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On the Regularization of Learnable Embeddings for Time Series Forecasting

Published 18 Oct 2024 in cs.LG and cs.AI | (2410.14630v2)

Abstract: In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers, specific to each time series, often implemented as learnable embeddings. Ideally, these local embeddings should encode meaningful representations of the unique dynamics of each sequence. However, when these are learned end-to-end as parameters of a forecasting model, they may end up acting as mere sequence identifiers. Shared processing blocks may then become reliant on such identifiers, limiting their transferability to new contexts. In this paper, we address this issue by investigating methods to regularize the learning of local learnable embeddings for time series processing. Specifically, we perform the first extensive empirical study on the subject and show how such regularizations consistently improve performance in widely adopted architectures. Furthermore, we show that methods attempting to prevent the co-adaptation of local and global parameters by means of embeddings perturbation are particularly effective in this context. In this regard, we include in the comparison several perturbation-based regularization methods, going as far as periodically resetting the embeddings during training. The obtained results provide an important contribution to understanding the interplay between learnable local parameters and shared processing layers: a key challenge in modern time series processing models and a step toward developing effective foundation models for time series.

Summary

  • The paper investigates and proposes regularization techniques to prevent learnable embeddings in time series models from devolving into static identifiers, thereby improving model generalization and transferability.
  • Empirical results show regularization methods like dropout, variational regularization, and periodic resetting ("forgetting") significantly enhance performance across various deep learning architectures and improve transfer learning with limited data.
  • The findings suggest that directly regularizing embedding learning is crucial for developing robust, scalable, and transferable global-local time series models applicable to diverse datasets and real-world problems.

Regularization of Learnable Embeddings in Time Series Processing

The paper, "On the Regularization of Learnable Embeddings for Time Series Processing," explores the critical challenge associated with processing multiple time series using deep learning models. Specifically, it addresses the role of learnable local embeddings in conjunction with global model components for forecasting tasks. The study investigates the limitation that arises when embeddings, learned as end-to-end components of forecasting models, devolve into static sequence identifiers, potentially hindering the transferability and scalability of such models across various applications.

Summary of Findings

The authors conduct a comprehensive empirical investigation to evaluate different regularization techniques aimed at mitigating the co-adaptation of local embeddings and global model parameters. They highlight this co-adaptation as a primary issue that restricts the generalization capability of global models when applied to unseen contexts. The study distinguishes between several regularization methods, including L1 and L2 penalties, dropout, clustering, variational regularization, and a novel "forgetting" strategy wherein embeddings are periodically reset during training.

Numerical Results and Observations

The study's experimental results demonstrate that regularizing local embeddings significantly enhances performance across a spectrum of deep learning architectures, including RNNs, STGNNs, and attention-based models. It emphasizes dropout, variational regularization, and forgetting as particularly effective techniques. These methods, by actively perturbing the embeddings during training, prevent the model from over-relying on sequence identifiers, thus fostering better generalization and robustness. The results also show that embedding regularization not only benefits transductive learning environments but also significantly enhances model performance in transfer learning contexts with limited data.

Implications

The findings underscore the importance of learnable embeddings in modern global-local hybrid architectures, where models must balance between modeling shared patterns and capturing the idiosyncrasies of each time series. The regularization strategies evaluated offer promising pathways to improve the transferability of deep learning models across different time series domains, an essential characteristic for developing foundational models capable of addressing diverse real-world datasets.

From a theoretical perspective, the study proposes a crucial design principle: adopting regularizations that directly influence the learning of embeddings could be a viable means to counteract limitations inherent in global-local models. This principle is shown to not only curtail overfitting but also enhance performance when local dynamics need to be captured, as demonstrated by substantial improvements in predictive accuracy across multiple benchmark datasets.

Future research could build upon this foundation to explore adaptive regularization techniques tailored to the intrinsic characteristics of varied time series datasets. Moreover, the integration of these findings into real-world time series applications offers practitioners improved tools for model optimization and deployment.

In summary, this paper makes a substantive contribution by elucidating methods to refine the learning of local embeddings in time series processing, focusing on their role in global-local model architectures. Through its comprehensive approach, it paves the way for developing more robust, scalable, and transferable time series models, instrumental in both advancing foundational models and optimizing domain-specific time series applications.

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