分离数据流可改善Transformer中间层的几何条件，提升线性干预可靠性。
Stream separation improves Bregman conditioning in transformers
- 通过分离数据流结构，缓解中间层表示空间的退化问题。
- 中间层有效秩从8提升至30（最高22点改善），显著增强几何条件。
- 该发现对安全可控的线性干预方法有重要指导意义。
用于调节Transformer表示的线性方法（如探测、激活工程、概念擦除）隐含假设表示空间为欧几里得几何。Park等人[2026]指出，Softmax引入了曲率的Bregman几何，其度量张量为对数归一化器的海森矩阵 $H(λ) = Cov[γ | λ]$。忽略此曲率会导致欧几里得调节产生概率质量泄漏。该分析原适用于输出层。本文在受控的2×2实验设计中，测量了中间层的海森矩阵，交叉对比数据流分离与逐层监督（每层使用词汇解码损失），所有设置保持相同词汇量和参数量。在标准单流Transformer中，中间层的 $H$ 严重退化（516维中有效秩仅8）。数据流分离可使有效秩提升最多22，即使无辅助监督亦然；逐层监督有帮助，但效果较弱。原始与对偶概念方向的余弦相似度可预测逐层调节在下游任务中的有效性，阈值约0.3。这些结果影响线性安全干预的可靠性，因其依赖于干预层几何的良条件性。
原文摘要 · Abstract (English)
Linear methods for steering transformer representations, including probing, activation engineering, and concept erasure, implicitly assume the geometry of representation space is Euclidean. Park et al. [Park et al., 2026] showed that softmax induces a curved Bregman geometry whose metric tensor is the Hessian of the log-normalizer, $H(λ) = Cov[γ | λ]$. Ignoring this curvature causes Euclidean steering to leak probability mass to unintended tokens. Their analysis applies at the output layer. We measure this Hessian at intermediate layers in a controlled 2x2 design crossing stream separation with per-layer supervision (vocabulary decoding loss at each layer), all at matched vocabulary and parameter count. In standard single-stream transformers, H is severely degenerate at intermediate layers (effective rank 8 in 516 dimensions). Stream separation improves conditioning by up to 22 in effective rank, even without auxiliary supervision. Per-layer supervision helps, but less. The cosine similarity between primal and dual concept directions predicts per-layer steering effectiveness on downstream tasks, with a threshold near 0.3. These results bear on the reliability of linear safety interventions, which depend on the geometry being well-conditioned at the layer where they are applied.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。