Shizhan Liu, Hang Yu, Cong Liao, Jianguo Li, Weiyao Lin, Alex X. Liu, Schahram Dustdar. “Pyraformer: Low-Complexity Pyramidal Attention for Long-Range Time Series Modeling and Forecasting.” ICLR 2022. PDF
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Summary of “Pyraformer: Low-Complexity Pyramidal Attention for Long-Range Time Series Modeling and Forecasting”
This paper proposes Pyraformer, a novel Transformer-based model designed to address the challenges of long-range time series forecasting. The key innovation lies in its pyramidal attention module (PAM), which efficiently captures both short-term and long-term dependencies in time series data.
Here’s a breakdown of the paper’s key aspects:
Problem: Existing time series forecasting methods struggle to balance computational efficiency with the ability to capture long-range dependencies. RNNs and CNNs are efficient but struggle with long sequences, while Transformers, while good at capturing long-range dependencies, suffer from quadratic complexity.
Proposed Solution: Pyraformer
Pyramidal Attention Module (PAM):
Employs a multi-resolution pyramidal graph to represent the time series.
Inter-scale connections: Form a C-ary tree where each level summarizes information at a different resolution (e.g., hourly, daily, weekly).
Intra-scale connections: Capture temporal dependencies within each resolution by connecting neighboring nodes.
This structure allows for efficient modeling of long-range dependencies by capturing them at coarser resolutions.
Coarser-Scale Construction Module (CSCM): Initializes the nodes at coarser scales using convolutions applied to finer-scale representations.
Prediction Module:
Single-step forecasting: Gathers features from all scales and uses a fully connected layer for prediction.
Multi-step forecasting: Offers two options:
Similar to single-step but maps to multiple future time steps.
Utilizes a decoder with two full attention layers for incorporating historical information.
Advantages:
Low Complexity: Achieves linear time and space complexity (O(L)) thanks to the sparse connections in the pyramidal graph.
Long-Range Dependency Capture: Maintains a constant maximum signal traversing path length (O(1)), enabling efficient modeling of long-range dependencies.
Improved Accuracy: Outperforms existing methods in both single-step and long-range multi-step forecasting tasks.
Key Results:
Pyraformer consistently achieves higher prediction accuracy compared to other Transformer variants and traditional methods on various real-world datasets.
It achieves this while maintaining significantly lower time and memory consumption, especially for long sequences.
Overall, Pyraformer presents a promising solution for long-range time series forecasting by effectively balancing model complexity and the ability to capture long-term dependencies.
我们的目标是提取代表潜在的、可概括的处理的短语簇,这些处理会影响特定结果。为此,我们想象 N 个文本(Ti)被随机分配到一个过程中,通过该过程它们被映射到一个结果(Yi)。让 i 也索引评估文本 i 的个体。我们寻求识别和估计这些文本的 m 维潜在表示(Zi)的效果,该表示总结了可能在反复实验中影响结果的短语或概念簇。我们将 Zi 称为文本 i 的“文本处理”。例如,Zi 的每个元素可以表示某个短语或语法结构的存在或不存在,Zi ∈ {0, 1}m。Zi 也可以包含表示连续文本特征的实值元素,如与某个词汇或概念一致的相似性。
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