English(EN) On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials

新定理证明深度神经网络中梯度轨迹的收敛性

作者 PulseAugur 编辑部 · [2 个来源] · 2026-10-21 05:06

一篇新发表在arXiv上的论文介绍了一个定理，该定理解决了可定义势函数在无穷远处梯度猜想的问题。研究证明了此类势函数的梯度轨迹具有有限的球形长度并具有方向收敛性。这一发现对深度神经网络（DNN）的训练有影响，表明当激活函数和损失函数是可定义的且连续可微时，训练流会收敛。 AI

影响这项研究在特定条件下暗示了DNN训练中的理论收敛特性，可能影响优化策略。

排序理由该集群包含一篇研究论文，详细介绍了具有深度神经网络训练意义的数学定理。

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arXiv cs.LG TIER_1 English(EN) · Thang Do, Arnulf Jentzen, Benno Kuckuck · 2026-10-22 04:00

关于无穷远处的梯度猜想：可定义势能的梯度轨迹的有限球面长度

arXiv:2610.29211v1 Announce Type: cross Abstract: We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $\theta(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has finite length and, in particular…
Hugging Face Daily Papers TIER_1 English(EN) · 2026-10-21 05:06

关于无穷远处的梯度猜想：可定义势能的梯度轨迹的有限球面长度

We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $θ(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has finite length and, in particular, converges (directional convergence). In other words, …