不同训练的Transformer模型功能相同，但内部表示因随机旋转而互不相通。
Polymorphism Is Rotation: Operational Mechanistic Interpretability from a Two-Layer Transformer to Pythia-70m
- 通过单次正交配准旋转，可让不同模型的稀疏自编码器特征对齐
- 同一模型内不同种子间解码层相似度达98%，但跨种子重建效果为负值
- 该现象在传统评估指标下被掩盖，适合研究模型可解释性与泛化
独立训练的Transformer在残差流基底上计算相同函数，但基底间存在统一随机旋转（SO(d_model)）。我们称此为多态性：功能一致，内部坐标互不相通。每对模型仅需一次矩阵乘法——在单批激活值上进行正交普罗克拉斯拟合，即可无须重训地转移稀疏自编码器特征字典与转向向量。该现象无法被标准SAE通用性指标察觉：尽管解码列跨种子余弦相似度达98%（即所谓通用性），但用一个种子训练的SAE在另一种子上重建时解释方差为负，甚至劣于预测均值。解码列对齐，编码器则读取旋转后的坐标系。一个正交旋转矩阵R可使所有内部节点重建误差恢复至同种子上限的0.025 EV以内。R服从哈尔分布：当d_model=512时，||R−I||_F与随机正交预测√(2d_model)一致，偏差仅0.1%；对特征值谱的柯尔莫哥洛夫-斯米诺夫检验，总体与成对结果均得p≈1.000。差分均值转向向量依R的不变子空间分为三类：共享输出权重时完全对齐，重叠旋转子空间时部分对齐，否则反向。在无共享输入输出（Pythia）情况下，三类均坍缩为普遍反向。该旋转解释在单次训练过程中的多个检查点也成立。已在104k参数的Dyck-3 Transformer及九个独立训练的Pythia-70m种子（The Pile）上验证，采用预注册四步操作框架。10B+规模复制仍待开展。
原文摘要 · Abstract (English)
Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually unintelligible interior coordinates. One matrix multiplication per model pair removes it: an orthogonal Procrustes fit on a single batch of activations transfers sparse-autoencoder feature dictionaries and steering vectors between independently trained models, with no retraining. The phenomenon is invisible to the standard SAE universality metric. Decoder-column cosine similarity matches across seeds at 98%, the SAE-universality headline number, while an SAE trained on one seed reconstructs another seed's activations at negative explained variance, worse than predicting the constant mean. The decoder columns align; the encoder reads from a rotated frame. A single Procrustes rotation $R$ restores reconstruction to within 0.025 EV of the within-seed ceiling at every internal site. $R$ is Haar-distributed: $\|R - I\|_F$ matches the random-orthogonal prediction $\sqrt{2 d_{\mathrm{model}}}$ to 0.1% at $d_{\mathrm{model}} = 512$, and a Kolmogorov-Smirnov test of $R$'s eigenvalue spectrum against Haar $\mathrm{SO}(d_{\mathrm{model}})$ returns $p \approx 1.000$ pooled and per-pair. Diff-of-means steering vectors transfer in three regimes by alignment with $R$'s invariant subspace: clean when pinned by shared output weights, partial when overlapping the rotated subspace, inverted otherwise. With no shared I/O (Pythia), all three collapse to universally inverted. The same rotation account holds across training checkpoints within a single run. Validated on a 104k-parameter Dyck-3 transformer and nine independently-trained Pythia-70m seeds on The Pile, via a pre-registered four-bar operational framework. Frontier-scale (10B+) replication remains open.
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