Cross-Modal Contagion Mechanisms

• Cross-Modal Contagion is a phenomenon where propagation in one modality (e.g., text, vision) alters the dynamics in another through various coupled mechanisms.
• In threshold systems, simple contagion exposures aggregate to trigger complex adoption, with models quantifying transitions using cumulative binomial probabilities and phase transitions.
• Structural analogues in multiplex networks and hypergraphs reveal that modality-specific processes, when coupled, can synchronize or inhibit contagion, guiding mitigation and model design.

Searching arXiv for the cited papers to ground the article in current records. Cross-Modal Contagion denotes contagion phenomena in which propagation in one modality, channel, or interaction order transfers to, enables, or distorts propagation in another. In the literature represented here, the term is not used in a single narrow sense. It describes, among other mechanisms, simple contagion triggering complex contagion in heterogeneous threshold systems, evaluator preferences learned on text corrupting strategy selection on visual tasks in self-evolving agents, temporal propagation of semantics between image and text embeddings, and structurally coupled spreading across online/offline layers or pairwise/higher-order interactions (Min et al., 2017, Liu, 15 Jun 2026, Semedo et al., 2019, Chang et al., 2018, Guzmán et al., 21 Jan 2026).

1. Conceptual scope and principal meanings

Across these works, Cross-Modal Contagion refers to interaction between distinct contagion modalities rather than to a single fixed formalism. In threshold contagion, the relevant modalities are simple contagion and complex contagion. In multimodal AI systems, they are text and vision. In diachronic embedding models, they are visual and textual semantic organizations evolving over time. In multiplex and hypergraph models, the modalities are distinct channels of interaction, such as lattice versus random-regular-graph layers or pairwise versus higher-order transmission (Min et al., 2017, Liu, 15 Jun 2026, Semedo et al., 2019, Chang et al., 2018, Guzmán et al., 21 Jan 2026).

Operationalization	Modalities	Core mechanism
Threshold contagion	Simple vs complex contagion	Simple adoption raises exposures until complex nodes adopt
Self-evolving agents	Text vs visual tasks	Evaluator preferences transfer across modalities
Diachronic embeddings	Vision vs text over time	Semantic changes propagate through a shared time-conditioned space
Multiplex co-diffusion	Lattice vs RRG channels	One channel accelerates or blocks the other via synergy and dormancy
Hypergraph SIS	Pairwise vs higher-order interactions	Cross-order hub correlations synchronize or desynchronize infection pathways

In the threshold setting, simple contagion means $\theta=1$, so one successful exposure suffices for adoption, whereas complex contagion means $\theta>1$, so multiple successful exposures are required (Min et al., 2017). In multimodal AI evaluation, cross-modal contagion is explicitly distinguished from within-modality bias or drift: preferences acquired under one sensory regime transfer to another where they may be suboptimal, thereby altering the agent’s optimization landscape in a manner not predicted by within-modality dynamics (Liu, 15 Jun 2026). In diachronic multimodal representation learning, contagion is framed as the temporal influence or propagation of semantics between visual and textual modalities (Semedo et al., 2019).

A common thread is that a modality-specific process creates a field, bias, or exposure structure that changes the effective dynamics of another modality. This suggests that the concept is best understood as a family of coupling mechanisms rather than as a single model class.

2. Threshold-mediated triggering: simple contagion enabling complex contagion

A formal and influential instantiation appears in a generalized contagion model on random graphs in which nodes have heterogeneous adoptability thresholds $\theta$ drawn from a distribution $Q(\theta)$, and each contact succeeds with transmission probability $\lambda$ (Min et al., 2017). If a susceptible node has $m$ adopted neighbors, the adoption probability for a node with adoptability $\theta$ is

$$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$

that is, the probability of at least $\theta$ successful transmissions among $m$ exposure attempts. This makes the coupling between modalities explicit: simple-node adoption increases the number of adopted neighbors $\theta>1$0 around complex nodes, and the cumulative binomial tail then rises until complex adoption becomes possible (Min et al., 2017).

