一种 masked 扩散模型缓解反转诅咒的理论分析
A Theoretical Analysis of Why Masked Diffusion Models Mitigate the Reversal Curse
AI总结：
本文探讨了 masked 扩散模型如何通过参数级耦合缓解反转诅咒，证明了其在反向查询中的有效性。
摘要：
自回归语言模型（ARMs）面临反转诅咒：学习「A 是 B」后，往往在反向查询「B 是 A」时表现不佳。Masked 扩散语言模型（MDMs）在这一问题上表现较弱，但其原因尚不明确。常见解释认为，其缓解源于任何顺序的掩码训练目标。然而，训练中观察到「[M] 是 B」会教会在一个位置配置中从 B 恢复 A，但本身并不能解释为何学习到的证据能转移到反向提示「B 是 [M]」。本文提供了一种理论分析，表明这种转移源于前向和反向位置条件之间的参数级耦合：共享的 Transformer 参数存储 token-pair 证据，而相对位置编码通过查询和键路由注意力，而无需改变值侧证据的检索。在单层 MDM 中，我们证明了前向掩码训练增强了可用于反向查询的证据，诱导了相关前向-反向注意力路由，并产生了正向对齐的共享存储梯度组件，从而将反向损失降低到一阶。受控单层实验和大规模 LLaDA/Dream 实验验证了这些特征，并显示它们能转化为改进的反向预测。
英文摘要：
Autoregressive language models (ARMs) suffer from the reversal curse: after learning ''$A$ is $B$,'' they often fail on the reverse query ''$B$ is $A$.'' Masked diffusion language models (MDMs) exhibit this failure in a much weaker form, but the underlying reason has remained unclear. A common explanation attributes this mitigation to their any-order masked training objective. However, observing ''$[\mathbf{M}]$ is $B$'' during training teaches recovery of $A$ from $B$ in one positional configuration, and does not by itself explain why the learned evidence should transfer to the reverse prompt ''$B$ is $[\mathbf{M}]$.'' We provide a theoretical analysis showing that this transfer arises from a parameter-level coupling between forward and reverse positional conditionals: shared Transformer parameters store token-pair evidence, while relative positional encodings route attention through queries and keys without changing the value-side evidence being retrieved. In a one-layer MDM, we prove that forward masked training strengthens evidence that is reusable in reverse queries, induces correlated forward--reverse attention routes, and yields a positively aligned shared-storage gradient component that decreases the reverse loss to first order. Controlled one-layer experiments and large-scale LLaDA/Dream experiments verify these signatures and show that they translate into improved reverse prediction.
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