief exchange. Category theory determines how to translate beliefs and understand each other at the interface between heterogeneous HDTs whose internal world model representations may be incompatible. Spatiotemporal integrated information Φ determines whether the resulting coordination leads to collective intelligence that justifies its communication cost."

The paper critiques existing DT implementations across four dimensions:

Limitation 1: Passive Observation Without Active Cognition. "Existing DT frameworks for wireless networks focus on synchronization between physical and virtual replicas and emphasizes simulation fidelity... However, these DT frameworks built on statistical AI solutions do not reason about the world... they do so reactively, without any mechanism to assess the reliability of their own predictions, identify what they do not know, or direct sensing resources to fill knowledge gaps. This creates a fundamental epistemic limitation—the twin cannot identify what it does not know"—which hinders safe operation when the network enters unfamiliar regimes.

Limitation 2: Absence of Compositional Guarantees for Heterogeneous Agents. Using a disaster response scenario with ground robots (LiDAR occupancy grids), aerial drones (3D camera models), vehicles (radar tracking), and human XR users, the authors show that "when the ground robot attempts to fuse the information received from other agents to update its world model, conflicts arise between representations that describe the same physical reality in incompatible ways... resulting in plans that appear individually rational but prove collectively catastrophic when executed in the shared physical environment."

Limitation 3: Data-Driven Models Without Causal Understanding. No historical dataset can anticipate all futures. Moreover, neural models extrapolate poorly beyond their training distribution since they learn purely statistical associations between inputs and outputs. The authors give the counterfactual example: "a correlational model accurately learns that robot positions could be correlated with channel quality degradation. But it cannot answer: 'If I command this robot to move behind the metal shelving, will the link fail before it completes its task?' Additionally, these models provide point predictions without principled uncertainty quantification" and cannot support risk-aware decision making.

Limitation 4: Data Synchronization via Centralized Processing. "Current physical-virtual twin synchronization schemes assume centralized processing in which raw sensing data is communicated to a central location, processed there, and then decisions are distributed back... Physical AI coordination fundamentally inverts this model. The authors note that robots should coordinate by exchanging inferred beliefs such as 'northeast corridor has 90 percent probability of collapse within 60 seconds' or 'agent 3 trajectory will intersect this position in 200ms' rather than raw sensor streams, and that the round-trip latency to a central server exceeds the time available for safety-critical decisions."

Realizing HDTs requires: (1) From observation to causal inference—HDTs should actively maintain generative causal models P(stµt, at) that explain how hidden environmental states µt... causally give rise to observed measurements st... upon performing an action at, supporting interventional queries via do-calculus and counterfactual reasoning; (2) From centralized to collective intelligence—HDTs must determine which agents are causally relevant to each other's decision-making and prioritize transmissions that maximize cognitive value at the receiver, dynamically establishing coordination relationships only when causal coupling justifies communication overhead; and (3) From data to meaning to cognitive value—"Communication between HDTs should transmit beliefs rather than raw data... The network must therefore evaluate each transmission by its cognitive value, how much the transmitted belief reduces the receiver's uncertainty about causally relevant hidden states and improves its next physical action, rather than by the number of bits it carries."

The MB of a variable X in a causal Bayesian network is defined as MB(X) = Pa(X) ∪ Ch(X) ∪ CoP(X), yielding the conditional independence property: P(XMB(X), W MB(X)) = P(XMB(X)). Crucially, "For an intervention do(A) on variables outside MB(X)... P(Xdo(A), MB(X)) = P(XMB(X)). This means that variables outside the MB have no causal influence on the agent's internal beliefs. Consequently, the agent need not sense, communicate with, or respond to any entity outside its MB, enabling principled pruning of sensing resources, communication links, and coordination relationships."

The authors extend this to dynamic MBs since traditional formulations assume static partitions where distinct network parameters maintain fixed roles as internal, boundary, or external states, which fails for mobile agents and time-varying coordination. In practice, "each HDT tracks its blanket boundaries by periodically evaluating the conditional mutual information between its internal states and candidate boundary variables using local observations. When causal coupling with a neighboring agent increases... the neighbor's states enter the blanket and a coordination link is established. When coupling decreases, those states exit the blanket and the link is released. The active inference loop drives MB adaptation as a byproduct of free energy minimization rather than requiring a separate blanket detection algorithm."

