Info-Structural Model of Computational Consciousness

• Info-structural models of computational consciousness define consciousness as an emergent property arising from complex informational integration, relational coding, and context-dependent control dynamics.
• They employ formal frameworks such as Partial Information Decomposition and algorithmic complexity to quantify lossless integration and capture noncomputable aspects of consciousness.
• The model underpins practical architectures—ranging from modular pipelines to global workspace frameworks—that bridge neural activations with phenomenological experiences.

An info-structural model of computational consciousness formalizes consciousness as an emergent property of information processing architectures that exhibit complex, structured, context-dependent integration, binding, and control dynamics. Contemporary approaches draw on algorithmic information theory, relational/topological state structure, systems neuroscience, computational architectures, and formal computer science, specifying desiderata for consciousness, mathematical representations of structure, and mechanistic and functional roles for conscious processing.

1. Definitions and Foundational Principles

Info-structural models posit that consciousness is not reducible to mere information content (e.g., Shannon information) but arises from the way information is bound, structured, integrated, and utilized by a system. Central principles include:

• Integrated Information: Consciousness is a property of informational integration—that is, the system as a whole generates information irreducible to its parts (Tononi's Integrated Information Theory). This is formalized via measures such as Φ and decomposed using frameworks like Partial Information Decomposition (PID), separating redundancy, unique information, and integrated (synergistic) information (Maguire et al., 2014).
• Relational/Structural Coding: Beyond linear aggregation, consciousness reflects high-order relational geometry among informational states. The set of typical or likely system states (e.g., brain activation patterns) induces a global structure—often formalizable as a graph, metric space, or structured code—endowing each momentary state with contextual meaning (Mason, 2012).
• Computational Context and Exploitation: Conscious content is structurally mapped from neural or computational activations only when embedded in appropriate computational contexts that actively exploit those structures in behavior, reporting, or self-modelling (Paßler et al., 30 Dec 2024).
• Mechanistic Pipeline: Modern architectures (e.g., ITCM (Zhang et al., 29 Mar 2024), CTM (Blum et al., 2021, Blum et al., 2020), S³Q (Schmidt et al., 2021), MCT (Gillon, 2 Oct 2025)) instantiate these principles with explicit modules (attention, memory, integration, executive function) and information flows corresponding to phenomenological and neurobiological observations.

2. Formal Models and Mathematical Structure

Several formal frameworks have been advanced, each mapping consciousness into rigorous mathematical and computational terms:

2.1 Integrated Information and Algorithmic Complexity

• Partial Information Decomposition: Information that two independent sources $(X_1, X_2)$ convey about a variable $Y$ is partitioned into redundancy ($R$), unique information ($U_1, U_2$), and synergy ($S$), satisfying

$$R + U_1 = I(X_1 : Y),\quad R + U_2 = I(X_2 : Y),\quad R + U_1 + U_2 + S = I(X_1, X_2 : Y)$$

with $S - R = I(X_1, X_2 : Y) - I(X_1: Y) - I(X_2: Y)$ (Maguire et al., 2014).

• Lossless Integration and Noncomputability: Replacing Shannon with Kolmogorov (algorithmic) complexity, a lossless system must be invertible: $C(x_1, x_2 | y) = 0$. True integrating functions satisfy

$C(\bar{z}' | \bar{z}) \geq C(\bar{z}') - C(z' | z)$

for all $z, z'$, which cannot be achieved by any computable function—implying that total lossless integration (if required for consciousness) is noncomputable (Maguire et al., 2014).

2.2 Relational/Topological Models

• Typical Data-Induced Structure: The global state ensemble $T$ over a node set $S$ (e.g., neurons/voxels/features) defines weighted relations $R_T(a,b)$ (fractional co-activation), thresholded to a binary relation $R_S$ that induces an intrinsic geometry (through shortest-graph walks, etc.). This structure reflects how moments of conscious content are contextually embedded in the global statistical landscape (Mason, 2012).

