Can AI’s semantic maps measure changes in meaning? A preprint proposes a metric

Meaning as a position on a map

The paper, posted to arXiv on November 6, 2026, introduces the Contextual Information Differential, or CID. It is a conceptual and mathematical proposal, not an experimentally validated measure of cognition.

Its starting point is the embedding: a list of numbers that represents information within a model’s high-dimensional space. These representations can capture semantic relationships, placing related ideas near one another. Fulbright calls the position of an information representation its “semantic state.”

Under this framework, transforming an input into an output moves information between two semantic states. The author defines that movement as “cognitive work.” This is a particular theoretical definition, distinct from the everyday sense of working hard on a problem.

The proposal also differs from Shannon information theory. Shannon’s framework concerns uncertainty and information transmission; CID asks how much a representation’s meaning changes. Fulbright presents the two approaches as complementary rather than competing.

A distance adjusted for the surroundings

CID uses an established statistical tool, Mahalanobis distance. Its proposed contribution is applying that tool to semantic-state changes and interpreting the result as cognitive work.

A simple straight-line distance treats every direction in an embedding space equally. But embedding spaces have uneven statistical structure: representations vary more along some directions than others, and their coordinates can be correlated.

Mahalanobis distance adjusts for those differences through a covariance matrix, which describes how the coordinates vary together. A displacement along a low-variance direction receives more weight than an equally sized displacement along a high-variance direction.

In accessible terms, CID asks not only how far two representations are apart, but how large that separation is relative to the space’s statistical structure. Fulbright argues that this adjustment could make the distance more informative about semantic transformation than unadjusted distance or angular similarity.

That interpretation remains a hypothesis. The paper does not demonstrate that covariance-adjusted displacement reliably tracks conceptual importance or novelty.

Illustrations, not measured results

The manuscript describes transformations expected to produce different amounts of displacement. A paraphrase should move relatively little because its meaning remains similar. A summary removes and reorganizes detail. An explanation adds concepts and relationships. Conceptual synthesis combines ideas into a broader interpretation.

These examples explain the intended behavior of CID; they are not experimental findings. The paper reports no calculated CID scores showing that these transformation types consistently follow the proposed ordering.

Translation illustrates another important distinction. In a suitable multilingual embedding model, sentences conveying the same meaning in different languages should occupy nearby positions. Fulbright proposes zero CID as an ideal translation target. A low score would therefore describe preserved meaning, not prove that translating required little effort.

Proposed uses in education and AI

Fulbright suggests comparing student answers with a reference concept, tracking their distance from that reference over time, and potentially using CID in automated grading. These are proposed applications, not evaluated educational outcomes.

For AI, the paper proposes measuring changes across intermediate reasoning steps or successive transformer layers. Adding the distances between successive states would produce a path measure, distinct from the direct distance between the initial input and final output.

The author also suggests comparing path distance with end-to-end distance as a possible indicator of reasoning depth or complexity. The manuscript does not establish that interpretation experimentally.

What the number would not establish

The limitations are central. CID measures transformation, not correctness, factual accuracy or logical validity. A large change could introduce errors rather than insight. A larger score would not, by itself, mean a better answer.

The result also depends on the embedding model and its covariance structure. Different models may produce values that cannot be compared directly. Although the framework is intended to describe outputs from either humans or machines, its measurement still depends on the chosen representation.

Finally, the proposal assumes embeddings adequately capture the relevant meaning. The paper acknowledges that this remains an open research question. It explicitly distinguishes CID from direct measurements of neurological activity or mental effort.

The preprint therefore offers a mathematical framework to investigate—not evidence that meaning, learning or cognitive achievement can already be reduced to a validated universal score.