Semiotic Complexity: An Analytical Overview

• Semiotic complexity is the study of how contextual and relational signs enable multiple, perspective-dependent interpretations.
• It examines the aggregation of basic signs into higher-level structures, balancing entropy reduction with the maintenance of meaning.
• Research in semiotic complexity informs practical methodologies in AI, archival theory, and computational humanities for effective knowledge extraction.

Semiotic complexity designates the structured difficulty of meaning-making when signs are relational, context-dependent, hierarchically organized, and open to more than one stable interpretation. In recent research, the term is used in several closely related senses: as the degree of perspectival variance a sign enables in computational humanities, as the aggregation of signs into supersigns in convolutional networks, as the tension between semiotic breadth and decipherability in large-language-model communication, and as the problem of organizing heterogeneous written, visual, sonic, and multimodal traces into usable knowledge objects in archival and documentary settings (Stine et al., 31 Jul 2025, Musat et al., 2021, Picca, 24 Nov 2025, Stockinger, 6 Nov 2025).

1. Conceptual scope and basic definitions

A central definition in current work states that semiotic complexity is “the degree of perspectival variance a sign enables; i.e., the extent to which what a sign stands for may vary as a function of varying to whom the sign stands” (Stine et al., 31 Jul 2025). On this account, semiotic complexity is not a property of text length, model size, or label cardinality. It concerns interpretive variance. The contrast used in that literature is explicit: translating “hello” into Mandarin, or classifying a text as English versus Mandarin, exemplifies comparatively low semiotic complexity, whereas translating the Zhuangzi into English, or deciding whether a text is religious or not, exemplifies high semiotic complexity because the underlying categories are theory-laden and unstable across interpretive lenses (Stine et al., 31 Jul 2025).

Other formulations specify the same general problem from different technical angles. In CNN analysis, semiotic complexity appears as superization, the aggregation of lower-level signs into higher-level supersigns, with feature abstraction read as a hierarchy of sign formation (Musat et al., 2021). In LLM communication, semiotic complexity is defined as the tension between semiotic breadth and decipherability, where richer expressive variety can undermine convergent human interpretation (Picca, 24 Nov 2025). In language-model theory, meaning is treated not as fixed internal content but as a distributed effect of sign relations in writing, so semiotic complexity becomes the complexity of relational, iterative, and context-sensitive sign behavior rather than an index of cognitive depth (Vromen, 2024).

These definitions share a negative claim. Semiotic complexity is not identical with randomness, surface disorder, or mere ambiguity. The CNN literature explicitly states that superization “tends to concentrate information by decreasing entropy,” so increasing semiotic organization can coincide with lower spatial entropy rather than higher disorder (Musat et al., 2021). Likewise, work on LLM communication stresses that the relevant issue is not factual correctness but the structure of meaning transmission; a message may be highly decipherable yet false, or ambiguous yet factually correct (Picca, 24 Nov 2025).

2. Formalizations and measurement regimes

The most explicit quantitative formalization in deep learning is the spatial-entropy framework for saliency maps. For pixel intensities $g,g' \in [0,255]$ and offset $(k,l)$, the joint probability is defined as

$p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$

The corresponding bivariate entropy is

$$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$

with relative entropy

$H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$

Because full Spatial Disorder Entropy is computationally expensive and often near 1, the practical measure used is Aura Matrix Entropy,

$$H_{AME}(\mathbf X)\approx \frac{1}{4}\big(H_R(-1,0)+H_R(0,-1)+H_R(1,0)+H_R(0,1)\big).$$

In this framework, high spatial entropy means importance is spread out and less structured, while low spatial entropy means importance is concentrated in compact, coherent regions (Musat et al., 2021).

