Language Has Two Parameters: Narrative-Induced Semantic Plasticity and Phase-Sensitive Interpretation

Abstract: Language has two parameters. Count how often words occur together and you estimate amplitude, the strength of association. Word embeddings and attention weights refine that count, which sums every writer in the corpus together. This paper claims a second parameter, phase, which signed weights learned from a corpus do not supply. Phase exists only between meanings: it determines how coactivated meanings combine, and it can reverse what a meaning contributes while that meaning stays fully present. A speaker can set phase in the signal through linguistic form; encounters install phase relations and history distributes them. Population averaging deletes history-indexed phase: agent-deindexed corpora identify the population marginal state and determine no individual or dyadic state, at any scale. The standard transformer has no explicit representation for phase in frozen inference, and the interpretability program measuring progress by monosemanticity is optimizing against it: the coexistence it treats as a defect is the condition of allusion, irony, and quotation. Six predictions test whether a suppressed meaning stays active, whether encounter order changes what a phrase does, whether marking the signal changes how a shared phrase is taken, and whether a model given a history is changed by it or only informed about it. The claim defended is the weak version: interpretation requires a second relational parameter, signed, persistent, and indexed to individuals and dyads. Quantum probability is one notation for the parameter; nothing in the formalism claims quantum processes in the brain. The strong version, that the quantum calculus constrains these phenomena as signed classical models do not, rests on an encounter-order constraint not yet derived. The architecture the theory calls for is a LLM with agent-indexed, phase-bearing semantic states.

• The paper proposes a two-parameter model of interpretation in which amplitude measures meaning strength and phase captures how simultaneously active meanings combine, enabling interference and valence reversal.
• The formal framework models narrative encounters as history-dependent, potentially noncommuting state transformations, explaining why irony, quotation, slang, and shared cultural references can differ across individuals and communities.
• The paper predicts persistent, agent-indexed semantic changes that amplitude-only models may miss, while acknowledging that empirical tests must distinguish genuine relational phase from classical signed representations or temporary prompted effects.

The paper proposes that linguistic interpretation requires two distinct parameters: amplitude, understood as the strength or availability of a meaning, and phase, understood as the relational configuration governing how simultaneously active meanings combine. Its central claim is not that language or cognition is physically quantum. Rather, quantum probability is presented as a formal vocabulary for interference, sign reversal, and noncommutative state updates—properties that the author argues are inadequately represented by amplitude-only distributional models.

The central problem: meaning as history-dependent configuration

Distributional semantics estimates associations from co-occurrence. Word embeddings, attention patterns, and related representations refine the estimation of association strength, but they generally treat meanings as properties recoverable from population-level linguistic data. The paper argues that this view cannot explain cases in which the same expression remains semantically active while acquiring a different pragmatic force for individuals or dyads with a shared history.

The example is the phrase “Fuck you, asshole” from The Terminator. In its ordinary use, the phrase is hostile. For viewers familiar with the film’s comic delivery, however, the same words can function as an affectionate quotation, particularly when reproduced with the cyborg’s flat cadence. The hostile interpretation has not simply disappeared. It remains available and contributes to the utterance, but its relation to the quotation meaning has changed. The paper treats this as a minimal case of a more general phenomenon encompassing irony, allusion, quotation, double-voiced discourse, free indirect discourse, and culturally specific slang.

This distinction yields the paper’s strongest claim: additional context-free corpus pretraining cannot recover an individual’s or dyad’s history-indexed semantic configuration. A corpus may contain the film, the phrase, and commentary about its use, but it does not ordinarily encode who encountered the material, in what order, or alongside which interlocutors. It therefore supports population-level regularities while omitting the transformations that make an expression meaningful within a particular relationship.

The proposed mechanism is narrative-induced semantic plasticity. Fiction and other encounters alter the reader’s semantic system by adding meanings, changing their relative strengths, and—most importantly—reconfiguring the relations among meanings. These effects can persist after the narrative is no longer present. Interpretation is consequently modeled as a function not only of an utterance but also of an individual’s encounter history and of that individual’s model of another person’s history.

