New Proof: Perfect VAE Reconstruction Can't Verify Encoder-Decoder Codebook Agreement
burny_tech · x · 2026-10-21
Yusuke Hayashi proves that no standard training report can reveal whether codes written into a VAE's latent space read back as written. He constructs two VAEs with exact inference, identical per-example ELBOs and code histograms, and perfect reconstruction—yet codebook agreement is 1 in one and 0 in the other. ELBO terms bound measurable agreement (variational gap for exact inference, rate for prior sampling); on 240 trained VAEs, a rate-based floor rules out certification for 66 models in advance, and none certifies. The paper yields a simple Certify-or-Measure protocol for any pipeline reading VAEs as discrete codes.
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