In long-term time series forecasting (LTSF) tasks, existing deep learning
models overlook the crucial characteristic that discrete time series originate
from underlying continuous dynamic systems, resulting in a lack of
extrapolation and evolution capabilities. Recognizing the chaotic nature of
real-world data, our model, \textbf{\textit{Attraos}}, incorporates chaos
theory into LTSF, perceiving real-world time series as observations from
unknown high-dimensional chaotic dynamic systems. Under the concept of
attractor invariance, Attraos utilizes the proposed multi-scale dynamic memory
unit to memorize historical dynamics structure and predicts by a
frequency-enhanced local evolution strategy. Detailed theoretical analysis and
abundant empirical evidence consistently show that Attraos outperforms various
LTSF methods on mainstream LTSF datasets and chaotic datasets.

在长期时间序列预测任务中，现有的深度学习模型忽视了离散时间序列起源于连续动态系统的关键特性，导致缺乏外推和演化能力。我们的模型 'Attraos' 将混沌理论引入长期时间序列预测中，将真实世界时间序列视为未知高维混沌动态系统的观测。在吸引子不变性的概念下，Attraos 利用提出的多尺度动态记忆单元来记忆历史动态结构，并通过频率增强的局部演化策略进行预测。详细的理论分析和丰富的实证证据一致表明，Attraos 在主流长期时间序列预测数据集和混沌数据集上优于各种长期时间序列预测方法。

长期时间序列预测的吸引子记忆：混沌视角

Attractor Memory for Long-Term Time Series Forecasting: A Chaos  Perspective

Sequential learning of tasks using gradient descent leads to an unremitting
decline in the accuracy of tasks for which training data is no longer
available, termed catastrophic forgetting. Generative models have been explored
as a means to approximate the distribution of old tasks and bypass storage of
real data. Here we propose a cumulative closed-loop memory replay GAN (CloGAN)
provided with external regularization by a small memory unit selected for
maximum sample diversity. We evaluate incremental class learning using a
notoriously hard paradigm, single-headed learning, in which each task is a
disjoint subset of classes in the overall dataset, and performance is evaluated
on all previous classes. First, we show that when constructing a dynamic memory
unit to preserve sample heterogeneity, model performance asymptotically
approaches training on the full dataset. We then show that using a stochastic
generator to continuously output fresh new images during training increases
performance significantly further meanwhile generating quality images. We
compare our approach to several baselines including fine-tuning by gradient
descent (FGD), Elastic Weight Consolidation (EWC), Deep Generative Replay (DGR)
and Memory Replay GAN (MeRGAN). Our method has very low long-term memory cost,
the memory unit, as well as negligible intermediate memory storage.

本文提出了一种基于累计的闭环记忆重放生成对抗网络的方案，并引入了外部正则化进行最大样本多样性的小型内存单元。实验结果表明，在使用动态内存单元的条件下，该方案在处理硬任务学习方面具有很高的性能增长。