Loading
Life sciences · Preprint
arXiv · November 6, 2026
No summary has been generated for this record yet. What follows is drawn from its source metadata only.
Preprint.
No findings were extractable from the material analysed.
Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.
The source did not state who this applies to in practice.
Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.
This record has not been graded across any dimension yet. Treat the label above as provisional and read the source.
What is missing. This record has no bottom line, key findings, reported figures, evidence dimensions. That is a gap in the analysis, not a judgement about the study.
Adam estimates second moments coordinatewise, but typically adds the same scalar $\varepsilon$ to every denominator. We study how this shared $\varepsilon$ affects convergence when noise and curvature vary across coordinates. Under coordinatewise finite-$p$ noise moments, $p\in(1,2]$, choosing $\varepsilon_i$ from the noise and curvature bounds for each coordinate attains the heavy-tailed $\ell_1$-stationarity benchmark $O(T^{-\frac{p-1}{3p-2}})$, matching the known optimal time exponent for smooth nonconvex stochastic optimization. For $1<p<2$, Adam with a shared $\varepsilon_t$ admits a lower bound of order $Ω(T^{-\frac{p-1}{2p}})$. This lower bound holds for every predictable scalar choice of $η_t$, $β_{1,t}$, $β_{2,t}$, and $\varepsilon_t$, precluding a dimension-uniform benchmark rate for this class.