Semantic Models in Computational Systems

• Semantic models are formal or learned representations that encode meaning in lexical, discourse, and multimodal contexts, offering structured and scalable insights.
• They employ varied methodologies—from explicit symbolic frameworks to neural retrieval systems—that balance interpretability against computational efficiency.
• Recent advances integrate hybrid belief systems, semantic communication protocols, and executable ontologies to improve task-specific retrieval and decision-making.

Semantic models are formal or learned representations of meaning used to encode lexical content, discourse structure, multimodal correspondences, world state, and task-specific relevance. Recent work uses the term for universal semantic paraphrase in the Natural Semantic Metalanguage, for first-stage retrieval models defined by query and document encoders plus a matching function, for shared intermediate spaces across languages and modalities, for explicit world-centered ontologies with normative and causal layers, and for hybrid semantic-geometric beliefs in planning under uncertainty (Baartmans et al., 17 May 2025, Guo et al., 2021, Wu et al., 2024, Mantsivoda et al., 1 Apr 2026, Lemberg et al., 20 Jan 2025).

1. Formal conceptions of semantic modeling

One mathematically explicit usage defines a semantic model as

$$\text{SM}=\bigl(\Sigma,\;D,\;I,\;\Gamma,\;\mathcal{C}\bigr),$$

where the vocabulary $\Sigma=(C,P,F)$ contains constants, predicates, and functions; $D$ is a nonempty domain; $I$ interprets symbols over $D$; $\Gamma=(E,R,S,A,T)$ provides the operational state in terms of entities, relations, state space, admissible actions, and a transition relation; and $\mathcal{C}$ is a set of first-order normative constraints that must hold in every reachable state. On top of this ground layer, the same formalism adds a causal-knowledge layer $\mathcal{K}$ consisting of probabilistic implications $(\alpha\xrightarrow{p}\beta)$ above a reliability threshold $\theta$, so that semantics includes ontology, dynamics, norms, and learned causal regularities rather than taxonomy alone (Mantsivoda et al., 1 Apr 2026).

A second, highly influential formalization treats semantic modeling as a relevance function for search. In that setting, a first-stage retrieval model learns a query encoder $\Sigma=(C,P,F)$0, a document encoder $\Sigma=(C,P,F)$1, and a matching function $\Sigma=(C,P,F)$2, yielding

$\Sigma=(C,P,F)$3

This unified framework covers classical term-based retrieval, early latent semantic methods, sparse neural retrieval, dense dual encoders, and hybrid systems, and makes semantics operational as a scoring relation between text objects rather than as an ontology of a world (Guo et al., 2021).

A third formulation encodes meaning as a discrete hierarchical identifier. In LMIndexer, a semantic ID for a document $\Sigma=(C,P,F)$4 is a sequence

$\Sigma=(C,P,F)$5

with coarse-to-fine structure across positions. Here semantics is represented not by a dense vector alone but by a prefix-structured code suitable for inverted indexes and generative retrieval (Jin et al., 2023).

Taken together, these definitions indicate that “semantic model” is not a single formal object. It may denote an explicit symbolic world model, a task-conditioned similarity function, or a discrete sequence whose prefix structure encodes semantic locality. A plausible implication is that the field is best understood by the representational commitments it makes: what counts as meaning, what object is being represented, and which operations must remain computationally tractable.

2. Lexical, sentence-level, and discourse-semantic models

In lexical semantics, the Natural Semantic Metalanguage (NSM) treats meaning as reducible to a small, universal inventory of semantic primes, described as a set of approximately 65 primitive meanings attested in virtually all human languages. Complex words are paraphrased by explications that use predominantly primes and permitted molecules, avoid circularity, remain as minimal as possible, and preserve key entailments under substitution. The LLM-based NSM task takes a target word $\Sigma=(C,P,F)$6 and 2–5 example sentences and generates a multi-line explication $\Sigma=(C,P,F)$7 under these constraints. Using WordNet 3.0 senses, the study filtered 88,078 unique senses into a final dataset of about 44,000 entries, then fine-tuned DeepNSM-1B and DeepNSM-8B with standard autoregressive next-token loss. On a 149-word benchmark, DeepNSM-8B obtained the best Exp. Score, Legality, Substitutability, and Primes % among the evaluated systems, with an Exp. Score of 24.6 versus 22.9 for GPT-4o; it also led or matched the strongest baselines in cross-translatability across five low-resource languages (Baartmans et al., 17 May 2025).

