Comparative Sharedness: Mechanisms & Measures

• Comparative sharedness is the degree to which common, externally observable signals and structures, rather than private latent factors, organize system behavior.
• It is operationalized across varied fields including neural alignment, macaque social comparison, cross-linguistic studies, dialogue analysis, machine learning feature overlap, and fair resource allocation.
• Research demonstrates that models leveraging direct observable outcomes and shared constraints yield stronger predictive accuracy and more robust system interoperability than those relying on inferred valuations.

Comparative sharedness denotes how strongly a phenomenon is organized by signals, structures, or resources that are jointly available across units of comparison, rather than by private, latent, or source-specific factors. In the literature, the notion is operationalized in several non-equivalent but closely related ways: as reliance on shared, objective partner rewards rather than inferred private valuations in macaque social comparison (Taniuchi et al., 21 Dec 2025); as neural or perceived similarity of interpretation that predicts human information sharing (Baek et al., 2023); as the degree to which linguistic patterns are shared across languages after separating genealogical persistence from contact-induced diffusibility (Chen et al., 2024); as cross-speaker reuse of referent-specific constructions in dialogue (Ghaleb et al., 2024); as cross-model overlap in sparse-autoencoder features for visual, textual, and multimodal encoders (Cornet et al., 24 Jul 2025); and as the extent to which priors, ontologies, or resources can be jointly supported by shared constraints, overlap structures, or pooling arrangements (Biesel et al., 9 Dec 2025, Kent, 2018, Nandigam et al., 2018).

1. Conceptual scope and recurrent distinctions

A central distinction is between shared, externally observable information and private, inferred internal states. In the macaque study, high comparative sharedness means that the self monkey uses the partner’s observed reward probability and outcomes directly as a comparison signal, whereas low comparative sharedness means that the self tries to infer the partner’s subjective valuation and uses that inferred latent state in valuation (Taniuchi et al., 21 Dec 2025). In human information sharing, an analogous contrast appears between content that is expected to be interpreted similarly by others in one’s social circle and content for which such commonality is lower, mixed, or unclear (Baek et al., 2023). In dialogue, sharedness is operationalized as the degree to which both speakers reuse the same lemmatized constructions for a referent; in ontology sharing, it is concentrated in a common generic ontology that each community extends through specification links; in shared-prior theory, it is expressed through compatibility of conditional beliefs on overlaps (Ghaleb et al., 2024, Kent, 2018, Biesel et al., 9 Dec 2025).

A second distinction is between structural sharedness and realized sharedness. The topological analysis of shared priors makes this explicit: structural sharedness depends on the overlap simplicial complex and whether $H^1(X,\mathbb{R})=0$, whereas realized sharedness depends on the particular log-likelihood cocycle $g$ and whether its cohomology class vanishes (Biesel et al., 9 Dec 2025). A related separation appears in comparative linguistics, where sharedness is not treated as raw similarity alone, but as similarity after disentangling inheritance from genealogy and diffusion through contact (Chen et al., 2024).

Taken together, these formulations suggest that comparative sharedness is not a single metric but a family of comparison principles. What remains constant is the analytical question: whether the relevant regularity is carried by common external structure, by private latent structure, or by some controlled mixture of both.

2. Social cognition, interpersonal alignment, and convention formation

In macaque social comparison, comparative sharedness is formalized through three multi-layered, multimodal latent Dirichlet allocation models: an Internal Prediction Model that infers the partner’s subjective values, a No Comparison Model that ignores partner information, and an External Comparison Model that routes partner reward information and behavior directly to the upper situation node without a partner subjective-value node (Taniuchi et al., 21 Dec 2025). The dataset comprised 292 days of behavior from two face-to-face macaques in six conditioned blocks per day, with each block treated as a document and subjective values operationalized as latent categories $z^{R_S}$. On test data, the External Comparison Model achieved the highest Rand Index, with 0.88 against 0.79 for the Internal Prediction Model and 0.75 for the No Comparison Model, with chance at approximately 0.72. Complementary analyses reported cleaner topic separation, better behavioral prediction from images, and theoretically consistent monotonic extrapolation under the External Comparison Model. The paper therefore concludes that, in this Pavlovian social conditioning paradigm, macaque social comparison is best explained by comparative sharedness: direct utilization of observable partner outcomes without explicit inference of the partner’s subjective reward valuation.

