Backward Coherence and Hidden-State Stability in Recurrent Neural Networks: A Quasi-Reverse-Martingale Theory
Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear. We study hidden-state stability through \emph{backward coherence}: the extent to which $h_t$ can be reconstructed from $h_{t+1}$ by a learned backward projector $g_φ$. Under contraction and summable backward drift, the hidden-state sequence forms a quasi-reverse-martingale. This yields almost-sure convergence, rates under mixing, an interpretable limiting representation, finite pathwise stopping times, and a theoretical framework for time-uniform confidence sequences. Simulations support the theory. Backward-coherence regularisation reduces the empirical quasi-martingale total $\hat Q$...
| Authors | Yuan-chin Ivan Chang |
|---|---|
| Primary category | cs.LG |
| Published | 8 June 2026 |
| Last updated at source | 8 June 2026 |
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