English(EN) On the Rate of Convergence of GD in Non-linear Neural Networks: An Adversarial Robustness Perspective

新研究揭示神经网络中梯度下降的收敛速率缓慢

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-12 04:00

研究人员分析了一个简化的两神经元ReLU神经网络在两种训练实例下的梯度下降（GD）收敛速率。他们从理论上证明，虽然GD可以达到最优鲁棒性裕度，但其收敛速率极其缓慢，尺度为\Theta(1/\ln(t))。这一通过经验模拟验证的发现，首次为非线性模型中的鲁棒性裕度收敛速率建立了明确的下界。分析涉及对GD轨迹和系统动力学的详细检查，以界定决策边界的移动。 AI

影响强调了某些神经网络架构在训练效率方面存在的潜在局限性。

排序理由学术论文，详细阐述了关于神经网络收敛的理论发现。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.AI TIER_1 English(EN) · Guy Smorodinsky, Sveta Gimpleson, Itay Safran · 2026-10-12 04:00

非线性神经网络中梯度下降收敛速率的对抗鲁棒性视角

arXiv:2603.02095v2 Announce Type: replace-cross Abstract: We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying a…

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非线性神经网络中梯度下降收敛速率的对抗鲁棒性视角

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