Compact-Support Telegraph Latent Sampler

Insert the module between a neural encoder and decoder, or use it to replace Gaussian perturbations in a diffusion or latent-energy sampler. Given latent state z_n, compute the learned deterministic drift b_phi(z_n,t_n), update the telegraph force with u_(n+1) = exp(-gamma dt) u_n + [1 - exp(-gamma dt)] sum_k v_k s_(k,n)/gamma, and then use z_(n+1) = z_n + dt b_phi(z_n,t_n) + beta dt u_(n+1). Each sign flips independently with probability 1 - exp(-lambda_k dt). Keep gamma, lambda_k, and v_k fixed initially; tune only beta to match the variance of a Gaussian baseline. The exact relaxation and bounded-support equations come from the paper, while interaction with the learned drift must be evaluated empirically. First test on a two-dimensional mixture of Gaussians or checkerboard distribution using a small score network. Compare Euler-Maruyama Gaussian noise, standard colored OU noise, and telegraph-driven noise. Plot latent increments, radius distributions, mode coverage, and stability failures. With the learned drift disabled, the predicted stationary variance must match the formula within 10% and |u| must never exceed sum_k v_k/gamma. With one or two channels, histograms should show non-Gaussian edge structure; with many equal small channels, excess kurtosis should approach zero.