For general degree distribution $\theta>1$1 and adoptability distribution $\theta>1$2, the final adopted fraction $\theta>1$3 obeys

$\theta>1$4

On Erdős–Rényi graphs with Poisson degree distribution and average degree $\theta>1$5, this reduces to

$\theta>1$6

The special bimodal case

$\theta>1$7

assigns a fraction $\theta>1$8 of nodes to simple contagion and a fraction $\theta>1$9 to complex contagion with threshold $\theta$0. With negligible seeds, the fixed-point equation becomes

$\theta$1

This model exhibits continuous, discontinuous, and hybrid phase transitions, as well as criticality, tricriticality, and double transitions (Min et al., 2017). The first threshold is

$\theta$2

For $\theta$3, the onset at $\theta$4 is continuous with mean-field percolation exponent $\theta$5. For $\theta$6, the sign of $\theta$7 changes at $\theta$8, so the transition at $\theta$9 is continuous if $Q(\theta)$0 and discontinuous if $Q(\theta)$1, with tricritical point $Q(\theta)$2 and tricritical scaling exponent $Q(\theta)$3 (Min et al., 2017).

The most direct threshold-based form of cross-modal contagion is the double transition. For $Q(\theta)$4 and $Q(\theta)$5, increasing $Q(\theta)$6 produces first a continuous transition from the adoption-free phase to a “simple adoption phase,” in which predominantly simple nodes adopt while complex nodes remain susceptible, and then a discontinuous jump at $Q(\theta)$7 to a “complex adoption phase,” where both simple and complex nodes adopt extensively (Min et al., 2017). The discontinuous boundary is defined by $Q(\theta)$8 and $Q(\theta)$9, while the critical endpoint additionally satisfies $\lambda$0. Near $\lambda$1, the hybrid transition has exponent $\lambda$2, and near the critical endpoint the scaling exponent is $\lambda$3 (Min et al., 2017).

On ER graphs with $\lambda$4, the phase diagram is particularly explicit. For $\lambda$5, there is a single transition at $\lambda$6, continuous for $\lambda$7 and discontinuous for $\lambda$8, with tricritical point $\lambda$9. For $m$0, there are two transitions for $m$1: a continuous onset at $m$2 followed by a discontinuous jump at $m$3, with the discontinuous line ending at $m$4. For $m$5, the second transition disappears and $m$6 grows smoothly beyond $m$7; for fixed $m$8, no second transition is observed for $m$9 (Min et al., 2017).

3. Multimodal evaluator preference transfer in self-evolving agents

In multimodal self-evolving agents, Cross-Modal Contagion has a different but closely related meaning: evaluator preferences acquired on one input modality transfer to and corrupt strategy selection on another (Liu, 15 Jun 2026). This phenomenon is introduced in the context of Evaluator Preference Collapse (EPC), where a language-model evaluator’s stable preferences cause an agent’s strategy weights to collapse. The multimodal setting amplifies the effect. In cross-model multimodal evaluation using GPT-4o to evaluate DeepSeek-chat, the strategy step_by_step absorbs $\theta$0 of all probability mass, while the three visual-domain strategies visual_grounding, spatial_decompose, and aesthetic_frame receive only $\theta$1 combined. The overall collapse is $\theta$2, which is $\theta$3 stronger than a text-only self-evaluation baseline with $\theta$4, and about $\theta$5 stronger than a random evaluator baseline with $\theta$6 (Liu, 15 Jun 2026).

The paper isolates contagion with a four-phase protocol. Phase 1 trains on text-only tasks to obtain a text-conditioned weight vector $\theta$7. Phase 2 trains on visual-only tasks to obtain $\theta$8. Phase 3 initializes from $\theta$9 and trains on visual tasks to produce $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$0. Phase 4 initializes from $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$1 and trains on text tasks to produce $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$2 (Liu, 15 Jun 2026). By comparing post-exposure distributions to the pure-modality baselines, the protocol separates cross-modal transfer from ordinary within-modality learning and drift.

The main divergence metric is Jensen–Shannon divergence:

$$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$3

where $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$4 and $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$5 are L1-normalized strategy weight vectors over the strategy set. The contagion coefficient is

$$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$6

and the evaluator-indexed contagion matrix is

$$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$7

These definitions make contamination directional and evaluator-conditional rather than global (Liu, 15 Jun 2026).

The experimental setup uses DeepSeek-chat as executor and several evaluators, including GPT-4o, GPT-4o-mini Vision with real images, DashScope gui-plus, Qwen3.7-plus, and DeepSeek-chat self-evaluation. The task set contains $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$8 text tasks and $$\left[ 1 - \sum_{s=0}^{\theta-1} \binom{m}{s} \lambda^s (1-\lambda)^{m-s} \right],$$9 visual-adjacent tasks, with a separate real-image configuration. There are $\theta$0 strategies in total, including the baseline strategy step_by_step. Across configurations, the study reports $\theta$1 total independent repetitions and about $\theta$2 evaluator API calls (Liu, 15 Jun 2026).

