arXiv Machine Learning By Yuan-chin Ivan Chang

Backward Coherence and Hidden-State Stability in Recurrent Neural Networks: A Quasi-Reverse-Martingale Theory

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arXiv:2606. 08934v1 Announce Type: new Abstract: Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear.

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arXiv Machine Learning
Sep 14

Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization

The paper presents a theoretical study of Adam in non‑stationary stochastic optimization, distinguishing two regimes: Euclidean tracking under adaptive strong monotonicity and high‑probability projected stationarity for general smooth objectives. It derives finite‑time bounds that decompose into initialization, objective drift, first‑moment tracking error (β₁), and preconditioner perturbation (β₂), and characterizes burn‑in times for constant and step‑decay schedules. The analysis reveals a noise–drift tradeoff, showing that in noise‑dominated settings Adam’s adaptive mechanisms can improve guarantees, while in drift‑dominated settings they may worsen tracking, potentially making vanilla SGD preferable.

By Sharan Sahu, Abir Sarkar, Cameron J. Hogan, Martin T. Wells