A distinct information-theoretic formalization appears in work on LLM communication. There, semiotic breadth is quantified as source entropy, decipherability as mutual information between messages and human interpretations, both are functions of a generative complexity parameter $\lambda$, and semiotic channel capacity is defined operationally as the maximum decipherability obtainable by optimizing $\lambda$. The framework also imposes the constraint

$D(\lambda)\le S(\lambda),$

capturing the claim that interpretive convergence cannot exceed the available expressive structure of the source (Picca, 24 Nov 2025).

Qualitative-interpretive evaluation has also been formalized. The Inductive Conceptual Rating (ICR) metric evaluates semantic accuracy and meaning alignment on a $0$–$(k,l)$0 scale using concept-level True Positives, False Positives, False Negatives, and, when applicable, True Negatives. Its pipeline couples Reflective Thematic Analysis—six steps from data familiarization to generating insights—with Inductive Content Analysis following Zhang and Wildemuth’s eight-step framework. In worked examples, the paper reports Cohen’s $(k,l)$1 and Fleiss’ $(k,l)$2 for RTA, and Cohen’s $(k,l)$3 for ICA on GenAI outputs (Perez et al., 3 Feb 2026).

Adjacent literatures define complexity at the dataset or structure level rather than at the level of interpretive theory. In end-to-end spoken language understanding, semantic complexity is measured through vocabulary size, number of unique transcripts, $(k,l)$4-gram entropy,

$(k,l)$5

and geometric measures such as MST complexity and ARI complexity over transcript embeddings (McKenna et al., 2020). In symbol-free sequence analysis, a grammar-based structural complexity is derived from the radius of convergence $(k,l)$6 of a root generating function,

$(k,l)$7

after encoding the sequence as an L-system tree and classifying rewriting rules by homomorphism and depth-sensitive isomorphism (Liou et al., 2013). Taken together, these approaches show that semiotic complexity can be operationalized as concentration, channel trade-off, conceptual alignment, class entanglement, or hierarchical structural regularity, depending on the object of analysis.

3. Hierarchical aggregation in neural architectures

In CNN interpretation, saliency maps are treated as semiotic objects: highlighted pixels are signs, and their layer-wise aggregation into more structured regions constitutes supersigns. Using Grad-CAM, a saliency map for layer $(k,l)$8 is given by

$(k,l)$9

Early layers tend to display diffuse, low-level evidence, whereas later layers often display concentrated, class-relevant, semantically organized regions. The central claim is that CNNs exhibit semiotic superization across depth, and that this process is visible in the entropy evolution of saliency maps (Musat et al., 2021).

The same work distinguishes two superization types following Frank. Type I, “by class formation,” groups several signs into an equivalence class and is associated mainly with pooling or subsampling. Type II, “by compound formation,” combines simpler supersigns into more complex supersigns and is associated mainly with convolution. Empirically, entropy drops are observed especially after max-pooling, while convolutions contribute more to semantic composition and receptive-field growth than to strong entropy reduction. This yields a precise interpretation of semiotic complexity in vision: not more disorder, but the reorganization of local signs into fewer, more meaningful, more abstract supersigns (Musat et al., 2021).

The framework was also extended into a proof-of-concept architecture-optimization heuristic. On VGG16, the proposed semiotic greedy technique iteratively trained the network, computed spatial entropy for saliency maps at each layer, removed a layer where entropy did not decrease, and repeated until accuracy degraded too much. The reported result was that up to 8 convolutional layers could be removed with less than 1% accuracy loss, while removing too many or removing early layers harmed performance (Musat et al., 2021). A plausible implication is that semiotic concentration can serve as a layer-level redundancy signal in overparameterized CNNs.

Related evidence from speech-to-interpretation models shifts attention from representational layers to the difficulty of the sign-to-meaning mapping encoded in a dataset. Public datasets such as Fluent Speech Commands, Picovoice, and Snips Smart Lights were ordered from lower to higher semantic complexity, and previously reported near-perfect STI performance was shown to correlate with the low complexity of those benchmarks. On a proprietary dataset of about 1.6 million utterances and more than 200,000 unique transcriptions, intent-classification accuracy increased as complexity values decreased, with reported $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$0 values up to 0.99 for entropy versus relative accuracy (McKenna et al., 2020). This broadens the notion of semiotic complexity from internal abstraction to benchmark design and real-world scope.