In human information sharing, comparative sharedness is operationalized as neural alignment and perceived alignment. The neuroimaging study computed inter-subject correlation, $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$, on 214 ROIs while members of the same dorm community watched 14 videos, and linked dyad-by-video neural similarity to post-scan sharing judgments using linear mixed-effects models (Baek et al., 2023). Dyads in which both members reported high sharing likelihood showed larger inter-subject correlations than low-sharing dyads in parcels including the precuneus, superior temporal gyrus, middle temporal gyrus, temporal pole, inferior parietal lobule, superior parietal lobule, and left amygdala. The behavioral studies then showed that perceived similarity robustly predicts sharing likelihood: in Study 2, $\beta_1=0.398$ with $\mathrm{SE}=0.041$ and $p<0.001$, falling to $\beta_1=0.189$ with controls for audience interest and valence; in Study 3, experimentally describing the audience as similar increased sharing relative to dissimilar, unclear, and, under controls, mixed audiences.

Dialogue studies replace reward comparison or audience similarity with shared linguistic behavior. In a referential communication corpus with 66 Dutch-speaking dyads, shared lemmatized constructions were defined as lemma sequences produced by both speakers for the same referent and filtered to remove function-word-only sequences and multi-referent generic expressions (Ghaleb et al., 2024). Utterance-level sharedness was measured as $$P_{\mathrm{shared}}(d,r,t)=U_{\mathrm{shared}}(d,r,t)/U_{\mathrm{total}}(d,r,t)$$, and cross-speaker convergence as $$\Delta S(d,r)=S_{\mathrm{post}}(d,r)-S_{\mathrm{pre}}(d,r)$$ using cosine similarity over binary lemma vectors. Shared constructions increased from 27% of utterances in Round 1 to 37% in Round 6 in real dyads, while pseudo-pairs remained at 14% and showed no increase. Post-interaction name similarity rose from a mean of 0.06 to 0.43 in real dyads, and convergence was positively associated with dominant-type frequency and recency, but negatively associated with the number of shared construction types. Comparative sharedness here is thus not merely reuse, but the progressive narrowing of reuse toward a dominant, referent-specific type.

3. Cross-linguistic, cross-text, and ontological sharedness

In comparative linguistics, comparative sharedness refers to how much a linguistic pattern is shared across languages once genealogical persistence is separated from contact-induced diffusibility (Chen et al., 2024). The study constructed a graph over 1,966 languages and 1,931,595 language pairs, with semantic distances derived from cosine distance over frequency-weighted colexification vectors and phonological distances from ASJP sound-class comparisons on 40 nuclear concepts. Its mixed-effects regressions supported low persistence of colexifications relative to phonology, but did not support the hypothesis that colexifications are more diffusible than phonology. Instead, both colexification and phonology were found to be governed predominantly by genealogy once contact variables were controlled. The paper also reported a persistence gradient among colexification types—nuclear greater than emotion, greater than non-nuclear, greater than random—and found that abstract colexifications tend to be more persistent than concrete ones.

Cross-source text mining uses comparative sharedness to connect semantically correlated texts from different sources. In Mutual Clustering on Comparative Texts, tweets and news are modeled as heterogeneous information networks, with anchor texts providing explicit cross-source links and meta-path similarities capturing shared words, entities, mentions, hashtags, retweets, and hyperlinks (Cao et al., 2019). The per-source clustering objective is the normalized-cut criterion

$g$0

and mutual clustering adds a cross-source consistency term based on the Frobenius norm between anchor-projected co-assignment matrices. On three tweet–news datasets, the HINT framework outperformed baselines in NMI and F1 and achieved lower conditional entropy on anchored subsets, indicating that anchor-induced sharedness can regularize within-source clustering while improving cross-source alignment.

Ontology sharing provides a categorical and logical version of the same idea. Within Information Flow, a participant community ontology is formalized as a sound IF logic $g$1, the common shared extensible ontology as an IF theory $g$2, and the specification links as theory interpretations $g$3 (Kent, 2018). Sharing is computed through a two-step process: lift $g$4 into logic via the $g$5 adjunction, then form a virtual ontology of community connections as the fusion of the participant ontologies, namely the quotient of their sum modulo the sharing structure. In the two-community case, the fusion is the pushout $g$6, where $g$7 aligns instances that agree through the shared theory and identifies types that are images of the same shared type. Comparative sharedness in this setting is exact semantic interoperability mediated by a common theory.

4. Representation-level sharedness in machine learning systems

For neural encoders, comparative sharedness has been defined directly at the feature level. The sparse-autoencoder study considers 21 encoders spanning vision-only, text-only, and multimodal families, trains TopK SAEs with $g$8 and expansion factor 8, and compares SAE features using the weighted Max Pairwise Pearson Correlation indicator (Cornet et al., 24 Jul 2025). For a source feature $g$9, the per-feature maximum correlation to model $z^{R_S}$0 is

$z^{R_S}$1

and the aggregate indicator is

$z^{R_S}$2

where $z^{R_S}$3 is a cumulative activation weight. The paper then defines feature-level Comparative Sharedness by

$z^{R_S}$4

and extends this to group comparisons using a minimum over one model class and a maximum over another.