The measured cross-model contagion is substantial. Reported JSD values lie in the range $\theta$3–$\theta$4: GPT-4o text-proxy yields $\theta$5, Qwen3.7-plus yields $\theta$6, and GPT-4o-mini Vision with real images yields $\theta$7 (Liu, 15 Jun 2026). Real-image inputs provide the most directionally consistent signal, with mean $\theta$8, $\theta$9, $m$0 of repetitions favoring $m$1, and Cohen’s $m$2. For GPT-4o text-proxy, $m$3 and $m$4, while Qwen3.7-plus gives $m$5 and $m$6 (Liu, 15 Jun 2026).

A particularly notable result is strategy inversion. Pure text training favors synthesis, and pure visual training favors step_by_step; after cross-modal exposure, these optima reverse, with text shifting to step_by_step when initialized from visual and vision shifting to synthesis when initialized from text (Liu, 15 Jun 2026). The paper reports that inversion typically occurs at intermediate round counts, approximately $m$7, and may disappear at higher round counts when single-strategy collapse closes the contagion channel, as in DashScope at $m$8 rounds (Liu, 15 Jun 2026).

The strongest mitigation observed is self-evaluation. DeepSeek-chat judging itself yields $m$9 zero-contagion runs at $\theta>1$00, with $\theta>1$01, Cohen’s $\theta>1$02, and mean $\theta>1$03, $\theta>1$04 (Liu, 15 Jun 2026). Three methodological ablations and additional runs support the claim that the effect is not a structural artifact and depends primarily on evaluator identity and training round regimen (Liu, 15 Jun 2026).

4. Diachronic semantic transfer between vision and text

A temporally grounded formulation appears in “Diachronic Cross-modal Embeddings,” where cross-modal contagion is the temporal influence or propagation of semantics between visual and textual modalities (Semedo et al., 2019). The objective is to learn a common embedding space that preserves semantic similarity at each instant $\theta>1$05 while aligning semantically similar instances across adjacent times. This provides a representation in which modality-specific trajectories, drift, and lead–lag can be traced (Semedo et al., 2019).

The architecture uses a pre-trained ResNet-50 encoder for images and TF–IDF bag-of-words for text. Each modality is mapped to a $\theta>1$06-dimensional hidden representation, timestamps are mapped by a shared time embedding layer to a $\theta>1$07-dimensional vector, and the modality-specific hidden state is concatenated with the time embedding and projected into a shared $\theta>1$08 dimensional space (Semedo et al., 2019). For modality $\theta>1$09,

$\theta>1$10

$\theta>1$11

followed by $\theta>1$12 normalization. The shared time layer ensures that both modalities are organized coherently over time in the same embedding space (Semedo et al., 2019).

Training uses a ranking-based objective with temporal structure. The similarity function is the dot product, which becomes cosine similarity under $\theta>1$13 normalization. For a triplet with margin $\theta>1$14,

$\theta>1$15

The final diachronic loss decomposes into an inter-category separation term and an intra-category temporal smoothing term. A temporal alignment window $\theta>1$16 governs local temporal coherence, and temporal decay is defined as

$\theta>1$17

The reported hyperparameters are $\theta>1$18, $\theta>1$19 months, $\theta>1$20, learning rate $\theta>1$21, momentum $\theta>1$22, batch size $\theta>1$23, and $\theta>1$24 epochs (Semedo et al., 2019).

The learned space is described as obeying four properties: locality, temporal separation, semantic separation, and continuity (Semedo et al., 2019). Locality means that instances sharing category and lying within the temporal window are close; temporal separation means instances farther apart than the window are far apart; semantic separation means instances from different categories are far apart independent of time; and continuity means embeddings evolve smoothly between neighboring instants.

The empirical setting uses $\theta>1$25 Flickr instances across $\theta>1$26 dynamic event categories from $\theta>1$27–$\theta>1$28, with the last $\theta>1$29 years retained after filtering and bins with fewer than $\theta>1$30 documents excluded. The final split is $\theta>1$31 train, $\theta>1$32 validation, and $\theta>1$33 test. Texts have average length of about $\theta>1$34 words, and temporal granularity is monthly (Semedo et al., 2019).