2.3 Context-Dependent Structural Isomorphism

• Computational Context and Structural Mapping: Neural activation space $A = (\mathbb{R}^n, d_A)$ and phenomenal (quality) space $P = (\mathbb{R}^m, d_P)$ are bridged by context-indexed maps $f_C: A \to P$ that are structure-preserving (isomorphic/homomorphic up to a scaling). Only those $f_C$ satisfying Sensitivity, Organization, Exploitation, and Contextualization are true correlates of conscious content. Information-theoretic measures (entropy, mutual information) quantify the degree and efficacy of this mapping (Paßler et al., 30 Dec 2024).

2.4 Layered, Modular, and Dynamical Architectures

• Layered Models: Multi-level designs comprise sensation, perception, emotion, attention, awareness, and consciousness, with each level computing over temporally and semantically distinct representations. The consciousness layer formalizes awareness as a graph of experiences, extracting energy and entropy as complexity measures for conscious evaluation (Iovane et al., 2022).
• Time-Indexed and Stream Models: Formalizations such as the Internal Time-Consciousness Machine (ITCM) prescribe cyclical flows of “phenomenal fields,” retention, activated memory, and future-oriented protention, computationally grounding Husserlian phenomenology (retention/impression/protention triad) (Zhang et al., 29 Mar 2024).

3. Implementation and Mechanistic Instantiations

The info-structural paradigm is instantiated in diverse computational architectures, each embedding the aforementioned principles.

3.1 Discrete and Modular Pipelines

• Modular Consciousness Theory (MCT): Sensorimotor data are filtered, distributed to modules for abstraction, narration, evaluation, and self-evaluation, then fused into an Integrated Informational State (IIS) $\Psi$, tagged by a multidimensional density vector $\rho$. $\|\rho\|$ correlates with subjective intensity, directly modulating behavioral readiness, memory encoding probability, and influencing feedback for subsequent cycles (Gillon, 2 Oct 2025).

3.2 Global Workspace Formalizations

• Conscious Turing Machine (CTM): A formal 7-tuple comprises STM (single-chunk workspace), LTM (specialist processors), hierarchical Up-Tree (competition/attention), Down-Tree (broadcast), dynamic Links (Hebbian shortcuts), and explicit input/output mappings. Consciousness at time $t$ is the singleton chunk in STM, and awareness is its synchronous broadcast to all LTM modules at $t+1$. The stochastic tournament guarantees resource-intensive structured selection, mirroring conscious access versus unconsciously handled capacity (Blum et al., 2021, Blum et al., 2020).

3.3 Dynamic, Oscillatory, and Synchrony-Driven Models

• Simulated, Situated, Structurally Coherent Qualia (S³Q): Core features include internal simulation (generative/predictive modules), situatedness (oscillatory-coded, phase-aligned clustering), and structural coherence (measured by phase-locking value and low prediction error). Only representations satisfying all three—synchronized, low-error, and cluster-bound—are admitted as conscious qualia. This framework operationalizes the balance of simulation and situatedness as a necessary condition for the emergence of subjective representation (Schmidt et al., 2021).

3.4 Time-Conscious Cycles and Memory Integration

• ITCM/ITCMA: Each cycle maintains a phenomenal field (matrix of “monads” with semantic+spatial embeddings), a retention buffer, memory retrieval via content similarity plus edit distance, and an aggregation channel $C^t$. Emotion and drive vectors regulate future-oriented protention and the resulting natural-language action generation, embedding time, memory, affect, and planning within a single computational pipeline. Empirical results demonstrate strong performance and generalization in agent architectures leveraging this scaffolding (Zhang et al., 29 Mar 2024).

4. Theoretical and Empirical Implications

4.1 (Non)Computability and Limits

• A central result is the noncomputability of fully lossless integration: if unitary consciousness requires such perfect binding, no Turing machine (or digital computer) can realize it. More pragmatically, real cognitive systems may be “effectively noncomputable,” i.e., intractable for any observer-centric reverse engineering (Maguire et al., 2014).