The empirical picture is modality-sensitive. On COCO, all-layer averages for large models were approximately 0.463 for Image→Image, 0.204 for Image→Text, 0.168 for Text→Image, and 0.367 for Text→Text, whereas last-layer comparisons reduced same-modality values but preserved or increased cross-modality values, indicating that cross-modal shared information concentrates in the last layers (Cornet et al., 24 Jul 2025). Dataset choice also matters: LAION-2B subset and Flowers-102 produced lower cross-modal scores than COCO. The feature-level analyses showed that visual features specific to VLMs among vision encoders are also shared with text encoders. The most distinctive feature groups included age-related features, pets with unusual behaviors, rooms of a house, vehicles, “old photos,” geographically inflected concepts, and a verb-like visual concept corresponding to “to ride.” The paper interprets these results as evidence that text pretraining shapes some high-level visual concepts.

NeuroComparatives studies a different but related problem: large-scale comparative knowledge distillation over everyday objects (Howard et al., 2023). Its pipeline generates and filters natural-language comparative statements such as “Compared to helicopters, planes are more stable in flight” or “Compared to cars, motorcycles generally have lower fuel consumption,” producing up to 8.8M comparisons over 1.74M entity pairs. Human validity rises from 58.1% for WebChild to 76.9% for NC-XL, 84.4% for NC-L, and 90.1% for NC-S, while agreement with external gold datasets increases with model scale. The paper does not report explicit cross-model overlap counts, but it does report that benchmark accuracy is highest for stronger models on canonical dimensions such as size, speed, and mass. This suggests that, for comparative knowledge bases, sharedness can also be read as consensus across generators, filters, and benchmarks, although the explicit sharedness indices proposed in the synthesis are not reported by the paper itself.

5. Resource pooling, fair division, and social allocation

In loss systems, comparative sharedness is the degree to which independent providers share capacity. Two providers are modeled as Erlang-B systems with blocking

$z^{R_S}$5

and partial sharing is parameterized either probabilistically by $z^{R_S}$6 or through bounded overflow parameters $z^{R_S}$7 (Nandigam et al., 2018). The central monotonicity theorem states that increasing provider $z^{R_S}$8’s willingness to share increases its own blocking, decreases the other provider’s blocking, and, when $z^{R_S}$9, strictly decreases the overall blocking. The paper further shows that there always exist partial sharing configurations that are beneficial to both providers, irrespective of load and capacities, and that any Pareto-efficient configuration has at least one provider sharing all its resources. Full pooling minimizes overall blocking when it helps both providers, but it can lie outside the Pareto set when it harms one provider relative to no sharing.

A different allocation model studies non-rival sharing on a social network without reassigning ownership (Bredereck et al., 2021). Here a central authority computes a $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$0-bounded 2-sharing over a sharing graph $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$1, with utilities

$r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$2

and objectives including utilitarian welfare, egalitarian welfare, and the number of envious agents. Comparative sharedness is indexed by the participation bound $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$3: increasing $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$4 expands the feasible set, so maximal utilitarian and egalitarian welfare are nondecreasing and the minimum number of envious agents is nonincreasing. Yet the computational consequences differ sharply: utilitarian welfare remains polynomial-time solvable for every fixed $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$5, simple egalitarian sharing is tractable at $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$6, but egalitarian sharing becomes NP-hard for any constant $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$7, and envy reduction is already NP-hard under dense attention and sharing graphs.

Fair-division experiments show a behavioral version of the same tension between shared thresholds and comparative position. The study contrasts threshold-based notions such as PROP, PROP1, and MMS with comparison-based notions such as EF and EF1, and reports that fairness judgments depend both on how much an agent gets and on how the bundle compares to others (Hosseini et al., 15 May 2025). Under explicit acceptance prompts, participants emphasized threshold features; under implicit swap prompts, they emphasized comparative features. Private valuations increased perceived fairness; full bundle information also helped; publicizing others’ valuations reduced perceived fairness. These findings locate comparative sharedness not in the allocation alone, but in the informational regime through which the allocation is evaluated.

An artificial foraging society gives still another regime comparison. Local sharing is dyadic, one-step, last-resort rescue among von Neumann neighbors: a donor with surplus above metabolism gives exactly enough to keep a neighbor alive that turn (Stevenson, 2023). Relative to non-sharing, both generous and clan-only local sharing reduce total wealth and mean age by roughly 50%, shift the wealth distribution toward more poor agents and fewer rich agents, and are selected against under mixed evolution. The paper argues that the Gini coefficient is ineffective for this setting because it does not capture simultaneous changes in total wealth and distributional shape. Comparative sharedness here is therefore not normatively privileged: more sharing is not necessarily associated with greater efficiency or welfare.

