Bayesian Logit Smoother with Bursty-Mask Marginalization

1. Integration point: use any framewise neural classifier, such as an MLP, CNN encoder, transformer encoder, or SSM, producing logits $\ell_\theta(x_t)\in\mathbb{R}^K$. Convert logits to positive emissions with $e_t(s)=\exp(\ell_\theta(x_t,s)-\operatorname{logsumexp}_j\ell_\theta(x_t,j))$; equivalently these are normalized neural likelihood scores. Maintain a belief vector $b$ outside the network and expose $b_t$ as the final prediction or feed it into a downstream recurrent policy. 2. Pseudocode: initialize $b=\pi_A$; for every timestep, compute the neural logits and mask $m_t$; set $e=\operatorname{softmax}(\ell)$ if observed and $e=\mathbf{1}$ if missing; compute $p=A^\top b$; update $b\leftarrow\operatorname{normalize}(e\odot p)$; return $b$. Train with cross-entropy on $b_t$ and optionally an auxiliary cross-entropy on the raw logits. Learn or tune $A$ using validation data, constraining rows to the simplex; start with a persistence parameter $a\in[0.8,0.99]$. 3. Computed from the paper: the Bayesian recursion and bursty missingness matrix. Estimated empirically: $A$, $a$, the dropout rate $\rho$, burst length $b$, and neural emissions. Estimate $\rho$ and $b$ directly from mask run lengths, and select $a$ by validation negative log-likelihood or by matching the empirical label dwell time. 4. First cheap experiment: train a small GRU or transformer classifier on sequential MNIST with synthetic three-class latent regimes, and separately on a real event sequence dataset such as Human Activity Recognition. Compare raw per-frame softmax, ordinary exponential moving average, and this Bayesian wrapper under clean, i.i.d., and bursty masking. Use $K=3$, $\rho=0.3$, and burst lengths $b\in\{2,5,10\}$. Measure accuracy, negative log-likelihood, expected calibration error, and flip rate. The quantitative prediction is that perturbations during missing runs decay according to $|\lambda_A|^q$ and that flip rate decreases monotonically with $a$ or $b$, while responsiveness worsens when the effective memory $\tau\approx b$ becomes longer than the event duration. Sweep $a$ and verify that the observed belief autocorrelation time agrees with $-1/\log|\lambda_A|$ within 20%; also test whether burst-trained marginalization loses substantially less accuracy than sentinel imputation as $\rho$ increases.