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Exact semantic readout from compressed vector representations

arXiv · AI, language, vision and robotics · article · Sep 16, 2026 · UTC

We characterize when compressed vector representations admit exact linear or affine readouts of a finite lexicon's truth conditions: one fixed map per predicate, sending each entity vector to the corresponding truth vector. A necessary and sufficient row-space condition determines existence; the augmented truth matrix has rank r, giving minimum dimension r in the linear case, and r-1 in the affine. Exact readouts return values in a shared truth basis on which Boolean connectives act unchanged; separability alone requires an intervening threshold. For binary relations, exact bilinear readout of

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