Mechanistic interpretability methods summarize a transformer component by a single importance score, conflating two distinct roles: a component may matter because it transports task-relevant content, or because the forward computation degrades when its contribution is removed. We introduce \emph{Interchange-Group Sobol Decomposition} (IGSD), a paired-intervention framework that compares matched activation replacement with zero ablation on the same component, estimates two Sobol-style variance indices, and uses their signed difference to separate the two roles, with intervention validity monitored by a symmetric off-manifold diagnostic ST>1. In factual recall, IGSD identifies an early-layer content channel in both GPT-2 small and Qwen2.5-1.5B that standard importance methods underestimate. A controlled subject and relation donor design shows that the early channel transports relation-frame content while late attention transports subject-retrieval content, refining at head granularity to the known AttnL9H8 head. Late-layer clamping confirms that the early signal is expressed through downstream transformations rather than residual pass-through. These results show that replacement and deletion are not interchangeable controls and their divergence provides a practical statistical diagnostic for content transport in transformer components.
Transformers achieve strong performance, but their internal computations remain opaque. We view each Transformer layer as a dynamic graph whose nodes are token representations and per-head attention outputs, with Multi-Head Attention (ATT) and MLP as module boundaries. On this graph we use LIG (Layer-wise Integrated Gradients), which applies set-to-set Integrated Gradients (IG) at nonlinear module boundaries. Set-to-set IG applies IG to a map from a set of input token representations to a set of output representations, evaluating token-to-token contributions, which is not standard in prior IG applications. This extends IG from the usual scalar-objective setting to set-to-set maps via an L2 scalarization, and composes within-layer contributions in the spirit of Layer-wise Relevance Propagation (LRP), with IG completeness playing the role of LRP-style conservation at each boundary. We use LIG to analyze (i) the agreement between module-wise composition and layer-whole attribution under an L2 criterion, and (ii) within-layer information flow by tracing separated ATT and MLP contributions. On BERT-base and PTB, configurations that best preserved within-layer consistency used the target token's embedding as the ATT baseline and either the ATT output at a=0 or Zero as the MLP baseline. We therefore present LIG as a diagnostic XAI tool at module-boundary granularity, without model-specific retraining or per-operation interpreter design. Code is available at https://github.com/eightsuzuki/layer-wise-integrated-gradients.
Mechanistic interpretability of transformers requires identifying not just which components matter but how they compose into the computational route that produced a prediction. Both attention and MLP follow a shared key-value template φ(S)U. We exploit this structure to develop Unpack, a backward recursion that decomposes credit through both sublayers, producing interaction strengths between any two components, named end-to-end paths with K/Q/V composition labels, and per-token attribution from a single forward pass, without intervention, gradients, or auxiliary training. We evaluate on the indirect object identification task. On GPT-2 small, the method recovers all three composition connections described by Wang et al. (2023), including the mode-specific routing of each connection (K, Q, or V). To test token-level attribution beyond trivial copying, we compare two occurrences of the same name in the same decomposition: the first mention retains strong credit while the duplicate-detection position is suppressed, a pattern absent in matched control prompts. Across the Pythia family from 160M to 6.9B parameters, this suppression pattern is consistently recovered at every scale, demonstrating that the method tracks mechanistic structure without ground-truth circuit labels. Code is available at https://github.com/Fun-Cry/unpacklm.
In mechanistic interpretability, attention heads are commonly elevated to role claims (e.g., "this head represents addition") when they are necessary for a behavior, encode it linearly, and recover that behavior when restored after ablation. We show this evidence is insufficient: across three 7-8B instruction-tuned models and five computation families, heads passing all three checks routinely fail to transfer the computation when their activations are patched into a different prompt under matched controls. We introduce KID (Knowing / Intent / Doing), a role-assignment lens for attention heads, and pair it with a three-stage pipeline: capability-selective screening (CSS), singular value decomposition (SVD), and activation transduction under matched controls. Our results document a preliminary role taxonomy (including prompt-trajectory stabilizers, answer-side logit-bias heads, and soft computation-pattern carriers) and show that the same-answer control (a transduction target sharing the answer string but not the requested computation) is an underused check that exposes broad state transfer masquerading as semantic specificity.