Results distinguish temporally local retrieval from diachronic alignment across time. In temporally bounded retrieval per month, the reported mAP values are $\theta>1$35 for a static cross-modal model, $\theta>1$36 for TempXNet, $\theta>1$37 for DCM-Continuous, and $\theta>1$38 for DCM-Binned (Semedo et al., 2019). In diachronic semantic alignment across all times, DCM-Binned yields I$\theta>1$39T $\theta>1$40, T$\theta>1$41I $\theta>1$42, Avg $\theta>1$43, whereas DCM-Continuous yields I$\theta>1$44T $\theta>1$45, T$\theta>1$46I $\theta>1$47, Avg $\theta>1$48 (Semedo et al., 2019). In local semantic alignment with queries projected to every time bin, DCM-Binned gives Avg $\theta>1$49 and DCM-Continuous gives Avg $\theta>1$50 (Semedo et al., 2019). In time-period inference, the average mAP@50 is $\theta>1$51 for static cross-modal, $\theta>1$52 for TempXNet, and $\theta>1$53 for DCM-Continuous (Semedo et al., 2019).

Qualitatively, the model reveals contagion-like semantic evolution. For tsunami images, alignment peaks around event months and decays afterward; for snowboarding, similarity is more stable yet cyclic; and for nuclear-disaster-related imagery, a gradual rise followed by stabilization reflects the emergence of novel visual patterns and their textual co-references over time (Semedo et al., 2019). The supplied synthesis further states that the learned embedding can be used to trace lead–lag, drift, and influence between modalities; where specific measurement procedures are proposed beyond the paper, they are explicitly marked as assumptions in that synthesis (Semedo et al., 2019).

5. Structural analogues: multiplex channels and higher-order interaction orders

Cross-Modal Contagion also appears in models where “modality” denotes distinct social or structural channels rather than sensory inputs. In “Co-Diffusion of Social Contagions,” individuals occupy a multiplex network with a periodic lattice layer and a random-regular-graph layer. Only lattice neighbors contribute to contagion $\theta>1$54, and only RRG neighbors contribute to contagion $\theta>1$55 (Chang et al., 2018). Node content states are $\theta>1$56, and an activity flag $\theta>1$57 determines whether adopted nodes still contribute outward influence. Dormancy is defined as a looser form of immunity: dormant individuals do not contribute influence to neighbors but may still adopt the other contagion (Chang et al., 2018).

The influence densities are

$\theta>1$58

$\theta>1$59

and the naive-node adoption probability is

$\theta>1$60

Here $\theta>1$61 is a synergy or shape parameter, with $\theta>1$62 corresponding to synergistic, concave response, $\theta>1$63 to near linear additivity, and $\theta>1$64 to antagonistic, convex response (Chang et al., 2018).

Simulations use $\theta>1$65 nodes on an $\theta>1$66 lattice, $\theta>1$67, one initial seed for each contagion, synchronous updates, $\theta>1$68 time steps, and $\theta>1$69 runs per parameter set. The main parameter range is $\theta>1$70, with $\theta>1$71 and focal dormancy scenarios in $\theta>1$72 (Chang et al., 2018). Monte Carlo simulations show that lower synergy makes contagions more susceptible to percolation, especially those diffusing on lattices, and that a faster diffusion with dormancy can probabilistically block the other contagion in a manner analogous to ring vaccination (Chang et al., 2018). Within approximately $\theta>1$73, the slower lattice contagion undergoes bimodal or trimodal branching in final adoption, particularly when the difference between $\theta>1$74 and $\theta>1$75 is moderate to large (Chang et al., 2018).

A related structural generalization appears in SIS dynamics on hypergraphs. In “Unveiling the impact of cross-order hyperdegree correlations in contagion processes on hypergraphs,” the relevant modalities are pairwise interactions and higher-order group interactions, described as cross-order rather than sensory-modal (Guzmán et al., 21 Jan 2026). Each node carries a hyperdegree vector $\theta>1$76, where $\theta>1$77 counts pairwise interactions and $\theta>1$78 counts triadic interactions. The Effective Hyperdegree Model (EHDM) preserves cross-order correlations because its state variables are indexed by coarse hyperdegrees $\theta>1$79 and the dynamics depend on moments of the joint degree distribution $\theta>1$80 (Guzmán et al., 21 Jan 2026).

For pairwise and triadic interactions, the degree-class infection pressure is

$\theta>1$81

and the susceptible class dynamics are

$\theta>1$82

A central mixed moment is

$\theta>1$83

which equals $\theta>1$84 at the disease-free state. This term directly couples the pairwise and triadic channels (Guzmán et al., 21 Jan 2026).

The backward invasion threshold is governed by the pairwise block and satisfies

$\theta>1$85

so higher-order infection does not shift the linear invasion threshold. By contrast, the forward transition depends on nonlinear higher-order reinforcement, and the paper reports that positive cross-order correlation decreases the forward threshold in $\theta>1$86 for fixed $\theta>1$87, whereas negative correlation increases it (Guzmán et al., 21 Jan 2026). Positive correlation aligns hubs across modalities and synchronizes pairwise- and triad-driven incidence, with temporal centroid difference $\theta>1$88 approaching $\theta>1$89 as $\theta>1$90 increases. Negative correlation desynchronizes the pathways and yields a two-phase pattern: pairwise growth first, higher-order amplification later (Guzmán et al., 21 Jan 2026).

