Markov-coded synchronization-robust latent streams

Integrate this at the discrete latent or tokenizer output of a small sequence autoencoder, or use it for a redundant control stream prepended to transformer inputs. Start with a binary latent stream of length $m$ per example. Map each bit to a learned embedding and feed the embeddings, together with the semantic input, to a transformer encoder-decoder. Generate the stream using the symmetric Markov prior: sample the first bit uniformly, then sample each next bit equal to the previous bit with probability $1-q$ and flipped with probability $q$. For differentiable training, use straight-through Bernoulli samples, Gumbel-Softmax, or continuous bit logits, and add the Markov negative-log-prior to the objective: $-\log P(z_{1:m})=-\log P(z_1)-\sum_{t=2}^m\log P(z_t\mid z_{t-1})$. During training, insert $\lfloor\delta m\rfloor$ random latent tokens at uniformly sampled positions; train the decoder to recover the semantic target. Choose stream length and codebook size so that $R_{\mathrm{NN}}\leq(1-\varepsilon)R_{\mathrm{ins}}(\delta)$ for $\varepsilon\in[0.1,0.3]$. The capacity expression is computed exactly; $q$, the margin, and the corruption distribution are empirical choices. First test on binary sequence classification or byte-level ListOps with a 6-layer transformer, comparing iid binary latents against Markov latents at equal latent length and FLOPs. Evaluate clean accuracy, accuracy after 10%, 25%, and 50% insertions, and examples needed to reach a fixed corrupted-data accuracy. Success is a robustness gain at fixed clean accuracy with less than 10% training overhead.