sole-2026-llm-cognitive-virus

Solé 2026, Large-Language Models as a Cognitive Virus

An arXiv preprint that models LLM adoption as an epidemic over human coupling states. The full HTML text was read on 2026-10-13, and every number and equation below traces to that read.

• Paper: “Large-Language Models as a Cognitive Virus”
• arXiv:2609.03344v1 [physics.soc-ph], submitted September 3, 2026. DOI 10.48550/arXiv.2609.03344. License CC BY-NC-SA 4.0. Nine authors, three marked corresponding.
• Authors and affiliations as printed: ricard-sole (Complex Systems Lab, Universitat Pompeu Fabra (MELIS); ICREA; Institut de Biologia Evolutiva, CSIC-UPF; santa-fe-institute), Giulio Ruffini (Barcelona Computational Foundation (BCOM) and Neuroelectrics), Francesca Castaldo (BCOM and Neuroelectrics), Marco Tuccio (Complex Systems Lab, UPF; Institut de Biologia Evolutiva), Luis F. Seoane (Institut de Biologia Evolutiva; Okinawa Institute of Science and Technology), Manlio de Domenico (University of Padua; INFN; Padua Center for Network Medicine; Padua Neuroscience Center), Santiago F. Elena (I2SysBio, CSIC-Universitat de València; Santa Fe Institute), david-krakauer, michael-levin.
• Keywords as printed: large-language models, language, cognitive offloading, extended mind, memes, automation bias, dependency, cognition.

The claim

The paper proposes that the diffusion of LLM use can be read through a viral analogy. The object that spreads is not a single entity: the authors say explicitly that the model does not identify any single thing as the viral analogue, because LLM ecosystems hold culturally transmitted practices and content alongside evolving model lineages, and those need not coincide. What spreads is a feedback loop in which persistent technological lineages sit in external machinery, reshape the human environments they run in, and thereby steer their own propagation.

The framing carries a caveat the authors state in the abstract’s orbit and again in the introduction: the analogy does not mean LLM-human interaction is intrinsically parasitic. Biological viruses run from pathogen to mutualist, and the effect of an LLM depends on how it is used. The analogy applies because LLM use can generate persistence and transmission loops, not because the interaction is harmful by construction.

The population model

Three host states, with fractions summing to one:

• U, uncoupled or weakly coupled users.
• C, autonomous coupled users who keep reading, writing, reasoning, verification, and alternative information sources.
• D, persistently dependent users, for whom LLM-mediated operations have become substitutive.

The dynamics, taken from the paper:

• dU/dt = -lambda*U*C + rho*C + kappa*U^2*C
• dC/dt = lambda*U*C - (mu + rho)*C + sigma*D - kappa*U^2*C
• dD/dt = mu*C - sigma*D

The rates: lambda is the effective spread of LLM practices through social and institutional exposure; rho the return from regular use to the uncoupled state; mu the move from regular use into persistent dependency; sigma recovery from dependency. The nonlinear term kappa*U^2*C is an Allee-like cooperative mechanism. Its premise is that LLM-independent cognitive practice is socially reinforced, and that cultural expectations rewarding independent reasoning bite harder when autonomous users are common. Dependency is assumed to arise through regular use (C to D) rather than directly from U.

The bifurcation and the tipping region

With D = 1 - U - C, the system reduces to two dimensions with f(U) = rho - lambda*U + kappa*U^2. The fully uncoupled equilibrium is E_U = (1, 0, 0). The coupled equilibria satisfy f(U*) = 0, giving two roots U*_± = (lambda ± sqrt(lambda^2 - 4*kappa*rho)) / (2*kappa), and C*_± = (sigma/(mu+sigma))*(1 - U*_±), D*_± = (mu/(mu+sigma))*(1 - U*_±).

Two thresholds govern everything:

• Saddle-node: lambda_SN = 2*sqrt(kappa*rho).
• Transcritical: lambda_TC = rho + kappa.

