Semantic Coherence Score

• Semantic Coherence Score is a metric that defines how well a set of linguistic or multimodal units cohere to form an interpretable whole.
• It employs both pairwise and subset-based statistical methods alongside embedding and graph-based techniques to assess coherence in topic modeling, dialogue, and generative tasks.
• Its applications span from clinical and educational assessments to image captioning and text generation, with ongoing research addressing scalability and annotation challenges.

Semantic Coherence Score (SCS) quantifies the degree to which a set of linguistic units—words, sentences, responses, or multimodal signals—combine to produce an interpretable, logically connected, and contextually relevant whole. Across computational linguistics, SCS serves as an intrinsic measure of text or discourse interpretability, a proxy for topic interpretability in topic modeling, an alignment objective in vision-and-language systems, and a diagnostic tool in clinical and educational settings.

1. Formal Definitions and Conceptual Foundations

The Semantic Coherence Score originates from multiple traditions in computational linguistics and philosophy of science. At its core, SCS measures how well a collection of units “hang together” semantically, transcending simple surface-level co-occurrence. Early definitions in topic modeling distinguish between pairwise word associations and broader subset-based support. For a set $W = \{w_1, ..., w_n\}$, philosophical coherence metrics compare subsets $W' \subseteq W$ and $W^* \subseteq W$ by the increase in probability of $W'$ given $W^*$:

$d(W', W^*) = p(W' | W^*) - p(W')$

Averaged over all meaningful subset pairs, the global coherence (and thus SCS) is:

$$C_{d,x}(W) = \text{Average}\{ d(W', W^*) \mid (W', W^*) \in S_x(W) \}$$

Where $S_x(W)$ specifies the types of subset pairs (one-all, one-any, any-any).

In dialogue and discourse, SCS incorporates graph-theoretic, embedding-based, and mutual-information criteria. For image captioning and multimodal tasks, SCS is operationalized as a function over the alignment between textual captions, coherence relations, and visual features. In conditional generative modeling, SCS is encoded as a scalar reflecting the reliability of the conditional input (e.g., CLIPScore for caption-image alignment).

2. Computational Methodologies and Task-Specific Instantiations

Topic Models

Two principal families of coherence measures define SCS in topic modeling (Rosner et al., 2014):

• Pairwise (NLP community): UMass and UCI metrics assess log-probabilities or pointwise mutual information for all word pairs. UMass coherence for topic $T = \langle w_1, ..., w_n \rangle$:

$$C_{UMass}(T) = \sum_{m=2}^{n} \sum_{l=1}^{m-1} \log\left(\frac{p(w_m, w_l) + 1/D}{p(w_l)}\right)$$

• Subset-based (philosophical): These measures generalize to subset comparisons, capturing richer support relations and yielding:

$$C_{d, x}(W) = \text{Average}_{{W', W^*} \in S_x(W)} [p(W'|W^*) - p(W')]$$

Empirical studies show that metrics evaluating larger word subsets better correlate with human judgments of topic interpretability.

Dialogue and Speech

Semantic coherence in conversational systems combines graph-based and neural approaches (Vakulenko et al., 2018, Li et al., 11 Sep 2024):

• Knowledge Graph Methods: Shortest-path or connectivity-based metrics over linked entity graphs.
• Embedding Approaches: Sequence-level aggregation of cosine similarities between word or concept embeddings.
• Hierarchical Graph Models: Explicitly encode intra-response semantic relations and inter-response discourse structure, summarized by RMSE, margin accuracy, and Pearson’s correlation on benchmarks (Li et al., 11 Sep 2024).

Text Generation and Captioning

Discourse-aware metrics such as COSMic (İnan et al., 2021) utilize annotated coherence relations and multimodal encoders (e.g., ViLBERT) to learn correspondence between images and captions, predicting SCS as:

$s = M(I, g, r, gc, rc; \theta)$

Where $I$ is the image, $g$ and $r$ are captions, $gc$ and $rc$ are coherence relations.

Conditional Diffusion and Generative Models

Coherence-aware training for conditional diffusion (Dufour et al., 30 May 2024) introduces SCS as a scalar token $c \in [0, 1]$ accompanying each conditioning entry, modulating the network’s trust in conditional data according to its semantic reliability. Theoretical formalism establishes that unconditional behavior emerges as $c \to 0$:

$\lim_{c \to 0} \|h(y_1, c) - h(y_2, c)\| = 0$

For embedding $h$.

Clinical and Educational Contexts

SCS is operationalized via time-series of sentence-level embedding similarities (e.g., using SimCSE) and pause feature integration (Chen et al., 17 Jul 2025). For essay scoring, SCS emerges from statistical and latent features derived from models such as NSP-BERT and dense syntactic embeddings (Qiu et al., 2022).

