可扩展的分析分类器与关联漂移补偿用于视觉变换器的类别增量学习
Scalable Analytic Classifiers with Associative Drift Compensation for Class-Incremental Learning of Vision Transformers
AI总结：
本文提出LR-RGDA和HopDC，通过低秩因子化和关联漂移补偿，实现视觉变换器在大规模类别增量学习中的高效可扩展分类器。
摘要：
类别增量学习（CIL）与视觉变换器（ViTs）面临一个主要的计算瓶颈，即在分类器重建阶段，大多数现有方法依赖于成本高昂的迭代随机梯度下降（SGD）。我们观察到，分析正则化高斯判别分析（RGDA）提供了一个贝叶斯最优的替代方案，其准确性与基于SGD的分类器相当；然而，其二次推断复杂性限制了其在大规模CIL场景中的应用。为克服这一问题，我们提出了低秩因子化RGDA（LR-RGDA），一种可扩展的分类器，它结合了RGDA的表达力和线性分类器的效率。通过利用协方差的低秩结构，通过Woodbury矩阵恒等式，LR-RGDA将判别函数分解为一个通过低秩二次扰动细化的全局仿射项，将推断复杂性从O(Cd²)降低到O(d² + Crd²)，其中C是类别数，d是特征维度，r << d是子空间秩。为缓解由主干更新引起的表示漂移，我们进一步引入了基于Hopfield的分布补偿器（HopDC），一种无训练机制，利用现代连续Hopfield网络通过在未标记锚点上使用关联记忆动态来重新校准历史类别统计，同时伴有对估计误差的理论界。在多样化的CIL基准测试中，我们的框架实现了最先进的性能，提供了一种适用于大规模类别增量学习的可扩展解决方案，使用ViTs。代码：https://github.com/raoxuan98-hash/lr_rgda_hopdc。
英文摘要：
Class-incremental learning (CIL) with Vision Transformers (ViTs) faces a major computational bottleneck during the classifier reconstruction phase, where most existing methods rely on costly iterative stochastic gradient descent (SGD). We observe that analytic Regularized Gaussian Discriminant Analysis (RGDA) provides a Bayes-optimal alternative with accuracy comparable to SGD-based classifiers; however, its quadratic inference complexity limits its use in large-scale CIL scenarios. To overcome this, we propose Low-Rank Factorized RGDA (LR-RGDA), a scalable classifier that combines RGDA's expressivity with the efficiency of linear classifiers. By exploiting the low-rank structure of the covariance via the Woodbury matrix identity, LR-RGDA decomposes the discriminant function into a global affine term refined by a low-rank quadratic perturbation, reducing the inference complexity from $\mathcal{O}(Cd^2)$ to $\mathcal{O}(d^2 + Crd^2)$, where $C$ is the class number, $d$ the feature dimension, and $r \ll d$ the subspace rank. To mitigate representation drift caused by backbone updates, we further introduce Hopfield-based Distribution Compensator (HopDC), a training-free mechanism that uses modern continuous Hopfield Networks to recalibrate historical class statistics through associative memory dynamics on unlabeled anchors, accompanied by a theoretical bound on the estimation error. Extensive experiments on diverse CIL benchmarks demonstrate that our framework achieves state-of-the-art performance, providing a scalable solution for large-scale class-incremental learning with ViTs. Code: https://github.com/raoxuan98-hash/lr_rgda_hopdc.
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