Why tensor structure breaks VLM-based scanner-effect projection
PTenigma · x · 2026-09-20
The author unpacks a neat mathematical result: symmetric matrices can always be disentangled into their eigenspace, and several matrices share one axis set iff they commute. Moving from 2 to 3 indices breaks this — some axes come out as stuck-together pairs of directions. Practical warning: if you use a VLM to project out scanner effects in deep learning data, the data may carry overall covariance plus per-scanner covariance (spectral mixing), forming a 3-tensor, and careless projection will go wrong.
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