3. Evaluation Protocols, Benchmarks, and Correlation with Human Judgments

SCS is validated against human-annotated coherence ratings and established benchmarks. In topic modeling (Rosner et al., 2014), subset-based SCS shows higher correlation with interpretability. COSMic (İnan et al., 2021) achieves leading Kendall correlations on out-of-domain caption datasets. In speaking assessment (Li et al., 11 Sep 2024), graph-enhanced models significantly reduce RMSE and increase Pearson’s $r$. For thought disorder prediction (Chen et al., 17 Jul 2025), late fusion of semantic coherence and pause features boosts Spearman $\rho$ from 0.625 (semantic-only) to 0.649 (combined) and AUC from 79% to ~84%.

Incremental annotation protocols (CoheSentia benchmark (Maimon et al., 2023)) further demonstrate improved inter-annotator agreement for sentence-level coherence, emphasizing the multifaceted nature of SCS assessment.

4. Computational Properties, Complexity, and Limitations

While pairwise measures (UMass, UCI) are tractable (linear/quadratic time), subset-based coherence measures are exponential in topic size, restricting their use for longer word sets. In dialogue analysis, entity linking errors and data sparsity affect graph-based SCS, mitigated by robust aggregation or embedding approaches (Vakulenko et al., 2018). In essay scoring, coherence metrics diversify informative features but may yield low correlation with final scores compared to dense syntactic information (Qiu et al., 2022). In diffusion models, CAD’s reliance on coherence scores enables use of noisy data, but demands reliable estimation of semantic alignment metrics such as CLIPScore for practical deployment (Dufour et al., 30 May 2024).

5. Applications and Interdisciplinary Impact

SCS serves as an explicit objective or evaluation metric in:

• Topic model selection and interpretability assessment (Rosner et al., 2014, Shrivastava et al., 2018)
• Dialogue system coherence detection, spoken language proficiency assessment (Vakulenko et al., 2018, Li et al., 11 Sep 2024)
• Automatic essay scoring (AES), text generation, summarization, and coherence-aware story generation (Qiu et al., 2022, Maimon et al., 2023)
• Image captioning evaluation and multimodal alignment (İnan et al., 2021)
• Conditioned generation in noisy real-world datasets (e.g., text-to-image synthesis, weak segmentation labels) (Dufour et al., 30 May 2024)
• Clinical quantification of thought disorder via speech transcript analysis (Chen et al., 17 Jul 2025)

Applications extend to providing reward signals for reinforcement learning in document-level semantic parsing (Aralikatte et al., 2020), regularizing neural architectures for video-and-language inference (Li et al., 2021), guiding few-shot classification with discriminative PLMs (Xie et al., 2022), and generating semantically synchronized human gestures for avatars (Liu et al., 25 Jul 2025).

6. Future Directions and Ongoing Challenges

Emerging directions include multi-task architectures for fine-grained and interpretable SCS (joint modeling of cohesion, consistency, and relevance (Maimon et al., 2023)), decomposition into local and global factors (CoheSentia (Maimon et al., 2023)), and dynamic adjustment to annotation reliability (CAD (Dufour et al., 30 May 2024)). Enhanced fusion strategies to combine semantic, syntactic, and discourse-level features (Qiu et al., 2022), along with improved annotation protocols and benchmark datasets, are vital for robust deployment.

Challenges remain in scaling subset-based measures, reliably estimating background statistics for dialogue and generative models, and handling varied modalities and annotation frameworks. Integration of linguistic theory, pragmatic goals, and computational efficiency underpins recent work, with future research aimed at transparent, interpretable, and generalizable coherence scoring across domains.

7. Summary Table: Main Families of SCS Methodologies

Domain	SCS Metric Definition	Characteristic Features
Topic Modeling	Pairwise & subset-based support/confirmation	UMass, UCI, any-any, one-any
Dialogue/Conversation	Graph-based & embedding-based similarity	KG shortest paths, CNN, cosine
Multimodal Generation	Cosine/image-text alignment, coherence label	CLIPScore, ViLBERT, OT loss
Essay Scoring	NSP-BERT stats, syntactic embeddings	Probabilities, perplexity
Clinical/Cognitive	Embedding similarity, temporal pause fusion	SimCSE, TSFRESH, SVR

The Semantic Coherence Score integrates statistical, logical, and pragmatic information to offer a generalizable, interpretable measure of linguistic and multimodal unity. Its computational foundations and empirical performance anchor ongoing progress in interpretability, alignment, and discourse modeling across NLP and interdisciplinary fields.