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新论文通过谱几何分析神经网络的“领悟”现象

两篇新的arXiv论文探讨了神经网络中“领悟”(grokking)现象,即模型在记忆训练数据后才能泛化。其中一篇论文提出“低秩衰减”(Low-Rank Decay, LRD)作为谱正则化器,通过压缩奇异值来改善领悟,并表明它可以加速秩崩溃并扩大泛化能力的数据分数边界。另一篇论文将领悟视为一个约束优化问题,证明了梯度下降在零损失流形上最小化权重范数,并推导出了记忆后动力学的闭式表达式。 AI

影响 这些论文为神经网络中延迟泛化提供了理论见解,可能指导未来的模型训练策略。

排序理由 两篇在arXiv上发表的学术论文,讨论了神经网络中的一个特定现象。

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新论文通过谱几何分析神经网络的“领悟”现象

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两篇在arXiv上发表的学术论文,讨论了神经网络中的一个特定现象。
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报道来源 [2]

  1. arXiv cs.AI TIER_1 English(EN) · Mingyu Li ·

    Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View

    arXiv:2606.04405v1 Announce Type: cross Abstract: Modern Transformer architectures frequently employ normalization mechanisms such as RMSNorm and Query-Key Normalization, making parts of the model approximately scale-invariant with respect to weight magnitudes. In this regime, st…

  2. arXiv cs.AI TIER_1 English(EN) · Tiberiu Musat ·

    Grokking 的几何学:零损失流形上的范数最小化

    arXiv:2511.01938v3 Announce Type: replace-cross Abstract: Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data. Previous research has linked this delayed gener…