LIG: Layer-wise Integrated Gradients for Within-Layer Flow Analysis in Transformers

We ask a simple question about decoder-only transformers: between which two layers is the probability of a predicted token actually produced? Existing layer-wise readout tools answer only approximately. The logit lens and its trained variant report a per-layer level of probability but give no additive decomposition; their estimates are biased and non-monotone across depth. Direct Logit Attribution and related residual-stream methods are additive, but only in logit space, the softmax nonlinearity breaks additivity in probability space, precisely the quantity one usually cares about. Layer Conductance integrates gradients per layer, but attributes each to its own baseline and so does not sum to the total change in prediction. We introduce IG-Lens, a telescoping application of Integrated Gradients along a single path through the hidden states from a baseline to the final layer. Crediting each segment to the layer it terminates at yields a layer-wise attribution whose sum is exactly the change in target probability, with the softmax inside the integration path rather than linearized away. Our default estimator credits each integration step its observed change in target probability (a prediction-aware reweighting in the spirit of IDGI) rather than its raw gradient. Because the readout is a one-dimensional probability, this collapses each segment to a telescoping sum of endpoint values, so completeness holds exactly (to floating point) at any step count, removing Riemann discretization error while suppressing steps that show gradient sensitivity without a change in output. We give the telescoping identity and its proof, verify completeness to floating point, and describe a single-pass batched implementation computing the full token-by-layer map without any backward call. Code: https://github.com/anhnda/IGLens.

Understanding the internal mechanisms of transformer-based large language models (LLMs) is crucial for their reliable deployment and effective operation. While recent efforts have yielded a plethora of attribution methods attempting to balance faithfulness and computational efficiency, dense component attribution remains prohibitively expensive. In this work, we introduce Dual Path Attribution (DPA), a novel framework that faithfully traces information flow on the frozen transformer in one forward and one backward pass without requiring counterfactual examples. DPA analytically decomposes and linearizes the computational structure of the SwiGLU Transformers into distinct pathways along which it propagates a targeted unembedding vector to receive the effective representation at each residual position. This target-centric propagation achieves O(1) time complexity with respect to the number of model components, scaling to long input sequences and dense component attribution. Extensive experiments on standard interpretability benchmarks demonstrate that DPA achieves state-of-the-art faithfulness and unprecedented efficiency compared to existing baselines.

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.