Recurrent State-Space Models › Summary

Michael BrenndoerferJune 25, 20262 min read
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  • An RSSM combines recurrent memory hth_t with a stochastic latent ztz_t. Deterministic computation is not certainty, and one sampled joint state is not a full belief distribution.
  • The prior predicts before the current observation; the posterior incorporates it during filtering, including at deployment. Their conditional KL trains the distinct prior head and regularizes the posterior, but is not forecast error or sensor-noise variance.
  • The deterministic recurrent edge bypasses fresh sampling operations; the latent distribution can carry observation-conditioned alternatives. PlaNet's ablations support this combination in its tested setup, not a universal necessity theorem.
  • The exact filtering ELBO averages over latent histories. A Monte Carlo estimate need not itself be a lower bound. The example uses a weighted, free-nat-clipped modification; free nats and KL balancing adjust gradients without guaranteeing prevention of collapse.
  • Imagination starts from independently sampled posterior histories and proceeds under actions with prior draws only. Compare ensemble-mean and point-forecast RMSE on equal terms, and evaluate intervals separately with coverage, width, and a known-model reference when available.
  • The worked example tests filtering, open-loop prediction, and linear state recoverability separately. A velocity probe does not establish Markov sufficiency, and a broad interval does not establish calibration.
  • Approximate inference, restricted conditional latent families, finite memory, and sequential computation motivate comparison with the architectures in the next chapter.