{"ID":2832598,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05790","arxiv_id":"2512.05790","title":"Learnability Window in Gated Recurrent Neural Networks","abstract":"We develop a statistical theory of temporal learnability in recurrent neural networks, quantifying the maximal temporal horizon $\\mathcal{H}_N$ over which gradient-based learning can recover lag-dependent structure at finite sample size $N$. The theory is built on the effective learning rate envelope $f(\\ell)$, a functional that captures how gating mechanisms and adaptive optimizers jointly shape the coupling between state-space transport and parameter updates during Backpropagation Through Time. Under heavy-tailed ($α$-stable) fluctuations, where empirical averages concentrate at rate $N^{-1/κ_α}$ with $κ_α= α/(α-1)$, the interplay between envelope decay and statistical concentration yields explicit scaling laws for the growth of $\\mathcal{H}_N$: logarithmic, polynomial, and exponential temporal learning regimes emerge according to the decay law of $f(\\ell)$. These results identify the envelope decay as the key determinant of temporal learnability: slower attenuation of $f(\\ell)$ enlarges the learnability window $\\mathcal{H}_N$, while heavy-tailed noise compresses temporal horizons by weakening statistical concentration. Experiments across multiple gated architectures and optimizers corroborate these structural predictions.","short_abstract":"We develop a statistical theory of temporal learnability in recurrent neural networks, quantifying the maximal temporal horizon $\\mathcal{H}_N$ over which gradient-based learning can recover lag-dependent structure at finite sample size $N$. The theory is built on the effective learning rate envelope $f(\\ell)$, a funct...","url_abs":"https://arxiv.org/abs/2512.05790","url_pdf":"https://arxiv.org/pdf/2512.05790v8","authors":"[\"Lorenzo Livi\"]","published":"2025-12-05T15:16:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"physics.data-an\"]","methods":"[]","has_code":false}