At the discourse level, semantic LLMs can be built over abstracted semantic frames and discourse markers. The two discourse-driven SemLMs are the Frame-Chain model, which represents a document as a sequence of frames and discourse markers, and the Entity-Centered model, which represents frame-argument labels and discourse markers along a coreference chain. Each is instantiated with a tri-gram model and three neural LLMs—Skip-Gram, CBOW, and Log-Bilinear. On NYT hold-out data, the Log-Bilinear model achieved the lowest perplexity in both settings, 108.5 for Frame-Chain and 109.7 for Entity-Centered. The same semantic LLMs also improved downstream semantic tasks: in coreference resolution, adding EC-LB conditional-probability and embedding features raised CoNLL12 F1 from 63.03 to 63.46, and in shallow discourse parsing, FC-LB features raised CoNLL16 Test overall F1 from 60.4 to 61.4 (Peng et al., 2016).

Evaluation work on semantic textual similarity complicates any simple equation between lexical overlap and semantic adequacy. A dataset of 775 English word-sentence pairs, annotated by human raters using Maximum Difference Scaling and a free-ranking alternative, showed that higher-order distributional models captured substantial variance in human judgments: mean Spearman correlation across targets reached 0.80 for UMBC Ebiquity, 0.78 for Word2Vec, and 0.72 for LSA. However, these systems were not sensitive to implicatures and entailments that human raters processed, including antonymy confusions, prototypical entailments such as “dime” for “small,” and event knowledge such as “negotiated” for “speak” (Glasgow et al., 2016).

Diachronic semantic modeling adds a temporal dimension. A study of synonym change recast the historical contrast between the Law of Differentiation and the Law of Parallel Change as binary classification over synonym pairs from the 1890s evaluated against WordNet in the 1990s. Using SGNS embeddings, Orthogonal Procrustes alignment, synchronic distances, diachronic distances, and frequency features, supervised Logistic Regression and SVM models reached balanced accuracy around 0.62 on the overall dataset. The empirical distribution favored differentiation: 15.1% of pairs remained synonymous, while 84.9% differentiated (Liétard et al., 2023). This suggests that semantic models used for historical inference must represent not only similarity at a time slice but also structured divergence over time.

3. Emergent semantics in neural representations and multimodal systems

A central current question is whether semantic structure is learned directly during pre-training or only during task-specific adaptation. For semantic role understanding, frozen decoder-only transformers trained only with the causal language modeling objective already contain substantial role information. On QA-SRL, frozen probes achieved 36.4, 39.6, 43.6, and 44.7 F1 for Tiny, Small, Base, and Medium models, respectively, while full fine-tuning reached 44.6, 53.3, 63.8, and 65.8. The Normalized Emergence Score,

$\Sigma=(C,P,F)$8

was approximately 0.60 for Tiny and approximately 0.47–0.51 for larger models, indicating that about 50–60% of the fine-tuned gain was already present in frozen representations. Representation analyses further showed that semantic role structure becomes more distributed with scale, with the first two principal components explaining 19.2% of variance in Tiny but only 7.3% in Medium (Griffiths et al., 9 May 2026).

A related account of internal semantics is the semantic hub hypothesis. It proposes that a single set of parameters projects heterogeneous inputs—different natural languages, code, arithmetic expressions, images, and audio—into a shared intermediate space in which semantically equivalent items lie near one another. In multilingual text, professionally translated English–Chinese sentences in LLaMA-3 70B reached a peak $\Sigma=(C,P,F)$9 of about 0.12 in mid-layers, and logit-lens analysis showed dominant-language anchoring: when processing Chinese prefixes, the probability of the English token “write” exceeded that of the Chinese token “写” by about 0.2 log-prob in layers 18–30. Analogous mid-layer alignment was reported for arithmetic, code, image-caption pairs, and audio-label pairs, and activation-space interventions in one modality predictably altered outputs in another (Wu et al., 2024). The paper explicitly notes that over-reliance on a dominant language may introduce cultural or linguistic bias.

Pixel-level semantics have also been extracted from diffusion models without additional training. EmerDiff identifies semantic correspondences between image pixels and low-resolution feature maps in Stable Diffusion by clustering 16×16 cross-attention query vectors, perturbing a selected cluster during denoising with $D$0, and measuring the resulting full-resolution difference map

$D$1

The final segmentation is produced by assigning each pixel to the cluster with maximal response, optionally after Gaussian smoothing. On unsupervised segmentation, EmerDiff improved over naïve upsampling of Stable Diffusion features across all reported datasets, including ADE150 (33.1 vs. 29.1 mIoU), PASCAL-Context-59 (45.7 vs. 41.5), and City19 (37.1 vs. 32.3). It also improved annotation-free open-vocabulary segmentation when combined with MaskCLIP or TCL (Namekata et al., 2024). The reported limitations are equally specific: tiny objects, tightly packed limbs, and homogeneous regions remain difficult because details collapse in 16×16 features or because color and location entangle with semantics.

