The Limits of Binding in Dual Encoders
Dual-encoder models such as CLIP score an image-caption pair by a single inner product of two independently computed unit vectors, and fail at binding, often scoring near chance when asked to distinguish "a red car and a blue dog" from "a blue car and a red dog". We give a mathematical account of when this failure is necessary and when it is contingent. Working within the ideal-encoder framework proposed by Kang et al., we first show the relevant axioms are satisfiable, so every impossibility must enter through an added, checkable hypothesis. We then prove three such obstructions. Depth: for recursive role-binding codes the swap margin obeys an exact law $m(D) = 2b^{-D}$ in the nesting de...
| Authors | Kin Ian Lo |
|---|---|
| Primary category | cs.LG |
| Published | 16 August 2026 |
| Last updated at source | 16 August 2026 |
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