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arXiv 2502.03383cs.LGcs.AI
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Transformer 及其作为时间序列基础模型的作用

Transformers and Their Roles as Time Series Foundation Models

Northwestern University(西北大学);Princeton University(普林斯顿大学);The University of Hong Kong(香港大学)

Dennis Wu, Yihan He, Yuan Cao, Jianqing Fan, Han Liu

AI总结:

本文从理论上分析了 Transformer 作为时间序列基础模型的逼近与泛化能力,证明其可通过梯度下降拟合自回归模型,并揭示了 MOIRAI 自动拟合任意数量协变量自回归模型的机制,同时给出 Dobrushin 条件下的预训练泛化界,实验验证了理论结论。

摘要:

我们对 Transformer 作为时间序列基础模型进行了全面分析,重点关注其逼近能力和泛化能力。首先,我们证明存在能够通过梯度下降在输入单变量时间序列上拟合自回归模型的 Transformer。随后,我们分析了 MOIRAI,这是一个能够处理任意数量协变量的多变量时间序列基础模型。我们证明它能够自动拟合具有任意数量协变量的自回归模型,从而为其设计和经验上的成功提供了见解。在泛化方面,当数据满足 Dobrushin 条件时,我们建立了预训练的界。实验支持了我们的理论发现,凸显了 Transformer 作为时间序列基础模型的有效性。

英文摘要:

We give a comprehensive analysis of transformers as time series foundation models, focusing on their approximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, a multivariate time series foundation model capable of handling an arbitrary number of covariates. We prove that it is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and empirical success. For generalization, we establish bounds for pretraining when the data satisfies Dobrushin's condition. Experiments support our theoretical findings, highlighting the efficacy of transformers as time series foundation models.

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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