$$\Delta = s_{\text{multi}} - s_{\text{text}}$$

Equation 3 · Foundation Models

Ten Failure Modes That Define Multimodal AI Systems

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The finding motivates a simple, checkable decomposition rather than a new metric: for any multimodal benchmark, let $s_{\text{multi}}$ be the score with all modalities present and $s_{\text{text}}$ be the same benchmark scored with the non-text modality removed. The quantity $\Delta = s_{\text{multi}} - s_{\text{text}}$. is the actual multimodal increment — what the removed channel contributed beyond what text alone already bought. A large $s_{\text{multi}}$ with a small $\Delta$ is not evidence of multimodal competence; it is evidence that the benchmark, not the model, is doing something unimodal. Reporting $\Delta$ alongside $s_{\text{multi}}$ costs one extra evaluation run and turns an unfalsifiable headline number into a…

Meanings in this article

• $\Delta$: the small.
• $s_{\text{multi}}$: the large.
• $s_{\text{text}}$: the actual multimodal increment — what the removed channel contributed beyond what text alone already bought.

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