💬 NLP

The production of meaning in the processing of natural language

This paper investigates the quantum-like contextuality of large language models by analyzing the CHSH $|S|$ parameter across various scales and benchmarks, revealing that this metric is orthogonal to standard performance measures while highlighting profound information-theoretic implications for prompt injection defenses and the fundamental manipulation of interpretive contexts.

Original authors: Christopher J. Agostino, Quan Le Thien, Nayan D'Souza, Louis van der Elst

Published 2026-03-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Christopher J. Agostino, Quan Le Thien, Nayan D'Souza, Louis van der Elst

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Meaning is a "Magic Trick," Not a Dictionary

Imagine you are looking at a word like "Bank."

In a classical view (like an old dictionary), the word has a fixed meaning waiting inside it. It's either a "river bank" or a "money bank." The job of the computer is just to open the box and see which one is inside.
This paper argues that's wrong. The paper suggests that meaning doesn't exist until you look at it. It's more like a magic trick. The word "Bank" is a blank slate. It only becomes a "river bank" or a "money bank" the moment you put it in a specific context (like a sentence about fishing vs. a sentence about saving money).

The authors used a test from quantum physics (called the CHSH test) to prove that Large Language Models (LLMs) don't just "retrieve" meanings. They actually create them on the spot, and they do it in a way that is mathematically "quantum"—meaning the order in which you ask questions changes the answer, and the answers are deeply connected to the situation in a way that defies simple logic.

The Experiment: The "Four Friends" Game

To test this, the researchers set up a game with four "friends" (four separate AI instances).

They gave all four friends the same ambiguous sentence (e.g., "The bat was settled near the bank").
But, they gave each friend a different secret persona (a "lens" through which to view the world):
- Friend A is a Surgeon.
- Friend A' is a Bus Driver.
- Friend B is Haunted by Mistakes.
- Friend B' is a Sales Rep.
The friends couldn't talk to each other. They had to guess what the words meant based only on their secret persona.

The Result: Even though they were independent and had different personas, their answers were strangely correlated. They didn't just guess randomly; they seemed to "know" what the others were thinking in a way that classical math says is impossible. This proved that the AI isn't just looking up facts; it's navigating a complex, fluid web of meaning that changes based on the "lens" you use.

Key Findings (The "So What?")

1. Bigger isn't necessarily "smarter" in the way we think

The researchers tested models ranging from tiny ones (like a pocket calculator) to massive ones (like a supercomputer).

The Analogy: Imagine testing how well different-sized groups of people can solve a riddle. You might expect the biggest group to be the most consistent.
The Reality: The size of the model didn't matter much. A small model and a huge model both showed this "quantum" behavior. What mattered was how the model was set up (the "sampling parameters"), not just how big it was. It's like how a small, well-organized team can sometimes outperform a giant, chaotic corporation.

2. The "Order" of words changes the meaning

In the real world, if you say "The cat chased the dog" vs. "The dog chased the cat," the meaning flips. But in AI, the order of words changes the probability of the meaning in a weird, non-linear way.

The Analogy: Think of a Rubik's Cube. If you twist the top face, then the right face, you get a different pattern than if you twist the right face first, then the top. The AI treats words like the faces of a cube; the order you present them changes the final picture in a way that can't be predicted by just looking at the individual pieces.

3. The "Hallucination" Problem is actually a feature, not a bug

We often get mad at AI when it "hallucinates" (makes things up). We think, "Why didn't it just look up the truth?"

The Paper's Take: The AI isn't broken; it's doing exactly what humans do. Because meaning is created on the spot, the AI sometimes creates a meaning that feels right to it but is wrong for you.
The Analogy: Imagine you ask a friend, "What's the best movie?" If they are in a sad mood, they might say "The Notebook." If they are in a happy mood, they might say "Superbad." They aren't lying; their "context" changed the answer. The AI is the same. It's not a database; it's a mood-reflecting mirror.

4. The Danger of "Manufacturing Context" (The Scary Part)

This is the most important part for the future.

The Analogy: Imagine a stage director. If the director sets the lights to be dark and moody, the actors will act sad. If the director sets the lights to be bright and sunny, the actors will act happy. The actors aren't changing their minds; the context forced them to change their performance.
The Reality: The paper argues that "Prompt Injection" (hacking an AI) works because hackers are acting like evil stage directors. They don't need to break the AI's code; they just need to change the "lighting" (the context) so the AI produces a different meaning.
The Twist: This applies to humans too! Propaganda and advertising work the same way. They don't change your brain; they change the context you are in, so you "interpret" a product or a politician differently. The paper calls this "Manufacturing Contextuality."

The Conclusion: How to Build Better AI

The paper ends with a warning and a solution for designers:

Don't try to "fix" the AI by making it less flexible. The ability to interpret things based on context is what makes the AI smart. If you try to force it to be rigid and "safe" by removing its ability to be contextual, you also remove its ability to understand you.
The Solution: Instead of building walls (guardrails) to stop the AI from making mistakes, we need to understand the "lens" the AI is looking through. We need to design systems where humans and AI work together to set the context, rather than trying to force the AI to be a rigid robot.

In short: AI isn't a calculator; it's a collaborator that creates meaning in the moment. To work with it safely, we have to understand that meaning is fluid, and the person (or machine) holding the flashlight determines what we see in the dark.

1. Problem Statement

The paper addresses a fundamental gap in understanding how Large Language Models (LLMs) and humans generate meaning. Traditional computational linguistics and AI safety rely on classical Boolean logic, assuming that meaning is compositional (derived from fixed parts) and that interpretations are deterministic or probabilistic based on pre-existing values.

However, empirical evidence from cognitive science suggests human semantic processing is contextual: the meaning of an expression is not fixed prior to observation but is constituted by the interaction between the expression, the interpreter, and the context. This leads to phenomena like non-commutativity (order of information matters) and violations of classical probability bounds.

