A Survey of Continual Learning with Deep Networks: Theory, Method and Application
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摘要: 自然界中的生物需要在其一生中不断地学习并适应环境，这种持续学习的能力是生物学习系统的基础。尽管深度学习方法在计算机视觉和自然语言处理领域取得了重要进展，但它们在连续学习任务时面临严重的灾难性遗忘问题，即模型在学习新知识时会遗忘旧知识，这在很大程度上限制了深度学习方法的应用。持续学习研究对人工智能系统的改进和应用具有重要意义。该文对深度模型的持续学习进行了全面回顾。首先介绍了持续学习的定义和典型设定，阐述了问题的关键。其次，将现有持续学习方法划分为基于正则化、基于回放、基于梯度和基于网络结构4类，分析了各类方法的优点和局限性。同时，该文强调并总结了持续学习领域的理论分析进展，建立了理论与方法之间的联系。此外，提供了常用的数据集和评价指标，以公正评判不同方法。最后，从多个领域的应用价值出发，讨论了深度持续方法面临的问题、挑战和未来研究方向。Abstract: Biological organisms in nature are required to continuously learn from and adapt to the environment throughout their lifetime. This ongoing learning capacity serves as the fundamental basis for the biological learning systems. Despite the significant advancements in deep learning methods for computer vision and natural language processing, these models often encounter a serious issue, known as catastrophic forgetting, when learning tasks sequentially. This refers to the model’s tendency to discard previously acquired knowledge when acquiring new information, which greatly hampers the practical application of deep learning models. Thus, the exploration of continual learning is paramount for enhancing and implementing artificial intelligence systems. This paper provides a comprehensive survey of continual learning with deep models. Firstly, the definition and typical settings of continual learning are introduced, followed by the key aspects of the problem. Secondly, existing methods are categorized into four main groups: regularization-based, replay-based, gradient-based and structure-based approaches, with an outline of the strengths and weaknesses of each group. Meanwhile, the paper highlights and summarizes the theoretical progress in continual learning, establishing a crucial nexus between theory and methodology. Additionally, commonly used datasets and evaluation metrics are provided to facilitate fair comparisons among these methods. Finally, the paper addresses current issues, challenges and outlines future research directions in deep continual learning, taking into account its potential applications across diverse fields.
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Key words:
- Deep learning /
- Continual learning /
- Catastrophic forgetting
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表 1 持续学习的不同任务设定
任务设定 数据分布 任务标识 域增量学习 $ p\left({\mathcal{X}}_{i}\right)\ne p\left({\mathcal{X}}_{j}\right),{\mathcal{Y}}_{i}={\mathcal{Y}}_{j}, \forall i\ne j $ × 任务增量学习 $ p\left({\mathcal{X}}_{i}\right)\ne p\left({\mathcal{X}}_{j}\right),{\mathcal{Y}}_{i}\bigcap {\mathcal{Y}}_{j}=\varnothing , \forall i\ne j $ √ 类别增量学习 $ p\left({\mathcal{X}}_{i}\right)\ne p\left({\mathcal{X}}_{j}\right),{\mathcal{Y}}_{i}\bigcap {\mathcal{Y}}_{j}=\varnothing , \forall i\ne j $ × 
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表 2 持续学习与相关研究领域的区别
研究领域 训练数据 测试数据 额外限制 监督学习 $ {\mathcal{D}}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}} $ $ {\mathcal{D}}_{\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}} $ $ p\left({\mathcal{D}}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}n}\right)=p\left({\mathcal{D}}_{\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}\right) $ 多任务学习 $ {\mathcal{D}}_{1},{\mathcal{D}}_{2},\cdots,{\mathcal{D}}_{t} $ $ {\mathcal{D}}_{1},{\mathcal{D}}_{2},\cdots,{\mathcal{D}}_{t} $ $ p\left({\mathcal{D}}_{i}\right)\ne p\left({\mathcal{D}}_{j}\right), $ $ i\ne j $ 元学习 $ {\mathcal{D}}_{1},{\mathcal{D}}_{2},\cdots,{\mathcal{D}}_{t-1} $ $ {\mathcal{D}}_{t} $ $ p\left({\mathcal{D}}_{i}\right)\ne p\left({\mathcal{D}}_{t}\right), $ $ i < t $ 迁移学习 $ {\mathcal{D}}_{\mathrm{s}\mathrm{r}\mathrm{c}},{\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $ $ {\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $ $ p\left({\mathcal{D}}_{\mathrm{s}\mathrm{r}\mathrm{c}}\right)\ne p\left({\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}}\right) $ 域适应 $ {\mathcal{D}}_{\mathrm{s}\mathrm{r}\mathrm{c}},{\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $ $ {\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $ $ {\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $无标注信息 域泛化 $ {\mathcal{D}}_{\mathrm{s}\mathrm{r}\mathrm{c}} $ $ {\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $ $ {\mathcal{D}}_{\mathrm{t}\mathrm{g}\mathrm{t}} $无法访问 持续学习 $ {\mathcal{D}}_{1},{\mathcal{D}}_{2},\cdots,{\mathcal{D}}_{t} $ $ {\mathcal{D}}_{1},{\mathcal{D}}_{2},\cdots,{\mathcal{D}}_{t} $ $ {\mathcal{D}}_{1},{\mathcal{D}}_{2},\cdots,{\mathcal{D}}_{t-1} $无法访问
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表 3 持续学习方法分类及特点
类别 方法 方法特点 优缺点 基于正则化 参数正则化
数据正则化
任务偏向修正通过参数重要性估计对参数进行保护
保持新旧模型对给定数据的输出一致性
针对网络任务偏向问题提出不同的解决方案无需回放样本，但难以有效估计参数重要性，性能较差
简单有效，但通常需要回放样本或特征以提高性能
需要额外的修正训练，或额外的计算资源基于回放 原始数据回放
原始特征回放
生成式回放回放部分任务的原始样本
回放样本特征或类别原型
使用生成模型进行数据回放简单有效，但回放样本占据空间较大
节省存储空间，面临特征偏移问题
生成数据的质量难以保证基于梯度 梯度情景记忆
子空间投影
平坦极小点基于历史数据的梯度构建约束
将参数梯度投影到子空间
获取平坦极小点需要回放样本，并计算额外梯度
能有效减缓遗忘，需要存储特征空间
使用额外的技术手段，增加训练成本基于网络结构 静态结构
动态结构
参数高效微调将网络参数分配给任务
动态地扩张网络结构
对预训练模型进行增量式微调模型容量有限，难以解决长序列任务的学习问题
能有效减缓遗忘，但扩张网络带来额外存储和推理负担
能有效减缓遗忘，但获取预训练模型需要成本
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表 4 持续学习理论工作总结
理论工作 主要结果 特点 对应方法 概率模型 $ {\theta }_{t}\approx {\mathrm{argmax}}_{\theta }\mathrm{log}p\left({\mathcal{D}}_{t}|{\boldsymbol{\theta}} \right)-{\left({\boldsymbol{\theta}} -{{\boldsymbol{\theta}} }_{t-1}\right)}^{\mathrm{T}}{\boldsymbol{F}}_{1:t-1}({\boldsymbol{\theta}} -{{\boldsymbol{\theta}} }_{t-1})/2 $ 通过对先前任务进行近似和估计，
得到网络训练的正则损失参数正则化 PAC学习 $ {\varepsilon }_{{\mathcal{D}}_{t}}\left(h\right)\le \dfrac{1}{t-1}{\displaystyle\sum }_{i=1}^{t-1}{\widehat{\varepsilon }}_{{D}_{i}}\left(h\right)+\dfrac{1}{2\left(t-1\right)}{\displaystyle\sum }_{i=1}^{t-1}{d}_{\mathcal{H}\Delta \mathcal{H}}\left({\mathcal{D}}_{i},{\mathcal{D}}_{t}\right)+{\lambda }_{t-1} $ 在PAC学习理论框架下，对网络的
泛化误差进行界定数据正则化
基于回放的方法神经正切核 $ {{\varDelta }}_{t-1}={\left\|\mathcal{{\boldsymbol{K}}}\left({{\boldsymbol{X}}}_{t-1},{{\boldsymbol{X}}}_{t}\right){\left(\mathcal{{\boldsymbol{K}}}\left({{\boldsymbol{X}}}_{t},{{\boldsymbol{X}}}_{t}\right)+\lambda {\boldsymbol{I}}\right)}^{-1}{\tilde{{\boldsymbol{y}}}}_{t}\right\|}_{2}^{2} $ 在神经正切核范式下，
分析神经网络的遗忘问题基于梯度的方法 任务分解 $ p\left({\boldsymbol{x}}\in {{\boldsymbol{X}}}_{t,j}|{\boldsymbol{\theta}} \right)=p\left({\boldsymbol{x}}\in {{\boldsymbol{X}}}_{t,j}|{{\boldsymbol{\theta}} }^{\left(t\right)}\right)p\left({\boldsymbol{x}}\in {{\boldsymbol{X}}}_{t}|{\boldsymbol{\theta}} \right) $ 将类别增量学习问题分解为任务
内预测和任务标识预测两个子问题基于网络结构
的方法
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表 5 持续学习常用数据集
数据集 年份 类别数 数据量 MNIST[212] 1998 10 60,000 CIFAR-10[213] 2009 10 60,000 CIFAR-100[213] 2009 100 60,000 CUB-200[214] 2011 200 11,788 Tiny-ImageNet[215] 2015 200 120,000 Sub-ImageNet[216] 2009 $ 100 $ 60,000 Full-ImageNet[216] 2009 1,000 1,280,000 5-datasets[217] 2020 50 260,000 CORe50[218] 2017 50 15,000 DomainNet[219] 2019 345 590,000 CCDB[220] 2023 2 --
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