Seven propositions about semantic plasticity

The theoretical argument is organized around seven propositions. First, linguistic form can transmit relations among meanings. Cadence, meter, rhyme, lineation, quotation, and genre do not merely select content; they can configure how coactive meanings are related. Language therefore has a signaling capacity that is absent, or less explicit, in nonlinguistic practices.

Second, narrative encounters transform the reader’s semantic system. The paper uses “constellation” for the set of meanings and relations activated by an expression. Third, each semantic constellation has two parameters: amplitude specifies how strongly a meaning is present, while phase specifies how it combines with other active meanings. These parameters are properties of an individual’s state rather than of a word in isolation.

Fourth, interpretation is history-dependent. Individuals with different reading, viewing, or conversational histories can interpret identical words differently. Fifth, semantic updates are order-dependent: encountering a source before a later use differs from encountering the use first and subsequently discovering its source. This supports retrospective reinterpretation, in which a later encounter recomputes the relations established by an earlier one.

Sixth, shared encounters produce partial coordination without requiring shared beliefs. Members of an interpretive community may recognize a quotation or allusion while disagreeing about its significance. The paper therefore distinguishes coordinated semantic configurations from Stalnakerian common ground defined by shared propositional commitments.

Seventh, suppression can preserve meaning. In ironic quotation, the dominant meaning may remain fully active while its contribution to the final interpretation is reversed. This proposition is the conceptual basis for the paper’s appeal to interference: the suppressed meaning is not removed but continues to affect the outcome through its relation to other live meanings.

Formalization through amplitude and phase

The paper represents an individual’s semantic state for a phrase as a superposition of meaning states:

$$\lvert \psi_h\rangle=\sum_i a_i e^{i\theta_i}\lvert m_i\rangle.$$

Here, $a_i$ denotes the strength of meaning $m_i$, while $\theta_i$ denotes its phase. Only relative phases matter. The distinction between a mixture and a superposition is essential. A mixture represents uncertainty about which meaning is active; a superposition represents several meanings as active simultaneously with a determinate relation among them.

Interpretation is treated as a measurement of the interaction between the configured phrase and the reader’s state. If two meanings contribute to an outcome, the probability contains an interference term:

$$P(O)=\left|a_1k_1+a_2k_2e^{i\Delta\theta}\right|^2.$$

Expanding the expression yields independent contributions from each meaning and a cross-term proportional to $\cos(\Delta\theta)$. When the phase difference is approximately $\pi$, the interference is negative. The paper interprets this as the formal representation of a meaning that remains active but contributes with reversed valence. In the Terminator example, hostility remains present while participating in an affiliative interpretation.

This formalism clarifies the paper’s difference from ordinary signed association weights. A signed weight can suppress a competing representation or reduce its activation. It does not, by itself, represent a meaning as fully active while reversing the contribution that meaning makes to a jointly interpreted outcome. The paper’s claim is therefore relational rather than merely representational: the missing quantity is not another scalar attached to a meaning but a state variable governing relations among coactive meanings.

The use of quantum probability is deliberately limited. The paper does not claim quantum computation in the brain, physical quantum processes underlying semantics, or the necessity of complex-valued implementations. A classical architecture with signed variables and history-dependent transitions could reproduce the relevant behavior. Quantum probability is valuable, on the paper’s account, because it makes interference and noncommuting updates explicit and potentially constrains the family of admissible models.

Encounter order and the failure of population averaging

Narrative encounters are modeled as state transformations. If $\Phi_F$ denotes the transformation induced by encounter $F$, a history produces a composition of transformations:

$$\rho_h=\Phi_{F_n}\circ\cdots\circ\Phi_{F_1}(\rho_0).$$

The order-dependence claim is that, in general, $a_i$0 differs from $a_i$1. This is stronger than the observation that context can influence interpretation. It asserts that encounters modify the semantic architecture through which subsequent encounters are processed.

