# Lost and Found in Translation: Variational Diagnostics for Neural Codebook Channels

arXiv: https://arxiv.org/abs/2605.18846 · HTML: https://mlsanity.com/paper/2605.18846/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 16 of 16)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Multi-Agent Cooperation and the Emergence of (Natural) Language](https://mlsanity.com/paper/1612.07182/) (2016)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Optimus: Organizing Sentences via Pre-trained Modeling of a Latent Space](https://mlsanity.com/paper/2004.04092/) (2020)
- [The continuous Bernoulli: fixing a pervasive error in variational autoencoders](https://mlsanity.com/paper/1907.06845/) (2019)
- [Autoencoding Variational Autoencoder](https://mlsanity.com/paper/2012.03715/) (2020)
- [Navigating the Latent Space Dynamics of Neural Models](https://mlsanity.com/paper/2505.22785/) (2025)
- [Beyond Vanilla Variational Autoencoders: Detecting Posterior Collapse in Conditional and Hierarchical Variational Autoencoders](https://mlsanity.com/paper/2306.05023/) (2023)
- [On the Encoder-Decoder Incompatibility in Variational Text Modeling and Beyond](https://mlsanity.com/paper/2004.09189/) (2020)

## Built on by (most cited first, 1 of 1)

- [Perfect Reconstruction Cannot Show Whether Two Codebooks on a VAE's Latent Space Agree](https://mlsanity.com/paper/2610.14012/) (2026)

## Abstract (arXiv)

Classical communication systems fail not only through random noise but also when transmitter and receiver use incompatible operational codebooks. Variational autoencoders (VAEs) train an encoder qφ and decoder pθ jointly, and practitioners treat the resulting latent space as a discrete code -- for clustering, conditional generation, and mechanistic interpretability. Yet standard VAE diagnostics -- ELBO, active units, mutual information, and code histograms -- certify only whether this code is used, never whether the decoder reads each latent under the encoder's code. We close this gap with the neural codebook channel Ke→ d(jmid i), a coupled encoder-decoder diagnostic whose off-diagonal mass is bounded by an architecture-free Bernoulli-KL certificate dbin(1-A ,|, barηp) ≤ barDelta controlled by the variational gap. The certificate is the operational specialization of the classical KL chain rule under disintegration to the encoder-decoder disagreement event, complemented by a constructive marginal-impossibility result: no combination of marginal histograms, entropies, active-code counts, or mutual information determines Ke→ d. We audit the certificate on four sklearn datasets (finite-grid exact, 5/5 seeds, 20/20 pairs satisfy the bound), a 2D model where the bound is non-vacuous at 2.71× the observed disagreement and the four-term identity closes within 10-4, MNIST under importance-sampling control, and a VQ-VAE attaining the predicted limit hatA=1.000. The package (Ke→ d, A, Reff, R, AU) is an audit-ready reporting unit. More broadly, the framework makes mismatched decoding -- a failure mode classical communication theory named decades ago -- visible inside a single deep generative model.