Class-incremental learning (CIL) under an exemplar-free constraint has presented a significant challenge. Existing methods adhering to this constraint are prone to catastrophic forgetting, far more so than replay-based techniques that retain access to past samples. In this paper, to solve the exemplar-free CIL problem, we propose a Dual-Stream Analytic Learning (DS-AL) approach. The DS-AL contains a main stream offering an analytical (i.e., closed-form) linear solution, and a compensation stream improving the inherent under-fitting limitation due to adopting linear mapping. The main stream redefines the CIL problem into a Concatenated Recursive Least Squares (C-RLS) task, allowing an equivalence between the CIL and its joint-learning counterpart. The compensation stream is governed by a Dual-Activation Compensation (DAC) module. This module re-activates the embedding with a different activation function from the main stream one, and seeks fitting compensation by projecting the embedding to the null space of the main stream's linear mapping. Empirical results demonstrate that the DS-AL, despite being an exemplar-free technique, delivers performance comparable with or better than that of replay-based methods across various datasets, including CIFAR-100, ImageNet-100 and ImageNet-Full. Additionally, the C-RLS' equivalent property allows the DS-AL to execute CIL in a phase-invariant manner. This is evidenced by a never-before-seen 500-phase CIL ImageNet task, which performs on a level identical to a 5-phase one. Our codes are available at https://github.com/ZHUANGHP/Analytic-continual-learning.

中文翻译：

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DS-AL：用于无示例类增量学习的双流分析学习

无范例约束下的类增量学习（CIL）提出了重大挑战。遵守此约束的现有方法很容易发生灾难性遗忘，远比保留对过去样本的访问的基于重放的技术要严重得多。在本文中，为了解决无样本 CIL 问题，我们提出了一种双流分析学习（DS-AL）方法。 DS-AL 包含提供解析（即封闭形式）线性解的主流，以及改善由于采用线性映射而固有的欠拟合限制的补偿流。主流将 CIL 问题重新定义为级联递归最小二乘 (C-RLS) 任务，从而允许 CIL 与其联合学习对应物之间的等价性。补偿流由双激活补偿 (DAC) 模块控制。该模块使用与主流不同的激活函数重新激活嵌入，并通过将嵌入投影到主流线性映射的零空间来寻求拟合补偿。实证结果表明，DS-AL 尽管是一种无样本技术，但在各种数据集（包括 CIFAR-100、ImageNet-100 和 ImageNet-Full）上提供的性能与基于重放的方法相当或更好。此外，C-RLS 的等效属性允许 DS-AL 以相位不变的方式执行 CIL。前所未见的 500 阶段 CIL ImageNet 任务证明了这一点，该任务的执行水平与 5 阶段任务相同。我们的代码可在 https://github.com/ZHUANGHP/Analytic-continual-learning 获取。