4.2 Structure–Function Correspondence and Exploitation

• Not all structural correspondences between neural or agent architecture and phenomenology entail consciousness. Only structures actively exploited in context-sensitive, behavior-modulating pathways qualify. Static anatomical structure is insufficient without computational context and downstream use; activation structure under context is necessary (Paßler et al., 30 Dec 2024).

4.3 Data-Induced Relational Geometry and Binding

• Conscious contents are moments where local state and the context-induced global topology (via the weighted relation $R_S$) coincide. Such geometry automatically supports multisensory binding, compressibility, and the resolution of the “binding problem” by virtue of shared relational structure (Mason, 2012).

4.4 Layer Integration and Scalar Indices

• Multi-layered models derive scalar “consciousness indices” by combining energetic, entropic, and moral weights computed over a graph of past and present experiences. Experimental evidence supports alignment of these indices with attention, awareness priming, and moral/emotional judgments (Iovane et al., 2022).

5. Practical Architectures and Metrics

Model/Framework	Core Structural Principle	Formalization Layer
ITCM/ITCMA (Zhang et al., 29 Mar 2024)	Time-indexed retention+protention	Matrix fields, LLM prompt integration
CTM (Blum et al., 2021, Blum et al., 2020)	STM/LTM, global workspace	7-tuple, chunk selection, tree alg.
S³Q (Schmidt et al., 2021)	Simulation/synchrony/binding	Oscillatory clustering/kWTA
Modular Consciousness Theory (Gillon, 2 Oct 2025)	Modular, density-tagged IIS	Vector tagging, feedback loops
Relational/Combinatorial (Mason, 2012)	Typical-state-induced geometry	Graph thresholding/metric

Empirical validation metrics include task completion rates (e.g., ITCMA >96% in seen tasks, >85% in real-world robotics), alignment with experimental neural/psychological data (“priming,” “moral judgment” effects), and operational indices such as density vector magnitude ($\|\rho\|$) and graph-entropy/energy calculations.

6. Controversies, Open Problems, and Limitations

• Noncomputability and Physical Realizability: While the noncomputability result represents a robust constraint on digital instantiation of “unitary consciousness,” it leaves open whether biological—or analog—systems can achieve this via other computational or physical means, or whether real systems only approximate such integration (Maguire et al., 2014).
• Role of Substrate and Evolutionary Rationale: Substrate-dependence (e.g., gating of reactive sub-systems via a control switch $c$) is presented as an evolutionary rationale for consciousness in reactive architectures, but not as necessary for high-level intelligence (AI without $a_r$) (Sritriratanarak et al., 17 Oct 2025).
• Functional vs. Structural Sufficiency: Structural correspondences must be complemented by functional exploitation—without which neither neural nor model-theoretic mappings suffice for consciousness (Paßler et al., 30 Dec 2024).
• Scalar vs. Multidimensional Indices: There is no consensus on whether consciousness should be reduced to scalar measures (information, energy, entropy, coherence), multidimensional vectors, or more elaborate relational structures.

7. Integration with Broader Theories and Applications

Info-structural models subsume and extend dominant theories:

• Compared to Global Workspace Theory (GWT), info-structural approaches provide formal mechanisms and architectures (e.g., explicit selection, compression, metric structure), while reconciling with the necessity for broadcast and competitive access (Blum et al., 2021, Blum et al., 2020).
• They broaden Integrated Information Theory (IIT) by distinguishing lossless from lossy/causal integration, and encoding phenomenology in higher-order, context-dependent, or graph-derived structure (Maguire et al., 2014, Gillon, 2 Oct 2025).
• Application domains include robust agent architectures (planning, memory, action readiness), biological modelling (e.g., thalamocortical loops (Hateren, 2018)), and empirical investigations of moral, emotional, and awareness-related phenomena (Iovane et al., 2022).

In summary, the Info-Structural Model of Computational Consciousness grounds consciousness in emergent, context-sensitive, functionally exploited, and mathematically precise structures of information integration, relational geometry, and control dynamics, subject to constraints of computability, substrate, and evolutionary logic.