The notion of semantic continuity addresses a different failure mode: semantic discontinuity in discriminative models. The proposed continuity loss,

$D$2

penalizes large representational changes under non-semantic perturbations such as brightness, contrast, saturation, hue, or adversarial noise. On CIFAR-100 and ImageNet, adding this loss reduced average $D$3 under non-semantic transforms and improved PGD robustness. For example, ResNet18 rose from 9.34 to 16.01 PGD-adversarial accuracy with the continuity constraint alone, and ResNet18Adv rose from 44.30 to 54.04 with the continuity constraint added; on ImageNet, ResNet50Adv rose from 8.25 to 32.55 (Wu et al., 2020). The same study reports smoother saliency maps, improved transfer, and a modest fairness gain on Colorful MNIST, while also noting a slight reduction in clean accuracy at large $D$4.

4. Retrieval, indexing, and semantic communication

In information retrieval, semantic models for first-stage retrieval are organized by their encoders and matching functions. Classical term-based models such as VSM and BM25 score sparse lexical representations; early semantic methods such as LSI, ESA, and translation models mitigate vocabulary mismatch through latent or concept spaces; and neural semantic retrieval uses sparse reweighting, sparse learned encodings, dense dual encoders, late interaction, or hybrid scoring (Guo et al., 2021). The survey reports typical MS MARCO passage retrieval figures that expose the retrieval trade-off directly: BM25 achieves recall@100 of about 0.88 and MRR@10 of about 0.17, docTTTTTquery + BM25 reaches recall@100 of about 0.93, DPR + ANN reaches recall@100 of about 0.90 and MRR@10 of about 0.24, and ColBERT reaches recall@100 of about 0.92 but with two orders of magnitude more FLOPs per query than BM25 (Guo et al., 2021).

LMIndexer reframes indexing itself as semantic sequence generation. A Transformer encoder-decoder produces hidden states for each ID position, selects codebook entries through a position-specific softmax, and trains progressively with three losses: self-supervised reconstruction, contrastive diversification, and commitment to previously learned positions. The result is a neural sequential discrete representation whose prefixes encode coarse-to-fine semantics. On self-supervised ID quality, LMIndexer achieved AMI of 0.3563 on Beauty, 0.4163 on Sports, and 0.3536 on Toys, outperforming rq-VAE and hierarchical clustering baselines. It also outperformed baselines in sequential recommendation, product search, and document retrieval on several datasets, although DPR remained strongest on MACRO-1M (Jin et al., 2023).

In semantic communication, foundation models are used not merely to encode language but to optimize transmission at ultra-low rate. The system extracts multimodal semantic features, maps them to binary streams, transmits them through a digital channel, and reconstructs the signal with a generative semantic decoder. Two decoder-side regimes are considered: uncoded forward-with-error and coded discard-with-error. The perception–error function is shown to be monotonic with respect to bit-error rate or block-error rate, which supports the definition of per-stream semantic values and semantic-aware power allocation. On Kodak images with prompt and edge-map streams decoded by ControlNet + Stable Diffusion, the semantic-aware schemes yielded up to 10% power saving in uncoded BPSK and up to 90% power saving in the coded discard-with-error case (Xu et al., 2024). This places semantic modeling in a communications-theoretic setting where “meaning” is operationalized as perceptual contribution under a rate–distortion–perception objective.

5. World-centered, ontological, and executable semantic models

World-centered architectures make semantics the shared substrate of a multi-agent system rather than an internal property of isolated agents. In this framework, worlds are classified along six binary dimensions—ontological explicitness, structural stability, normativity, observability, semantic growth boundedness, and perception versus deliberation—and archetypes such as institutional worlds, hybrid cyber-physical worlds, and physical/perceptual worlds are obtained by fixing the resulting 6-bit signature $D$5 (Mantsivoda et al., 1 Apr 2026). Coordination then proceeds through a semantic perception–action–learning loop: agents read the current state and causal context, choose actions, apply transitions only if the resulting state satisfies $D$6, and update the causal layer through semantic machine learning. Ontobox implements this design with an object-ontology repository, SML engine, inference/API layer, access control, and agent adaptor. Reported deployments include private clinic management with a 10× reduction in scheduling conflicts and 40% fewer compliance violations, car loan management in which default prediction accuracy rose from 72% to 85%, and hydroponic-farm automation with a 25% reduction in crop-yield variance and average reaction time of about 2 minutes versus 15 minutes in a heuristic baseline (Mantsivoda et al., 1 Apr 2026).