Objects in the category NetHDT are HDT states (s, a, µ), while morphisms are structure-preserving transformations including belief updates, state transitions, and coordination protocols. Morphism composition respects temporal causality, and associativity and identity laws guarantee that the order of grouping operations does not affect outcomes while preserving causal temporal ordering, critical for distributed multi-agent coordination where updates occur asynchronously.

Three functors enable multi-level reasoning: ΦDT (physical-to-virtual) maps physical entities to world model representations while preserving causal structure; Φabs (abstraction) maps detailed HDT states to coarse-grained representations for hierarchical reasoning—enabling an HDT at the edge server to coordinate in real-time hundreds of agents through low-dimensional causal abstractions; and ΦToM (theory of mind) maps the internal belief state µi of agent i to a prediction µ̂j of what agent j believes about the same physical environment, despite the two agents using incompatible world model representations. The authors stress that Without ΦToM, the cognitive value in (4) cannot be evaluated, and transmission decisions fall back to heuristic scheduling.

Pullbacks provide compositional operations: "The pullback HDT combines sensory states as s1 × s2, constrains active states such that (a1, a2) satisfy joint physical feasibility requirements, and represents joint beliefs µ1,2 that factor according to conditional independence: P(µ1, µ2s1, s2) = P(µ1s1, sshared) · P(µ2s2, sshared). This preserves each twin's individual MB by ensuring that beliefs about agent-specific local states remain conditionally independent given shared interface observations... while still ensuring coordination where physical causality demands it."

Natural transformations translate between incompatible semantic languages while preserving meaning. In the example of an aerial drone using visual embeddings and a ground robot using geometric structural models, the natural transformation α: FA ⇒ FB ensures the commutative property "αt+1 ◦ fA = fB ◦ αt... guaranteeing that translating then updating yields the same beliefs as updating then translating, enabling the drone to communicate 'northeast corner shows severe structural damage' in a form the robot can interpret for navigation planning."

The generative model factorizes as P(s̃, µ̃, π) = P(µ0) Πt P(stµt)P(µt+1µt, at)P(π). Perception corresponds to the HDT maintaining approximate posterior beliefs Q(µt) that minimize variational free energy: F = KL[Q(µt) ∥ P(µts<t, a<t)] − EQ[ln P(stµt)], where the complexity term penalizes unnecessary departure from what the HDT already knew and the accuracy term rewards beliefs that correctly predict incoming sensor observations.

Action selection minimizes expected free energy: G(π) = EQ[DKL[Q(sτπ) ∥ P(sτ)]] + EQ[H[P(sτµτ)]], where the pragmatic term drives the HDT toward preferred future observations (goal achievement) and the epistemic term drives actions that reduce ambiguity about hidden states (uncertainty reduction). Notably, exploration and exploitation are not separately engineered—the balance is determined entirely by the ratio of pragmatic to epistemic cost at the current belief state. Learning "further closes the loop where as actions produce new observations, the parameters of the generative model are updated to improve future predictions... The same VFE objective that drives belief updates also drives model improvement."

The expected free energy decomposition provides a principled formalization of the cognitive value of information: V(mi→j) ≜ Gj(πj* Qj(µ)) − Gj(πj* Qj(µ mi→j)), which decomposes into epistemic and pragmatic components: V(mi→j) = ∆Ve(mi→j) + ∆Vp(mi→j). "Unlike classical value of information, which measures reduction in statistical uncertainty independent of the decision context, cognitive value is inherently action-coupled. A message carries zero cognitive value if it reduces uncertainty about states that are causally irrelevant to the receiver's current pol…

Improved physical AI systems based on the HDT-Net framework can do the following:

1. Maintain causal world models instead of statistical correlations.

The system builds generative causal models of itself and its environment, and can answer interventional and counterfactual questions — e.g., “If I command this robot to move behind the metal shelving, will the link fail before it completes its task?” It can reason about the effects of its own actions and exogenous disturbances, quantify its own uncertainty, and detect when it is operating outside its training distribution. This enables safe long-horizon planning under deep uncertainty.