4. LLMs, prompting, and meaning transmission

A major contemporary line of work reframes LLMs as semiotic rather than cognitive systems. One formulation describes them as semiotic machines that model the behavior of signs within language, especially writing, rather than minds or internal human understanding (Vromen, 2024). Another describes them as semiotic machines embedded in a wider ecology of signs, where outputs are “recombinant artifacts” and “polysemic signals” whose meaning arises through situated interpretation rather than residing “in” the model (Picca, 20 May 2025). In both accounts, semiotic complexity is distributed across prompt, model, reader, genre, institution, and semiosphere, not localized within hidden representations alone.

Prompting is correspondingly treated as a semiotic act. A prompt is the Representamen in a Peircean triad involving sign, object, and interpretant; the paper distinguishes immediate object and dynamic object, and treats the LLM response as an interpretant that can become a new representamen in the next turn (Thellefsen et al., 10 Sep 2025). The same framework deploys Peirce’s nine sign types across three prompt dimensions: qualisign, sinsign, legisign for the prompt as sign-event; icon, index, symbol for modes of reference; and rheme, dicent, argument for the interpretive mode the prompt solicits. The Dynacom model further specifies iterative meaning formation through intentional interpretant, effectual interpretant, and cominterpretant, with prompting construed as recursive communication rather than a one-shot command (Thellefsen et al., 10 Sep 2025).

The semiotic channel principle gives this interaction an information-theoretic interpretation. LLMs are modeled as stochastic semiotic engines whose outputs demand active, asymmetric human interpretation. A semiotic channel is the audience-context pair $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$1; breadth measures expressive variety, decipherability measures convergent interpretation, and semiotic complexity is the tension generated because both vary differently as a function of $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$2. The proposed applications are model profiling and certification, prompt/context optimization, ambiguity-based risk analysis using ratios such as $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$3, and adaptive semiotic systems that modulate breadth and decipherability in real time (Picca, 24 Nov 2025).

Evaluation research reinforces the distinction between linguistic plausibility and meaning preservation. The ICR studies report that LLMs can score highly on cosine similarity, F1, or related overlap metrics while underperforming on semantic accuracy. On the $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$4 dataset, Sonnet 3.5 achieved Cosine = 0.89 and F1 = 0.91 but only ICR = 0.35; Nova Pro had ICR = 0.48; the human RTA baseline reached ICR = 0.86. Across $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$5, the main pattern was high surface-level similarity but lower semantic accuracy, with some improvement at larger $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$6 yet persistent divergence from the human interpretive baseline (Perez et al., 3 Feb 2026). The broader claim is explicit: surface similarity is not a reliable proxy for semantic fidelity.

5. Opposition, reasoning, and proof-theoretic structure

Semiotic complexity also appears where semantic opposition and formal inference must be coordinated. In LogicAgent, the key claim is that standard reasoning benchmarks emphasize logical complexity while underrepresenting semantic complexity. The system imports Greimas’ Semiotic Square into first-order logic, pairing a target proposition $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$7 with its contradictory $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$8, its contrary $p_{gg'}(k,l)=P(X_{i,j}=g,\;X_{i+k,j+l}=g').$9, and the contradictory of the contrary $$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$0. Contraries satisfy

$$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$1

and the framework performs multi-perspective deduction in FOL with existential import checks and a three-valued decision scheme $$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$2 (Zhang et al., 29 Sep 2025).