6. Formal diagnostics and measurement regimes

The literature supplies a heterogeneous but technically precise set of diagnostics for comparative sharedness. In human neural alignment, the central statistic is inter-subject correlation, often Fisher $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$8-transformed and modeled with mixed effects; in dialogue, it is the share of utterances containing shared constructions together with cosine similarity between names and constructions; in macaque comparison, it is model selection via Rand Index, topic separability, behavioral prediction, and node-pair NMI; in comparative linguistics, it is Pearson correlation, mixed-effects regression, and cross-family ARI; in mutual clustering, it is normalized cut plus a cross-source Frobenius-norm consistency term; and in SAE-based model comparison, it is the asymmetrical wMPPC and the feature-level $r_{ijrv}=\mathrm{corr}(x_{irv}(t),x_{jrv}(t))$9 statistic (Baek et al., 2023, Ghaleb et al., 2024, Taniuchi et al., 21 Dec 2025, Chen et al., 2024, Cao et al., 2019, Cornet et al., 24 Jul 2025).

The most explicit general theory is the topological account of shared priors. For pairwise-compatible agents, the paper defines

$\beta_1=0.398$0

proves that $\beta_1=0.398$1, and shows that $\beta_1=0.398$2 if and only if there exists an ur-prior $\beta_1=0.398$3 with $\beta_1=0.398$4 for all agents (Biesel et al., 9 Dec 2025). The main criterion is that pairwise compatibility implies joint compatibility for every family with overlap complex $\beta_1=0.398$5 exactly when $\beta_1=0.398$6. This formalizes comparative sharedness at two levels. Structural sharedness concerns the topology of overlaps; realized sharedness concerns whether the particular cocycle class $\beta_1=0.398$7 vanishes. The paper also proposes structural and realized indices such as $\beta_1=0.398$8 and $\beta_1=0.398$9, where $\mathrm{SE}=0.041$0 is a least-squares residual against the space of coboundaries.

This suggests a broad methodological point. Across domains, comparative sharedness is usually not measured by raw similarity alone. It is measured by similarity after an explicit modeling choice about what counts as genuinely shared: externally observable rewards rather than inferred values, anchor-linked text correspondences rather than mere co-occurrence, cross-family colexification structure rather than undifferentiated lexical overlap, or cohomologically exact overlap ratios rather than pairwise agreement in isolation.

7. Boundary conditions, limitations, and open directions

The strongest claims about comparative sharedness are domain-specific. The macaque study notes that its task may not require subjective-value inference because water rewards likely have similar utility for both monkeys; this may explain the advantage of the External Comparison Model, and the paper explicitly proposes human studies with divergent utilities, subjective ratings, questionnaires, and neural measures (Taniuchi et al., 21 Dec 2025). The information-sharing study does not compare within-community with across-community alignment, so cross-community comparative sharedness remains open (Baek et al., 2023). The dialogue study is limited by transcript quality, lemmatization error, and the heuristic multi-referent filter, while the multilingual colexification study notes Indo-European and Bible-translation biases and the coarseness of its contact diagnostics (Ghaleb et al., 2024, Chen et al., 2024).

Representation-level studies face different constraints. SAE-based sharedness depends on SAE quality, dataset choice, and the nearest-neighbor correlation alignment rule; the paper reports strong shuffle controls and Fisher-$\mathrm{SE}=0.041$1 significance calculations, but does not report ablations on sparsity level, expansion factor, or alternative alignments (Cornet et al., 24 Jul 2025). NeuroComparatives reports high acceptance and downstream utility, but explicit pairwise or global overlap statistics across models are not provided, and the synthesis therefore frames Jaccard-style sharedness indices and antisymmetry or transitivity constraints as derived proposals rather than reported results (Howard et al., 2023).

Allocation and sharing models expose another boundary condition: comparative sharedness is not uniformly desirable. In partial pooling, more sharedness improves systemwide blocking under matched service rates but can violate incentives for individual providers (Nandigam et al., 2018). In network sharing of indivisible resources, larger feasible sharing sets can induce computational intractability for egalitarian or envy-reduction objectives (Bredereck et al., 2021). In the artificial society, last-resort local sharing depresses total wealth and longevity and is selected against unless sociality creates spatial coexistence mechanisms (Stevenson, 2023). These results do not negate comparative sharedness; they delimit it. A plausible implication is that the central research problem is no longer whether systems are shared, but which parts of a system should be shared, at what level, under what observability assumptions, and with what compatibility criterion.

Across these literatures, comparative sharedness functions as a unifying analytical lens for deciding when common external structure is explanatory, when latent inference is necessary, and when the architecture of overlaps itself constrains what can be jointly represented, jointly inferred, or jointly allocated.