2. Actively identify and fill its own knowledge gaps.

Instead of passively synchronizing a digital twin, the system uses active inference to direct sensing toward states it is most uncertain about, while balancing exploration and exploitation in a single optimization objective. It can decide what it needs to observe next to reduce risk, rather than merely reacting to incoming data.

3. Compose into larger collective intelligence dynamically.

Using causal Markov blankets, each agent determines which other agents are causally relevant to its mission, establishes coordination links only when causal coupling justifies communication overhead, and prunes them when they no longer add value. The system can scale from a few robots to hundreds of agents without wasting communication or computation on causally irrelevant partners.

4. Communicate meanings, not raw data.

Agents exchange compressed beliefs such as “northeast corridor has 90% probability of collapse within 60 seconds” instead of raw sensor streams. Transmissions are prioritized by cognitive value — how much the message reduces the receiver’s uncertainty about causally relevant hidden states and improves its next physical action — not by Shannon information or bit count. This dramatically reduces communication bandwidth while improving coordination quality.

5. Understand and translate between incompatible world-model representations.

Category-theoretic natural transformations allow a ground robot using LiDAR occupancy grids, an aerial drone using visual embeddings, a vehicle using radar tracking, and a human XR user to share causally relevant beliefs even though their internal representations are incompatible. The system guarantees that translating then updating yields the same result as updating then translating, so fused plans remain physically coherent.

6. Predict how other agents will interpret and act on transmitted beliefs.

The system includes a theory-of-mind functor that lets each agent model what another agent believes about the shared environment, despite different internal representations. This enables the network to evaluate the true cognitive value of a message before sending it and to avoid miscoordination caused by misinterpretation.

7. Synchronize beliefs with real-world dynamics for safety-critical control.

The network co-designs belief delivery, inference scheduling, and action commitment, ensuring that communicated beliefs remain aligned with the physical state of the world. It avoids the hazard of agents acting on stale or temporally misordered information, even under differential latency across links.

8. Grow collective intelligence as a first-class network resource.

The system measures spatiotemporal integrated information Φ across agents — quantifying how much the collective exceeds the sum of its parts — and actively optimizes its growth through sensing, communication, computation, and control decisions. It can detect when agents genuinely form a coordinated cognitive unit and when coordination overhead outweighs its benefit, then adapt the topology accordingly.

9. Operate as a single networked cognitive agent with hierarchical reasoning.

Agent-side twins handle local causal reasoning, while network-side twins perform collective inference and abstraction for real-time coordination of large teams. The system can reason at multiple levels of granularity simultaneously, from an individual robot’s local actions to a network-wide coordinated mission.

10. Remain causally consistent and resilient under adversarial conditions.

The network protects belief integrity at the semantic level, detecting and mitigating false causal claims injected by compromised agents. It maintains a causally consistent collective world model even when individual agents attempt to deceive it, improving robustness against adversarial attacks on perception and communication.

Despite advances in artificial intelligence (AI) across multiple sectors, today's AI tools, including deep learning and generative AI, still fail when embedded into physical systems, such as robots and vehicles operating under real-world physical laws. This stems from their inability to maintain reliable world models for long-horizon planning under uncertainty and generalize to unseen scenarios. In this context, wireless networks, through pervasive sensing and communication, can orchestrate physical intelligence. However, current architectures optimize throughput, latency, and reliability and cannot support real-time physical AI coordination, requiring agents to maintain shared spatiotemporal context. To address these challenges, a network of holonic digital twins (HDT-Nets) framework is proposed to deliver real-time physical AI inference through holonic agents that actively reason about their environment rather than passively mirror physical assets. Each HDT is realized as a hierarchical structure spanning the physical agent and network edge, reasoning autonomously at the local level while cooperating with neighboring HDTs to form collectively intelligent units. In HDT-Net, causal Markov blankets spanning sensing, communication, and control determine which agents must coordinate and enable counterfactual reasoning over multi-domain interventions. Active inference within these boundaries unifies perception, action, and learning by minimizing expected free energy while deciding which beliefs to transmit based on their cognitive value to the receiver. Category theory ensures that transmitted beliefs preserve semantic structure across heterogeneous agents with incompatible representations. Finally, integrated information theory quantifies when collective intelligence exceeds independent operation and how network intelligence evolves through coordinated learning and information exchange.