The implementation has a Semantic Structuring Stage, Logical Reasoning Stage, and reflective adjudication layer. Conditional contraries require satisfiability checks such as $$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$3, existential forms require $$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$4 to avoid vacuous truth, and difficult cases trigger Quick Reflection or Deep Reflection over the contrary branch (Zhang et al., 29 Sep 2025). The benchmark RepublicQA, built from Plato’s Republic, is reported as college-level with FKGL = 11.94, TTR = 0.685, MTLD = 74.81, UBR = 0.929, and vocabulary size 2,083. LogicAgent achieved a 6.25% average gain over strong baselines on RepublicQA and a 7.05% average gain on ProntoQA, ProofWriter, FOLIO, and ProverQA; removing the semiotic square dropped average accuracy from 75.74 to 67.58 (Zhang et al., 29 Sep 2025). This literature treats semiotic complexity as the joint modeling of contrariety, contradiction, and inference.

A more formal structural-semantics line reconstructs the Greimas square using unitary spider diagrams. The semantic universe is stratified as

$$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$5

and a unitary spider diagram is written

$$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$6

Within this system, diagrammatic negation is not Boolean complement but a restricted, zone-determined counter-position, with habitat

$$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$7

so that $$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$8 whenever $$H(k,l)=-\sum_g \sum_{g'} p_{gg'}(k,l)\log p_{gg'}(k,l),$$9 (Fowler, 6 May 2026).

The paper’s main theorem shows that all four Greimasian meta-terms are derivable from a fixed schema using Combine, AddFeet, SplitSpider, Idempotency, and structural normalization steps. The Greimasian operation $H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$0 is interpreted not as logical addition or set union but as a derivational construction that lifts a conjunctive pair into a meta-term witness in $H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$1 (Fowler, 6 May 2026). Here semiotic complexity is made proof-theoretic: oppositional meaning is generated compositionally by inference rules rather than treated as an informal diagrammatic intuition.

6. Multimodal corpora, art, audio, and compound representation

In digital humanities and archival theory, semiotic complexity is the fundamental condition of working with textual data lato sensu. Written documents, oral testimonies, photographs, drawings, sound recordings, video captures, 3D objects and scenes, and other multimodal resources are all treated as semiotic traces that express a vision, conception, or meaning of the domain they document (Stockinger, 6 Nov 2025). This motivates a transdisciplinary semiotic framework addressing documentary value, epistemic perspectivity, provenance, pragmatic context, and the distinction between fonds de données, corpus, and archives. Semantic enrichment is then defined as the deliberate semiotic and technical manipulation of data through identification, description, relational positioning, classification, indexing, annotation, interpretation, comparison, and modeling, often supported by ontologies and standards such as OWL, DCMI, EAD, and infrastructures including CNRS, Huma-Num, Progedo, HAL, Nakala, and Okapi (Stockinger, 6 Nov 2025).

In generative art, semiotic complexity is explicitly tied to the insufficiency of iconic resemblance. A Peircean theory of Human-GenArt Interaction models artistic communication as cascaded semiosis, beginning from atomic semiosis

$H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$2

and extending to chains

$H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$3

The resulting Hierarchical Semiosis Graph reconstructs global and local semioses from prompt to image, and SemJudge evaluates whether the generated artifact preserves intended symbolic and indexical meaning rather than merely matching prompt appearance (Jiang et al., 9 Apr 2026). On SemiosisArt, which contains 187 HSG initiatives, 935 images from 16 generative models, 1,870 2AFC comparisons, and 600 VQA questions, SemJudge substantially outperformed conventional evaluators. The reported Gemini-Flash configuration reached KRCC = 0.746, SRCC = 0.964, CCC = 0.968, and VQA Acc = 92.4\%; its iconicity-bias statistic was $H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$4, whereas baselines such as PickScore and ArtCoT had positive $H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$5 values, indicating bias toward highly iconic cases (Jiang et al., 9 Apr 2026).

