[论文] [论文] On the stability of learning

论文概要

研究领域: ML 作者: John J. Vastola 发布时间: 2026-10-26 arXiv: 2610.35856

中文摘要

学习算法的分析通常假设信息性梯度持续可得，但这并不总成立——生物神经网络中的学习信号可能稀疏、局部、且在任何给定突触上间歇出现。本文证明：若梯度信息有噪声且只能间歇获得，学习可能不稳定。特别地，即使平均学习动态收敛到正确最优点，学习方差仍可能渐近无穷。我们在多个可解析求解的情形中探讨这一点（含单层与多层线性网络），推导学习稳定的显式条件。这些条件是对随机梯度下降稳定性条件的补充，但概念上与之不同。我们的工作表明：无偏的信用分配不足以保证可靠学习，反馈还必须足够频繁且足够信息——这给生物可行学习模型增加了新的约束。

原文摘要

Learning algorithms are usually analyzed under the assumption that informative gradients are continuously available. But this is not always true---learning signals in biological neural networks, for example, may be sparse, local, and only intermittently available at any given synapse. In this work, we show that if gradient information is noisy and only intermittently available, learning may be unstable. In particular, even if average learning dynamics converge to the correct optimum, variance in learning may be asymptotically infinite. We explore this point in a number of analytically tractable settings, including single-layer and multi-layer linear networks, and derive explicit conditions under which learning is stable. These conditions complement, but are conceptually distinct from, existing conditions related to the stability of stochastic gradient descent. Our work demonstrates that unbiased credit assignment is not enough for reliable learning; sufficiently frequent and informative feedback is also required, which yields an additional constraint on models of biologically plausible learning.

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*自动采集于 2026-10-28*

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