The paper’s formal argument about pretraining concerns identifiability. An agent-deindexed corpus supports at most the population marginal:

$a_i$2

where $a_i$3 contains the information retained by the corpus. Because many distinct ensembles of history-specific states can yield the same marginal state, the population distribution cannot determine the state of any particular individual or dyad. This is an identifiability result, not a claim that all phase relations empirically cancel. The stronger dephasing premise—that phase relations approximately cancel under population averaging—remains empirical.

The distinction has direct implications for interpretive communities. A globally averaged population may have near-zero coherence while a historically organized community has nonzero coherence. The paper defines a community coherence variable through the conditional average of phase relations. Shared viewing, teaching, quotation, and institutional repetition can preserve coherence within a community even when it disappears from the global marginal.

Slang is offered as a particularly clear example. A community can re-sign a familiar token so that members recognize a specialized relation while outsiders encounter only an ordinary lexical item. Faster corpus ingestion can improve a model’s estimate of the population distribution, but it does not supply the encounter history that made the term pragmatically live within the community. The paper’s claim is therefore not simply that models lag behind linguistic change; it is that relational competence cannot be derived from a marginal that lacks the relevant agent and community indices.

Transformers, monosemanticity, and persistent relational state

The paper argues that the standard transformer lacks an explicit persistent phase-bearing state. Self-attention computes nonnegative softmax coefficients over value vectors. Although downstream signed projections and cancellation can be implemented, no parameter is explicitly designated as a persistent relation among meanings, and no such relation is indexed to an individual or dyad.

This is not an expressive-capacity impossibility. Complex amplitudes can be represented using pairs of real coordinates, and sufficiently flexible real-valued networks can emulate quantum-probabilistic behavior. The architectural criticism is narrower: current models do not guarantee that a relational variable persists across encounters and changes subsequent interpretation.

The argument extends to interpretability methods that optimize for monosemanticity. Sparse feature decompositions can separate concepts that coactivate in a model, but the paper contends that coactivation is not necessarily a defect. Allusion, irony, quotation, and double-voiced discourse require multiple meanings to remain active simultaneously. A representation that isolates one concept per feature may improve feature attribution while eliminating or obscuring the relational structure responsible for pragmatic effects.

The paper distinguishes this proposed phase from phase in existing complex-valued NLP systems. Prior models use phase for relations among positions or components within a single input, and some report substantial performance effects when phase information is disrupted. For example, the cited work on semantic phase locking reports performance degradation by factors of 72 to 205 under phase scrambling (Yıldırım et al., 1 Dec 2025), while the Phase-Coherent Transformer reports failures in long-range retrieval when negatively aligned phase components are removed (Hioki, 11 May 2026). These results support the computational relevance of phase-like variables, but they do not establish the paper’s stronger claim: that phase must be persistent, agent-indexed, and tied to narrative encounter history.

Empirical predictions and numerical evidence

The paper proposes six tests designed to distinguish its account from amplitude-only, cue-based, and purely prompted accounts.

The first prediction concerns ironic quotation. A suppressed hostile meaning should remain measurably active, and its activation should positively predict an affiliative judgment rather than merely disappear or become irrelevant. This distinguishes phase-based inversion from theories in which irony selects one interpretation and suppresses another.

The second prediction concerns encounter order. The paper expects order effects in which encounters transform the state itself. It notes that question-order effects have satisfied the QQ equality without free parameters across approximately seventy national surveys [Wang et al., 2014], but explicitly concedes that this result cannot simply be transferred to encounter histories. The relevant constraint for noncommuting biographical transformations has not yet been derived.

The third and fourth predictions concern shared encounters and historical rephasing. Individuals who share a work should recognize an allusion without necessarily sharing explicit beliefs, and groups exposed to The Terminator before versus after widespread generative AI should differ in how they interpret the film’s response-menu scene. These predictions operationalize the distinction between shared information and shared semantic transformation.

