近年来，Transformer模型在自然语言处理领域掀起了一场革命，其强大的能力让世人惊叹。但随着模型规模不断扩大，训练和部署这些庞然大物也变得越来越困难，尤其对于个人用户和小型机构来说。
为了解决这一难题，研究者们提出了各种解决方案，其中低秩分解成为了一个重要的方向。LoRA[7] 就是一个典型的例子，它通过在预训练模型的每一层学习一个低秩增量来实现高效的微调。
本文则更进一步，提出了一个全新的模型设计范式——垂直LoRA (VLoRA)[7]。它基于一个全新的视角：将Transformer模型看作是密集型期望最大化（EM）算法[7]。
Transformer：隐藏的EM算法
在监督学习中，Transformer模型的目标是最大化后验概率 $P(y|x;\theta)$，其中 $x$ 是输入，$y$ 是标签，$\theta$ 是模型参数。本文指出，Transformer模型的每一层实际上都是EM算法的一次迭代，前向传播对应于E步，而下一层与当前层权重差异则对应于M步。
这个发现揭示了Transformer模型中一个重要的规律：每一层都是基于前一层学习一个增量。而正是基于这一规律，VLoRA应运而生。
VLoRA：垂直分解，层层递进
VLoRA 首先定义一个全秩基层，然后每一层都基于上一层学习一个低秩增量，并使用LoRA分解来逼近这个增量。这种垂直分解的方式，使得模型参数数量大幅减少，同时保留了原始模型的性能。
与传统的水平LoRA相比，VLoRA 更加高效，因为它减少了模型的总体参数，而不是仅仅针对微调阶段。
实验验证：性能提升，更少参数
本文在图像分类任务上进行了实验，使用 CIFAR-10 数据集[31] 对 12 层的 Vision Transformer[32] 进行了训练，并比较了其 VLoRA 版本的性能。
实验结果表明：
- VLoRA 版本的训练损失和准确率虽然略低于原始模型，但在评估阶段却展现出更强的泛化能力，不容易过拟合。
- VLoRA 版本的最佳评估指标与原始模型几乎相同，但参数数量却大幅减少。
- 即使使用较小的低秩（例如 r=2），VLoRA 依然能有效地对每一层的权重增量进行建模。
未来展望：更轻盈，更强大
VLoRA 的出现，为构建更轻盈、更强大的 Transformer 模型提供了新的思路。它不仅可以用于降低模型的训练和部署成本，还可以提升模型的泛化能力，使其在更多场景下发挥作用。
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