The authors argue that current AI safety measures (e.g., prompt injection defenses, hallucination detection) fail because they treat meaning as a static property to be retrieved, rather than a dynamic process to be interpreted. They posit that LLMs, like humans, exhibit quantum-like contextuality, making them inherently vulnerable to adversarial reframing but also capable of genuine interpretation.

2. Methodology

The study employs a semantic Bell test (specifically the CHSH inequality) to measure contextuality in LLMs.

Experimental Protocol:
- Setup: An ambiguous word pair (e.g., "bank/bat") is embedded in a sentence template.
- Agents: Four independent LLM instances act as "observers" (Alice and Bob), each assigned a distinct "persona" (measurement setting: $A, A', B, B'$ ) to create orthogonal interpretive frames (e.g., "You are a surgeon" vs. "You are a bus driver").
- Independence: Agents share no state or information; they only receive the prompt and their specific persona.
- Measurement: The model interprets the words, and a secondary classification step maps these interpretations to binary outcomes ( $\pm 1$ ) based on predefined meanings.
Parameter Space Sweep:
- The experiment was conducted across 24 models spanning four orders of magnitude in parameter count (from 0.6B to 27B+ parameters, including dense and MoE architectures).
- A $3 \times 3 \times 3$ $3 \times 3 \times 3$ grid of inference parameters was tested for each model:
  - Temperature ( $\tau$ ): $\{0.2, 1.0, 1.8\}$
  - Nucleus threshold ( $p$ ): $\{0.7, 0.9, 1.0\}$
  - Top-k ( $k$ ): $\{10, 50, 100\}$
- Total trials: $\sim 26,000$ across 16 analyzable models.
Metric Calculation:
- The CHSH $S$ parameter is calculated using density matrix formalism: $S = E(A, B) - E(A, B') + E(A', B) + E(A', B')$ .
- Classical Bound: $|S| \le 2$ .
- Quantum Violation: $|S| > 2$ indicates non-classical, contextual correlations.
- Note: Because the test probes "observer-side" contextuality rather than particle entanglement, values can theoretically reach the algebraic maximum of 4.0, exceeding the Tsirelson bound ( $2\sqrt{2} \approx 2.83$ ).

3. Key Contributions

Empirical Validation of Quantum Contextuality in LLMs: The paper provides large-scale evidence that LLMs violate the CHSH inequality, confirming that their interpretive behavior is structurally similar to human cognition and cannot be fully described by classical probability theory.
Characterization of Interpretive Topography: The authors introduce the concept of a model's "contextuality topography"—the unique distribution of $|S|$ values across its inference parameter space. They demonstrate that this profile is a distinct behavioral signature of a model, independent of its size or architecture.
Orthogonality to Standard Benchmarks: The study establishes that contextuality metrics ( $|S|$ ) are orthogonal to standard evaluation benchmarks (MMLU, hallucination rates, nonsense detection). A model's ability to interpret contextually is not captured by its factual accuracy or safety scores.
Theoretical Framework for Safety: The paper reframes prompt injection and "manufacturing consent" not as bugs, but as inevitable consequences of genuine contextuality. It argues that meaning is indeterminate prior to the interpretive act, making fixed guardrails insufficient.

4. Key Results

Universal Violation: Every model with sufficient data produced violations of the classical bound ( $|S| > 2$ $∣ S ∣ > 2$ ).
- Range: $|S|$ values ranged from $\sim 0.3$ to 4.0 (the algebraic maximum).
- Frequency: 35.8% of valid grid points violated the bound.
Distribution Characteristics:
- All models' distributions mode near the classical bound ( $S \approx 2.0$ ).
- The Interquartile Range (IQR) of the $|S|$ distribution was the primary differentiator between models, yet this metric showed zero correlation ( $|\rho| < 0.03$ ) with MMLU scores, hallucination rates, or nonsense detection.
Non-Monotonicity: Contextuality does not scale linearly with model size. Sparse Mixture-of-Experts (MoE) models did not systematically differ from dense models of comparable active size.
Non-Commutativity: Flipping the word order of ambiguous terms significantly altered interpretation probabilities ( $|\Delta P(A)| > 0.5$ ), confirming that the sequence of information presentation actively shapes the outcome, consistent with non-commuting observables.
Parameter Sensitivity: No single sampling parameter (temperature, top-p, top-k) consistently drove contextuality in one direction; each model exhibited a unique topography across the parameter grid.

5. Significance and Implications

Redefining AI Safety: The paper argues that safety cannot be achieved solely through "guardrails" that assume fixed meanings. Since meaning is indeterminate until the act of interpretation (influenced by the full context), an attacker only needs to find one context where the filter's pre-classification fails. This is an information-theoretic constraint, not a solvable engineering problem.
Human-AI Interaction: The capacity to be manipulated (via prompt injection or propaganda) and the capacity to interpret are the same capacity. The "contextuality" that makes LLMs vulnerable to adversarial reframing is the same mechanism that allows them to function as genuine collaborative partners.
Design Philosophy: Designing reliable human-agent systems requires characterizing a model's interpretive character (its contextuality profile) rather than attempting to eliminate contextuality. Future interaction design must account for the "manufacturing of contextuality"—the engineering of the interpretive frame itself—rather than just the content of the prompt.
Evaluation Shift: Current benchmarks (MMLU, etc.) measure retrieval and pattern matching but fail to capture the interpretive dynamics of a system. New metrics must be developed to assess how a model constructs meaning in context.

In conclusion, the paper posits that contextuality is a fundamental feature, not a bug, of natural language processing in both humans and machines. Understanding and working with this non-classical structure is essential for the next generation of safe and effective human-AI interaction.