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CID measures meaning changes as distances between embeddings

Key Takeaways

  • Ron Fulbright proposes using Mahalanobis distance to measure semantic change between embeddings.
  • The score depends on the model and covariance estimate.
  • Ron Fulbright proposes measuring a change in meaning by comparing two embeddings.
  • CID accounts for how those embeddings vary together instead of treating all directions in the space equally.
  • In the CID preprint, Ron Fulbright proposes a way to describe how meaning changes between two pieces of information.

In the CID preprint, Ron Fulbright proposes a way to describe how meaning changes between two pieces of information. The Contextual Information Differential, or CID, treats each representation as a point in an embedding space and measures how far one point moves from the other. It is a definition of semantic change that can be applied to a representation rather than a claim that meaning has one universal unit. The preprint was submitted to arXiv on November 6, 2026.

What counts as a semantic state?

Fulbright defines a semantic state as the vector representing information in a model's embedding space. Under this definition, a transformation has a before state and an after state. A researcher could compare embeddings for a passage and its revision, for example. The proposal measures the shift in the representation; it does not need to label the kind of editing or reasoning that produced the change.

Why account for covariance?

CID is based on Mahalanobis distance, which takes the covariance of the embedding space into account. This means the calculation treats a displacement relative to patterns of variation in that space. Two coordinate differences of the same raw size can carry different weights when they lie along directions with different variability. The author uses this distance to formalize what the paper calls cognitive work.

What would the number tell a reader?

A CID score would indicate the size of a change as seen by the chosen representation. It would not establish that a changed answer is more accurate or useful. Comparisons would also need a consistent embedding model and covariance estimate; changing either changes the geometry in which the measurement is made.
The paper lays out the metric and suggests uses for studying reasoning and human–AI collaboration. For a practical evaluation, one useful test would be to compare what the score does for an ordinary paraphrase, a factual correction and an unrelated replacement before treating larger movement as more meaningful.

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