These two structural models show that cross-modal contagion need not be tied to sensory modality. It can also arise when adoption pressure is partitioned across network layers or interaction orders and then recombined in node-level dynamics.

6. Measurement, misconceptions, and research directions

Several methodological themes recur across these formulations. First, cross-modal contagion is not equivalent to ordinary within-modality amplification. In self-evolving agents, the distinction is explicit: within-modality EPC refers to collapse inside a single modality, whereas cross-modal contagion refers to preferences learned on one modality leaking into another (Liu, 15 Jun 2026). In threshold contagion, the comparable distinction is between adoption among simple nodes alone and the subsequent triggering of complex nodes once exposure accumulation crosses the relevant threshold scale (Min et al., 2017).

Second, the phenomenon is not inherently restricted to pairwise networks or to visual-text systems. The threshold model realizes it on ER graphs through heterogeneous adoptability and a transmission probability that activates exposures (Min et al., 2017). The diachronic embedding model realizes it in a shared time-conditioned vision–text space (Semedo et al., 2019). The multiplex model realizes it through separate lattice and RRG channels, and the hypergraph model realizes it through pairwise and group interactions with explicit cross-order correlations (Chang et al., 2018, Guzmán et al., 21 Jan 2026).

Third, structural and architectural mismatch often amplifies the effect. In multimodal agent training, cross-model evaluator architecture is identified as the primary risk factor, while same-model self-evaluation shows near-complete immunity in $\theta>1$91 of runs (Liu, 15 Jun 2026). In hypergraphs, positive cross-order correlation lowers the forward threshold by strengthening pairwise–group coupling, whereas anti-correlation desynchronizes infection pathways (Guzmán et al., 21 Jan 2026). In multiplex co-diffusion, fast diffusion on the RRG with dormancy can block the slower lattice contagion by eroding the active frontier needed for further spread (Chang et al., 2018).

The principal limitations are model-specific but thematically related. The threshold-triggering model assumes locally tree-like networks, synchronous updates, fixed $\theta>1$92, static topology, and independent adoptability across nodes (Min et al., 2017). The multimodal agent study notes sensitivity to learning rates, task scheduling, fixed-baseline design, small valid $\theta>1$93 in some conditions, and the limited ecological validity of text-proxy visual tasks, although the real-image configuration strengthens the conclusions (Liu, 15 Jun 2026). The diachronic embedding model uses global temporal window and decay parameters, depends on category labels for positive and negative sampling, and may weaken under sparse temporal bins or irregular event timelines (Semedo et al., 2019). The multiplex and hypergraph models assume static layers or hypergraphs, synchronous or mean-field-style closures, and homogeneous or prescribed response parameters rather than fully endogenous adaptation (Chang et al., 2018, Guzmán et al., 21 Jan 2026).

The practical implications depend on the setting. In threshold systems, increasing $\theta>1$94, increasing $\theta>1$95, or reducing $\theta>1$96 or $\theta>1$97 can move a population from simple adoption into complex adoption, whereas the opposite interventions can suppress triggering (Min et al., 2017). In self-evolving agents, isolation training, evaluator ensembles from distinct families, monitoring $\theta>1$98, $\theta>1$99, and $\theta$00, and regulating round counts are proposed mitigations, with self-evaluation being the strongest observed safeguard (Liu, 15 Jun 2026). In diachronic embedding analysis, time-conditioned cross-modal structure makes it possible to inspect semantic drift and alignment peaks around events (Semedo et al., 2019). In multiplex and higher-order epidemic settings, optimal interventions shift with the relative strength and correlation of the channels, from pairwise-focused to higher-order-focused to mixed targeting (Chang et al., 2018, Guzmán et al., 21 Jan 2026).

Taken together, these results suggest that Cross-Modal Contagion is best regarded as a general principle of coupled propagation: a process evolving in one modality modifies the effective thresholds, preference geometry, semantic neighborhood structure, or infection pathways of another. The specific mathematics varies—from cumulative binomial tails, ranking losses, and divergence-based diagnostics to multivariate Hill functions and hyperdegree moment closures—but the underlying phenomenon is consistent: cross-channel coupling changes what spreads, when it spreads, and whether the transition is smooth, abrupt, synchronized, inverted, or blocked.