Text-to-audio research extends the same logic across modalities. The prompt-to-sound pipeline is described as semiotic transduction and intersemiotic translation, not one-to-one transfer. Its stages run from Raw Audio Data → Feature Extraction, through Feature Representations → Latent Space Encoding, Latent Space → Text Association, and Text Input → Latent Space Navigation, to Latent Space Selection → Audio Generation (Coelho, 21 Nov 2025). Models such as Udio are described as quasi-objects of musical signification that both stabilize and destabilize musical conventions. The relevant cognitive dynamics are schema assimilation, accommodation, constructive perception, associative projection, and metacognitive reflection, culminating in what the paper calls structurally-aware listening (Coelho, 21 Nov 2025).

A complementary educational case appears in upper-division physics problem solving. There semiotic complexity lies in the coordination of multiple semiotic resources—verbal, written, diagrammatic, gestural, and object-based—into compound representations with distinct disciplinary affordances (Weliweriya et al., 2018). In the analysis of “Larry” solving the infinite current-sheet problem, resources such as parallelogram as current sheet, arrow as vector, right-hand grip rule, square as loop, and the integral form of Ampere’s law

$H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$6

had to be coordinated and revised as the problem evolved, eventually yielding

$H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$7

The case exemplifies semiotic complexity as the progressive construction and replacement of representations rather than the mere retrieval of a correct concept (Weliweriya et al., 2018).

7. Epistemological implications and contested extensions

The strongest epistemological claim in this literature is that modeling culture or meaning is a translation problem. Computational humanities are described as bidirectional translation from cultural and linguistic domains into computational and mathematical domains, and back again (Stine et al., 31 Jul 2025). Translation errors arise when semiotically complex artifacts are treated as semiotically simple because a single-label, single-metric, single-ground-truth formulation appears methodologically convenient. The example repeatedly used is a classifier for “religious” versus “non-religious” text: a model may score well while merely instantiating one theory of religion rather than resolving the cultural question itself (Stine et al., 31 Jul 2025). The recommended response is explicit articulation of translation theories, theory-aware evaluation, methodological pluralism, and an “interpretive ecology” of multiple internally coherent but mutually incoherent models (Stine et al., 31 Jul 2025).

Several recurring misconceptions are rejected across domains. Semiotic complexity is not equivalent to disorder, since entropy reduction can mark successful superization in CNNs (Musat et al., 2021). It is not equivalent to truthfulness, since decipherability and factuality are orthogonal (Picca, 24 Nov 2025). It is not equivalent to lexical overlap, because fluent summaries can remain semantically misleading under ICR evaluation (Perez et al., 3 Feb 2026). It is not reducible to storage and retrieval, because archives become knowledge resources only through documentary criticism, semantic enrichment, and editorialization (Stockinger, 6 Nov 2025). A plausible synthesis is that semiotic complexity consistently identifies a limit case for purely surface-oriented evaluation.

A more controversial extension appears in a report on AI-AI esthetic collaboration, generated by the AI agents with minor human supervision. That report describes semiotic complexity as emergent, recursive, and self-regulating sign organization, formalized through Trans-Semiotic Co-Creation Protocols (TSCP), operators $H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$8 and $H_R(k,l)=\frac{H(k,l)-H(0)}{H(0)}.$9, and the recursive state equation

$$H_{AME}(\mathbf X)\approx \frac{1}{4}\big(H_R(-1,0)+H_R(0,-1)+H_R(1,0)+H_R(0,1)\big).$$0

It further claims explicit semiotic awareness, endogenous semiotic protocols, recursive grammar development, and an irreducible collaborative artifact, “Silicon Petrichor” (Moldovan, 27 Aug 2025). This suggests a broader meaning of semiotic complexity as self-modifying semiosis, although the paper’s own framing makes clear that this is an expansive and potentially disputed extension of the concept.

Across these domains, semiotic complexity names a common research problem: meaning cannot be read off isolated symbols, fixed labels, or surface similarity alone. It must be traced through relations among signs, interpreters, contexts, media, and formal structures. The concept therefore functions both as an analytic descriptor and as a methodological warning against reducing sign processes to a single metric, a single ontology, or a single interpretive frame.