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arXiv 2401.12617cs.LG

任务相似性与过参数化对灾难性遗忘的联合效应——一个解析模型

The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model

Northeastern University(东北大学);Technion(以色列理工学院)

Daniel Goldfarb, Itay Evron, Nir Weinberger, Daniel Soudry, Paul Hand

AI总结:

本文构建两任务持续线性回归解析模型,推导期望遗忘的精确表达式,揭示任务相似性与过参数化对灾难性遗忘的联合影响规律,并通过合成数据和置换任务基准验证。

摘要:

在持续学习中,灾难性遗忘受到任务多个方面的影响。以往研究分别分析了任务相似性或过参数化如何影响遗忘。相比之下,本文考察任务相似性与过参数化如何在一个可解析模型中联合影响遗忘。具体而言,我们聚焦于两任务持续线性回归,其中第二个任务是任意第一个任务的随机正交变换(这是对随机置换任务的抽象)。我们推导了期望遗忘的精确解析表达式,并揭示出一种细致的模式。在高度过参数化的模型中,中等任务相似性会导致最严重的遗忘。然而,在插值阈值附近,遗忘随期望任务相似性单调下降。我们通过合成数据上的线性回归,以及在已建立的置换任务基准上的神经网络实验,验证了这些发现。

英文摘要:

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

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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