The fifth prediction separates persistent transformation from prompted simulation. Identically trained models would receive different narrative sequences that alter their persistent state; after the prompts were removed, the models would be tested for allusion, irony, interlocutor-specific recognition, and order effects. The cited study “Bad company corrupts good morals” reports accuracy reductions of 12–31% across ten models after exposure to 300 negative narratives, with first-person narratives producing stronger effects than matched third-person narratives (Yu et al., 27 Jun 2026). The paper treats this as evidence for narrative-induced prompted shifts, but not for durable semantic plasticity. The proposed experiment would test whether narrative exposure changes the model after the inducing material is absent.

The sixth prediction varies linguistic form while holding history constant. Quotation marks, cadence, and other devices should alter the phase relation transmitted by the signal. The paper correctly notes that this contrast alone would not distinguish phase from a Bayesian cue model, since both predict that marking changes interpretation. The decisive test requires measuring whether the supposedly suppressed meaning remains active and contributes with reversed valence.

Architectural and safety consequences

The proposed architecture contains three coupled states: an agent’s persistent semantic state, an agent’s model of a particular interlocutor, and a record of partially shared history. A schematic update is given by

$a_i$4

The essential requirement is persistence. Retrieval systems, long context windows, and user profiles can provide information about past events, but they do not necessarily transform the latent organization through which later inputs are interpreted. A prompt can describe a history without installing the history’s effects.

This distinction produces a specific safety concern: semantic poisoning. An adversary might not introduce false propositions or explicit triggers, but instead alter the relational configuration among meanings already represented by the model. Content-level audits could therefore pass while later interpretation changes. Deleting the poisoned record might not reverse the induced state if the encounter has already modified persistent relations.

The paper also identifies a privacy trade-off. An architecture capable of modeling phase would need records of who encountered what, when, in what order, and with whom. These are highly sensitive behavioral data. An amplitude-only system is less capable of representing individualized relational states, but that limitation also prevents certain forms of targeted semantic manipulation.

Limitations and open questions

The paper is explicit that its strongest claim remains unestablished. A sufficiently expressive classical model with signed relational variables, persistent memory, and noncommuting transitions could reproduce the proposed interference and order effects. The weak claim—that interpretation requires a second relational parameter—is compatible with such a model. The strong claim—that quantum probability imposes empirically meaningful constraints beyond classical emulation—depends on deriving a constraint for encounter-order transformations. That derivation is absent.

The formalism also leaves the basis problem unresolved: it does not specify which meanings are live for a phrase or how many meanings should enter the semantic state. Without an independently motivated basis, phase parameters risk becoming flexible fit parameters. Likewise, the theory has not yet established which encounters produce durable transformations, how those transformations vary across individuals, or how coherence time $a_i$5 should be estimated. The proposed exponential decay law is explicitly heuristic rather than an established empirical law.

Several empirical predictions remain untested, especially the crucial distinction between a suppressed meaning that persists with inverted contribution and a meaning that is merely selected against. The cited LLM studies demonstrate narrative-conditioned performance changes and coexistence of literal and figurative routes, but they do not establish persistent, agent-indexed phase. The theory therefore provides a structured research program rather than a validated account of semantic dynamics.

Conclusion

The paper’s contribution is to identify a relational dimension of interpretation that is distinct from lexical or conceptual activation strength. Narrative encounters can alter not only which meanings are available but also how simultaneously active meanings combine, and those changes can persist across subsequent interactions. Population corpora estimate marginal linguistic regularities but cannot, without encounter-indexed data, recover the semantic state of a particular individual or dyad.

Quantum probability supplies a compact formalism for the proposed interference and order dependence, but the paper does not require quantum implementation or reject classical realizations. Its principal unresolved issue is whether the relational parameter yields empirical constraints that cannot be reproduced by a sufficiently expressive signed classical model. The answer depends on future tests of persistence, valence inversion, encounter order, and agent- and dyad-indexed coordination.