SUMO-based semantic modeling represents a different symbolic tradition. SUMO supplies a first-order ontology rooted at Entity, together with classes, instances, relations, predicates, and SUO-KIF axioms. The paper on semantic modeling with SUMO uses this ontology as the backbone of lightweight, programmatic constructs such as states, transitions, flows, and microworlds. State change is represented formally through predicates such as holdsDuring, and executable behavior is implemented with Python methods and run-time validation rather than full theorem proving. The proof-of-concept examples include an ignition switch and a four-stroke gasoline engine with Intake, Compression, Combustion, and Exhaust transitions, where world-state dictionaries are updated and checked after each step (Allen, 2020). The computational trade-off is explicit: full tooling with theorem provers such as Vampire/E is expressive but expensive, whereas the Python embedding avoids global proof search and instead rejects inconsistent transitions on the fly.

Executable semantic models extend the same idea beyond ontology-centric formalisms. In the object-oriented approach, classes combine typed attributes with methods implementing transitions and mechanisms, and systems are modeled as microworlds of interacting objects. The paper’s worked examples are a waterfall and the cardiopulmonary system. The waterfall model repeatedly instantiates WaterPortion objects and moves them through upper bed, drop, and pool states; the cardiopulmonary model links SA node, heart chambers, capillaries, medulla, phrenic nerve, diaphragm, lungs, and fluid portions in asynchronous circulation and respiration threads, including a diffusion mechanism for oxygen and carbon dioxide exchange (Allen, 2019). The contrast with ontology-only approaches is sharp: ontologies classify and constrain, but executable semantic models enact behaviors, state changes, and temporal interaction.

6. Hybrid belief, semantic safety, and recurring limitations

Semantic modeling in robotics often requires explicit coupling between discrete semantic variables and continuous geometry. The hybrid-belief POMDP framework represents the environment as a joint posterior

$D$7

where $D$8 contains robot trajectory and object poses, and $D$9 is the semantic mapping over object classes. The key reformulation factors this belief into a geometric marginal, an efficiently computable scalar aggregation term, and conditionally independent semantic posteriors for each object given the continuous state. Under suitable reward structure,

$I$0

the value function and the probability of semantic safety can be computed with explicit expectation over semantic assignments in polynomial rather than exponential time. In simulation, MCMC-Ours and PF-all-hyp tracked the exact-all-hyp estimator closely, while exact-all-hyp and PF-all-hyp scaled exponentially with the number of classes or objects but MCMC-Ours scaled linearly; in a replanning example with $I$1, exact-all-hyp and MCMC-Ours achieved 96/100 successful trials, SNIS-Ours about 94/100, and pruned methods about 81–91/100 (Lemberg et al., 20 Jan 2025).

Across the literature, limitations recur even when the representational form changes. Distributional STS models capture lexical co-occurrence and taxonomy overlaps but largely fail to incorporate world knowledge that triggers entailments and pragmatic implicatures (Glasgow et al., 2016). LLM-based NSM generation improves substantially over untuned baselines, yet substitutability tests depend on grader LLMs, prime-only decoding constraints have not been explored, and human verification remains recommended for authoritative use (Baartmans et al., 17 May 2025). Emergent semantic role structure from language modeling is substantial but incomplete, with fine-tuning still contributing 8–21 F1 points depending on scale (Griffiths et al., 9 May 2026). Shared hub spaces support cross-lingual and cross-modal transfer, but the same mechanism may privilege the dominant pretraining language (Wu et al., 2024). In diffusion-based segmentation, tiny objects and homogeneous regions remain challenging (Namekata et al., 2024). In retrieval, fixed-length semantic IDs and large codebooks create cost and scalability issues, and on some very large collections dense retrieval remains stronger (Jin et al., 2023). In semantic continuity, robustness gains may trade off against clean accuracy if the continuity weight is not tuned carefully (Wu et al., 2020).

These limitations do not reduce semantic modeling to a single unresolved problem; rather, they identify the principal tensions in the area. Current work repeatedly trades off explicitness against scalability, interpretability against raw performance, and universal or shared semantic structure against domain-specific constraints. This suggests that the most durable semantic models may be hybrid systems: explicit where norms, safety, or auditability matter, and learned where scale, coverage, or cross-modal generalization is required.