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文章背景与核心概要

本文是两篇系列论文中的第二篇（姊妹篇为《低秩权重空间消融下条件坍缩的理论》）。文章将关于激活修补（activation patching）和权重空间消融（weight-space ablation）先前的理论发现，从单一残差块和合成任务扩展到了多层及真实预训练模型。

文章的核心技术贡献包括：1）多层分解：将跨多个层的消融载体交互分解为同块项和跨层余数项；2）注意力雅可比边界：将余数精确隔离为混合二阶导数的二重积分，并推导出了注意力子块的闭式雅可比边界，该边界在 Qwen2.5-1.5B-Instruct 的真实权重上得到了成功验证；3）经验电路发现：在 Qwen2.5-1.5B-Instruct 中识别出涌现的间接宾语识别（IOI）电路，并对真实世界实例中的坍缩、解离和跨层交互进行了评估。

权重空间消融下的跨层交互：闭式注意力雅可比边界与真实预训练模型测试

作者： Abdallah Khemais
ArXiv ID： arXiv:2608.03629 [cs.AI]（两篇系列论文的第二部分）
提交时间： 2026年8月4日 | 最后修订： 2026年8月7日

📌 执行摘要

本文作为两篇系列论文的第二部分（姊妹篇：《低秩权重空间消融下条件坍缩的理论》），将先前关于激活修补（activation patching）和权重空间消融（weight-space ablation）的理论发现，从单一残差块和合成任务推广到了更广阔的场景。

核心贡献包括： 1. 多层分解：将跨越单一块的层交互模型扩展为同块项（same-block terms）和跨层余数项（cross-layer remainders）。 2. 注意力雅可比边界：将余数项隔离为混合二阶导数的二重积分，并推导出了注意力子块的闭式雅可比边界（closed-form Jacobian bound），该边界在 Qwen2.5-1.5B-Instruct 的真实权重上通过了严格验证。 3. 经验电路发现：在 Qwen2.5-1.5B-Instruct 内部识别出了一个涌现的间接宾语识别（IOI）电路，并评估了真实世界实例中的坍缩、解离以及跨层交互。

This paper serves as the second part of a two-part series (companion paper: "A Theory of Conditional Collapse under Low-Rank Weight-Space Ablations"). It extends prior theoretical findings regarding activation patching and weight-space ablation beyond single residual blocks and synthetic tasks.

Key contributions include: 1. Multi-Layer Decomposition: Extending layer interaction models past single blocks into same-block terms and cross-layer remainders. 2. Attention Jacobian Bound: Isolating the remainder as a double integral of a mixed second derivative and deriving a closed-form Jacobian bound for attention sub-blocks, verified successfully against the real weights of Qwen2.5-1.5B-Instruct. 3. Empirical Circuit Discovery: Identifying an emergent indirect object identification (IOI) circuit within Qwen2.5-1.5B-Instruct and evaluating collapse, dissociation, and cross-layer interactions across real-world instances.

📖 摘要与背景

姊妹篇论文在一个理想化模型中研究了激活修补与权重空间消融之间的理论对齐，在该模型中，条件计算通过残差流以相加的方式传播。对于涉及相关载体（即一个注意力头与其所在层的归一化-MLP组合）的单一架构组合，它建立了一个精确的一阶交互公式。当仅消融 MLP 时，该交互会消失；而当注意力头也被消融时，它仍然保持二阶有界。然而，该框架局限于在处理合成任务的小型 Transformer 上进行测试的单个残差块。

本文通过三大主要进展克服了这些局限性：

  • 跨层推广：跨越多个层的被消融载体所产生的交互，可以清晰地分解为同块项（涉及每个触及的层）以及一个需要仔细处理的跨层余数项。
  • 闭式雅可比边界：对于一个两层系统，余数项被精确地隔离为混合二阶导数的二重积分。研究所缺失的关键要素——注意力子块的雅可比边界——已通过闭式推导得出。这一边界在 Qwen2.5-1.5B-Instruct 的真实预训练权重上得到了验证，且没有出现一次违反情况。此外，本文还提供了姊妹篇中未曾展示的显式曲率常数。
  • 真实模型经验测试：使用相同的预训练模型（Qwen2.5-1.5B-Instruct），作者搜索并成功映射了一个用于间接宾语识别（未显式设计到架构中）的涌现电路。对坍缩、解离和交互指标的测试显示了混合结果：在五个测试实例中一致涌现出了一个共享载体，坍缩/解离性质在大多数情况下成立，并且在原始单块定理范围之外的层对上出现了可测量的非零交互。

A companion paper studies the theoretical alignment between activation patching and weight-space ablation within an idealized model where conditional computation propagates additively through a residual stream. For the single architectural composition involving dependent carriers—an attention head coupled with its layer's normalization-MLP composition—it established an exact first-order interaction formula. This interaction vanishes when only the MLP is ablated and remains second-order bounded when the head is also ablated. However, that framework was limited to a single residual block tested exclusively on small transformers tackling synthetic tasks.

This paper bridges those limitations through three primary advances:

  • Cross-Layer Generalization: The interaction resulting from ablated carriers spanning multiple layers decomposes cleanly into same-block terms (one for each touched layer) alongside a cross-layer remainder term that requires careful handling.
  • Closed-Form Jacobian Bound: For a two-layer system, the remainder is isolated precisely as a double integral of a mixed second derivative. The missing ingredient—a Jacobian bound for the attention sub-block—is derived in closed form. This bound is validated without a single violation against the real pretrained weights of Qwen2.5-1.5B-Instruct. Additionally, the paper provides the explicit curvature constant left unexhibited in the companion work.
  • Real-Model Empirical Testing: Using the same pretrained model (Qwen2.5-1.5B-Instruct), the author searches for and successfully maps an emergent circuit for indirect object identification (not explicitly engineered into the architecture). Testing collapse, dissociation, and interaction metrics reveals mixed results: a shared carrier consistently emerges across five tested instances, collapse/dissociation hold in the majority of cases, and measurable non-zero interactions appear at layer pairs outside the scope of the original single-block theorem.

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