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arXiv 2311.00235stat.MLcs.AIcs.LG

从后向误差分析视角看多任务与持续学习中的隐式偏置

Implicit biases in multitask and continual learning from a backward error analysis perspective

Google(谷歌)

Benoit Dherin

AI总结:

本文利用后向误差分析推导出多任务与持续学习中随机梯度下降隐式最小化的修正损失,揭示其中的冲突项(多任务为梯度对齐,持续学习为任务梯度李括号)可能损害收敛与隐式正则化。

摘要:

利用后向误差分析,我们计算了使用随机梯度下降训练的神经网络在多任务和持续学习设置中的隐式训练偏置。具体而言,我们推导出了训练过程中被隐式最小化的修正损失。它们包含三项:原始损失,负责收敛;一个与学习率成正比的隐式平坦性正则化项;以及最后一项,即冲突项,它在理论上可能同时损害收敛和隐式正则化。在多任务中,冲突项是一个众所周知的量,用于衡量任务之间的梯度对齐程度;而在持续学习中,冲突项是深度学习优化中的一个新量,尽管它是微分几何中的一个基本工具:任务梯度之间的李括号。

英文摘要:

Using backward error analysis, we compute implicit training biases in multitask and continual learning settings for neural networks trained with stochastic gradient descent. In particular, we derive modified losses that are implicitly minimized during training. They have three terms: the original loss, accounting for convergence, an implicit flatness regularization term proportional to the learning rate, and a last term, the conflict term, which can theoretically be detrimental to both convergence and implicit regularization. In multitask, the conflict term is a well-known quantity, measuring the gradient alignment between the tasks, while in continual learning the conflict term is a new quantity in deep learning optimization, although a basic tool in differential geometry: The Lie bracket between the task gradients.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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