Backward Coherence and Hidden-State Stability in Recurrent Neural Networks: A Quasi-Reverse-Martingale Theory
arXiv:2606.08934v1 Announce Type: new Abstract: 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 $g_\phi$. 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-u
The paper provides a theoretical framework for understanding hidden-state stability in recurrent neural networks, a crucial aspect for developing more robust and interpretable AI systems.
This research contributes to the foundational understanding of RNNs, potentially leading to more reliable AI models and accelerating progress in agentic systems.
The theoretical clarity around RNN hidden states could enable the design of more predictable and stable AI architectures, enhancing development in advanced AI.
- · AI researchers
- · Deep learning framework developers
- · Developers of AI agents
- · AI models lacking interpretability
Improved theoretical understanding of recurrent neural networks' internal workings.
Development of new, more stable, and interpretable RNN architectures.
Enhanced reliability and trustworthiness of autonomous AI systems and agents in critical applications.
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