论文精选

低秩权重空间消融下的条件坍缩理论:单块理论与合成验证

A Theory of Conditional Collapse under Low-Rank Weight-Space Ablations: I. The Single-Block Theory and Synthetic Validation

精选理由

论文把激活修补和权重消融的一致性讲透了,用39种配置验证,Spearman -0.83,值得搞可解释性的人看看。

AI 摘要

论文在残差流模型F(x)=F0(x)+Σαi(x)vi中推导出激活修补与权重消融一致的精确条件。对单块注意力头,删除载体子集使匹配输入坍缩到相同输出的充要条件是对称移除且无外部对比。注意力头与其层归一化及MLP组合的交互公式一阶精确,二阶余项在仅消融MLP时恒为零。三十九种消融配置下,测量交互与理想模型预测准确率的Spearman相关系数为-0.83。第二任务与架构复现相同模式,并出现极性反转。

原文 · arXiv cs.LG

A Theory of Conditional Collapse under Low-Rank Weight-Space Ablations: I. The Single-Block Theory and Synthetic Validation

Activation patching and weight-space ablation both claim a component is causally responsible for a behavior, yet they act on different objects: one forward pass versus the parameters behind every forward pass. We ask when they agree. We study an idealized model where a conditional computation is carried additively through a residual stream, $F(x)=F_0(x)+\sum_iα_i(x)v_i$, read out by a linear functional, and prove three exact results. First, deleting a subset of carriers collapses a matched input pair onto the same unconditional output \emph{if and only if} the removal is symmetric on the pair and leaves no outside contrast; the error is deterministic, and we give its exact form even when the two conditions hold only approximately. Second, patching a carrier moves the readout by its donor-receiver \emph{contrast}, while ablating it moves the readout by its \emph{absolute level}; neither bounds the other, and we construct pairs where every single-carrier patch flips the decision while no single-carrier ablation does. Third, for an attention head composed with its own layer's normalization and MLP, we derive an exact first-order interaction formula with a provably second-order remainder, vanishing identically when only the MLP is ablated but not, in general, when a head is. Small transformers trained on a synthetic conditional task illustrate all three predictions: across thirty-nine ablation configurations the measured interaction is strongly rank-correlated with the idealized model's predictive accuracy (Spearman $-0.83$), and a second task and architecture reproduces the same pattern, including a further polarity reversal. The single-block interaction result extends past one residual block, and the synthetic validation is tested against a real pretrained model, in a companion paper that takes this theory further along both axes.