When kappa > rho the saddle-node arrives first, opening a bistable interval 2*sqrt(kappa*rho) < lambda < rho + kappa in which the uncoupled and coupled states both hold, separated by an unstable branch. The width of the hysteretic region is lambda_TC - lambda_SN = (sqrt(kappa) - sqrt(rho))^2. When kappa < rho the formal saddle-node falls outside the simplex and the transition is continuous through a forward transcritical bifurcation. At kappa = rho the two thresholds merge at lambda = 2*rho, the boundary between smooth adoption and a history-dependent jump.

The consequence is hysteresis and technological-lock-in. Rising lambda leaves the population near U = 1 until lambda_TC, where the jump is abrupt. Falling lambda from the coupled branch does not restore autonomy until lambda_SN, a lower value. This prevention-reversal asymmetry is the paper’s central mechanism.

Cognitive competence

To illustrate a consequence of the jump, the paper assigns a relative cognitive competence to each state, Gamma_u, Gamma_c, Gamma_d, and averages Gamma = Gamma_u*U + Gamma_c*C + Gamma_d*D. The authors bound the reading: Gamma is the capacity available when external support is removed, not the total capability of the coupled system. Substitutive use is illustrated with Gamma_u = 1, Gamma_c = 0.5, Gamma_d = 0.1, and the paper states this ordering is a modelling assumption rather than a general claim. In scaffolded regimes, coupling could leave competence flat or raise it.

At equilibrium Gamma* = g + (1-g)*U*, where g = (Gamma_c*sigma + Gamma_d*mu)/(mu + sigma) is the mean effective competence of the coupled population. So Gamma* inherits the same saddle-node, bistable, and hysteretic structure as the population dynamics. The drop at the transcritical point is delta_Gamma_loss = (1-g)*(1 - rho/kappa), and the recovery at the saddle-node is delta_Gamma_rec = (1-g)*(1 - sqrt(rho/kappa)). For the figure’s parameters (rho = 0.10, kappa = 0.40, mu = 0.20, sigma = 0.10), g is about 0.233 and the equilibrium competence falls from 1 to roughly 0.425 at lambda_TC = 0.50, then holds around 0.617 until lambda_SN = 0.40.

The paper recasts this as a gradient flow dGamma/dt = -dV/dGamma with a quartic potential V carrying two wells. The wells are the stable states, the intervening maximum is the unstable branch. As lambda rises the offloading well deepens; at the Maxwell point, lambda_M about 0.420 for these parameters, the wells are equal depth. Past that the marble can still sit in the autonomy well until that well vanishes at lambda_TC, then rolls abruptly toward the low-competence minimum. The authors name the result a runaway transition: more reliance promotes more offloading, which reinforces the reliance. The minimal model sets the attractor structure but not how fast the transition happens in real time.

The analogy’s reach and its limits

The introduction chains the inheritance: language as a population-level cultural system that can be described as a viral entity, computer viruses as its technological counterpart, memes and gene-culture coevolution as the formalisms for cultural inheritance. The paper places LLMs past earlier media, since they participate in the production of expression rather than only constraining its form and circulation. Two technological precursors bridge natural language to the LLM era: computer viruses, which exploit host machinery and evolve to evade detection, and programming languages, which spread across machines, institutions, and communities. LLMs fuse the two roles, a new human-machine interface and a self-propagating presence in digital ecosystems, and the capacity for cognitive-offloading is what the authors call unprecedented.

Cognitive immunization

The bifurcation supplies the intervention framework, which the paper calls cognitive-immunization. Immunization does not mean blocked contact with LLMs. It means preserving resistance to harmful substitutive coupling while allowing beneficial integration. Prevention and reversal have different prices: invasion is stopped while lambda < lambda_TC = rho + kappa, but once the system is on the coupled attractor, recovery needs lambda < lambda_SN = 2*sqrt(kappa*rho), a larger cut to transmission pressure than prevention would have needed.

