Every Component Is a Lookup: One Linear Graph for Interaction, Composition and Attribution

Interpretability methods for transformers are typically built around separate questions: which components interact, how information routes to the output, and which input tokens contribute. Because these methods rely on different assumptions, their answers are difficult to relate. We argue that two architecturally motivated assumptions suffice to address all three questions: attention and MLPs share a key-value form, φ(S),U, in which φ(S) selects over values U, and components read from an additive residual stream, the sum of component outputs. Holding these selections at their forward-pass values turns the model into a computational graph, of which component interactions, composition paths, and token attribution are different readouts. We develop Unpack, a backward attribution procedure over this graph, and validate each readout against the corresponding established test: interaction scores predict ablation effects across models from 160M to 6.9B parameters, recovered routes reproduce established circuits down to the key, query, or value branch the circuit specifies, and token attribution passes the same faithfulness test as dedicated attribution methods. The results suggest that these two assumptions suffice for the interpretability questions above. On a task with a known circuit, we find that contribution and causal effect can differ, and that the difference has a recognisable signature: components that matter for the task change their contribution when the task is removed from the input, while components that act like a bias term do not. Code is available at https://github.com/Fun-Cry/unpacklm.