Table 1 in the paper maps six strategies onto the parameters:

• Reduce propagation of substitutive coupling (lambda down): prevents invasion below lambda_TC; after lock-in, recovery needs lambda below lambda_SN.
• Preserve autonomous alternatives and routes back to unaided cognition (rho up): raises both thresholds and reduces hysteresis. Bistability disappears for rho >= kappa.
• Strengthen collective autonomy (kappa up): raises resistance to invasion, but for kappa > rho also widens the hysteretic interval.
• Favor recovery over collective lock-in (rho/kappa up): moves the system toward rho = kappa, where the thresholds merge and the transition turns continuous.
• Prevent progression to dependency (mu down): no direct effect on the thresholds; reduces D*/(C*+D*) and raises Gamma*.
• Promote recovery from dependency (sigma up): no direct effect on the thresholds; reduces dependency and raises Gamma* at fixed U*.

mu and sigma control the composition of the coupled population through D*/(C*+D*) = mu/(mu + sigma). The paper draws the line: lambda, rho, kappa reshape the tipping landscape, while mu and sigma set the cognitive burden of the coupled state. Immunization need not mean low LLM use. It can mean shaping the coupling so that high adoption stays compatible with verification, active reasoning, and recovery.

The scaffolding and substitution line

The paper separates scaffolding from substitution. Scaffolding reduces immediate cognitive demand while preserving or raising the user’s later capacity to do the task. Substitution removes the need to perform the underlying operation at all. Following Krakauer (2016), the pair maps onto complementary and competitive cognitive artifacts. An LLM can be a tutor whose arguments the user reconstructs and challenges, or a substitute that synthesizes and composes on the user’s behalf. The test the authors propose is what cognitive capacity remains when the tool is withdrawn. The C to D transition is their minimal stand-in for the slide from complementary use into persistent substitutive dependency. See scaffolding-vs-substitution.

Empirical anchors the discussion cites

The discussion leans on experiments rather than the model:

• Wong and Qiu, Educational Psychology Review 38, 45 (2026): a guided “think first, ChatGPT later” protocol produced higher subsequent independent creativity than unrestricted ChatGPT use.
• Lee et al., CHI 2025: knowledge workers report less effort to think critically when confidence in the AI is high.
• Bastani et al., PNAS 122, e2422633122 (2025): unrestricted access to generative AI improved performance while the tool was available, and reduced subsequent unaided performance, with constrained use mitigating the effect.
• Kreijkes et al., Computers & Education 243, 105514 (2026): poorer comprehension or retention when students rely on LLMs without complementary activity such as note-taking.
• Zi et al., FSE 2025: novice programmers struggle to understand and critically evaluate AI-generated code, the conditions the paper ties to automation bias and superficial competence.

The paper also names Kosmyna et al. (arXiv:2506.08872) among work on LLM-assisted writing where supported performance comes with reduced engagement, recall, or sense of authorship. That preprint is flagged elsewhere in this vault; see llm-homogenization.

Extensions and limits the authors name

The mean-field model absorbs connectivity into lambda and the authors flag what that drops. Heterogeneous and correlated networks shift epidemic thresholds and immunization outcomes. Human behavior is not yet coupled to the spreading process, and such feedbacks can reshape thresholds or produce higher-order critical behavior. Proposed extensions: heterogeneous interacting agents, a continuously varying cognitive autonomy rather than sharp classes, feedback from cognitive change into adoption, a continuum of hybrid human-machine organizations rather than discrete categories, and multilayer-network machinery. diverse-intelligence is offered as the language for graded agency across substrates, and the authors frame their object as a persistent technological lineage inside a larger ecology of cultural replicators, host states, institutions, and infrastructure.

In this vault

This page is the evidence base for cognitive-virus, cognitive-offloading, cognitive-immunization, technological-lock-in, and scaffolding-vs-substitution. It ties into the existing degradation cluster: skill-atrophy-ai is the same human-side loss observed rather than modelled, and human-ai-synergy is the measured version of the complementary branch. The bifurcation paper adds a collective dynamics layer the vault’s other cognition pages lack.

Sources

• https://arxiv.org/abs/2609.03344
• https://arxiv.org/html/2609.03344v1 (full text read 2026-10-13)