Dual Path Attribution: Efficient Attribution for SwiGLU-Transformers through Layer-Wise Target Propagation

1. Problem Statement

Understanding the internal mechanisms of Large Language Models (LLMs) is critical for reliable deployment. A central challenge in mechanistic interpretability is attribution: identifying which input tokens or internal model components (e.g., attention heads, neurons) are causally responsible for a specific prediction.

Existing methods face a trade-off between faithfulness (accuracy in identifying causal mechanisms) and computational efficiency:

• Gradient-based methods (e.g., Integrated Gradients) are efficient but suffer from gradient saturation and noise.
• Decomposition-based methods (e.g., DePass) offer better faithfulness but often require multiple forward passes or complex approximations.
• Causal intervention methods (e.g., Activation Patching) are highly faithful but computationally prohibitive for dense attribution, as they require a separate forward pass for every component or interaction, scaling linearly ($O(M)$) with the number of components $M$.

The paper addresses the need for a method that achieves state-of-the-art faithfulness with constant time complexity ($O(1)$) regarding the number of components, without requiring counterfactual examples.

2. Methodology: Dual Path Attribution (DPA)

DPA is a decomposition-based framework designed specifically for SwiGLU-based Transformers (the architecture used in Llama, Mistral, Qwen, etc.). It operates by analytically decomposing the computational graph into distinct pathways and propagating a target vector backward through the frozen model.

Core Concept: Target Propagation

Instead of passing every input component forward to see its effect, DPA propagates the unembedding vector of the target token backward from the output layer to the input.

1. Forward Pass: The model processes the input once, caching all necessary activations (attention weights, gate values, normalized inputs).
2. Backward Pass: The target vector is recursively propagated backward through layers. At each residual position, an "effective target" is computed, representing the contribution required from that layer to produce the final output.

Dual Path Decomposition

The key innovation lies in how DPA handles the non-linearities of SwiGLU and Multi-Head Self-Attention (MHSA) by linearizing them into two distinct pathways:

A. SwiGLU (Feed-Forward) Decomposition
The GLU transformation is split into:

• Content Pathway (Up/Value): Propagates the representation through the value and up-projections. This path is treated as linear given frozen activations.
• Control Pathway (Gate): Governs the routing and transformation via the gate scores. Due to the SiLU activation non-linearity, this path is linearized using a first-order Taylor approximation (ratio of activation to pre-activation).
• Mechanism: The backward target is a weighted sum of the gradients flowing through these two paths.

B. MHSA (Attention) Decomposition
The attention mechanism is decomposed into:

• Value Path: Linear propagation of the value vectors weighted by attention scores.
• Query/Key Paths (Control): These involve the softmax operation. DPA uses a Taylor-based decomposition of the softmax to trace gradients through the query and key interactions, capturing how the "routing" logic (attention weights) affects the target.
• Mechanism: The target is distributed across Query, Key, and Value paths using weighting parameters ($\mu_Q, \mu_K, \mu_V$).

Complexity Advantage

Because DPA propagates a single effective target vector backward and computes attribution scores via dot products with cached activations, it requires zero additional forward passes regardless of the number of components being analyzed.

• Time Complexity: $O(1)$ with respect to the number of components $M$.
• Contrast: Activation Patching requires $O(M)$ forward passes.

3. Key Contributions

1. Novel Framework: Introduction of Dual Path Attribution (DPA), a method that achieves faithful attribution in a single forward and single backward pass without counterfactuals.
2. Theoretical Decomposition: Analytical derivation showing that SwiGLU Transformers can be decomposed into separable content and control pathways, allowing for the linearization of bilinear interactions.
3. Efficiency: Demonstrates $O(1)$ scaling for dense component attribution, making it feasible to analyze millions of parameters (e.g., all neurons in a 7B model) in seconds rather than hours.
4. Empirical Validation: Extensive experiments showing DPA outperforms existing baselines in both input token attribution and component-level (neuron/head) attribution.

4. Experimental Results

The authors evaluated DPA on Llama-3.1-8B, Llama-2-7B, Qwen3-4B, Qwen2.5-32B, and Mistral-7B across three datasets:

• Known 1000: Factual knowledge completion.
• SQuAD v2.0: Reading comprehension.
• IMDb: Sentiment analysis.
• IOI (Indirect Object Identification): Circuit discovery benchmark.

Key Findings:

• Faithfulness: DPA consistently achieved the highest "Total Faithfulness" scores (aggregate of Disruption and Recovery) across all models and datasets. It significantly outperformed gradient-based methods (Integrated Gradients) and decomposition baselines (DePass).
• Component Localization: In the IOI task, DPA successfully isolated the specific circuit responsible for indirect object identification, achieving near-zero disruption and high recovery. It identified causal mechanisms earlier (with fewer components ablated) than baselines.
• Efficiency:
  • On the SQuAD v2.0 dataset with Llama-3.1-8B, DPA completed attribution in ~129 seconds.
  • Baselines (Activation Patching and DePass) required ~1.5 hours (~5400 seconds) for the same task.
  • This represents a ~40x speedup while maintaining comparable memory footprints.
• Sensitivity: The method is robust to hyperparameter variations ($\mu$), though optimal performance for component-level attribution relies heavily on balancing the control (routing) and content pathways.

5. Significance and Limitations

Significance:

• Scalability: DPA removes the computational bottleneck of dense attribution, enabling researchers to map the internal reasoning of large models at the level of individual neurons and heads in real-time.
• Mechanistic Insight: By separating "content" (what is being processed) from "control" (how it is routed), DPA provides a more nuanced view of transformer mechanics than standard linear approximations.
• Practicality: The method is ready for deployment in analyzing massive models where exhaustive patching is impossible.

Limitations:

• Architecture Specificity: The current mathematical derivation is optimized for dense SwiGLU Transformers. Adapting it to Mixture-of-Experts (MoE) or State Space Models (e.g., Mamba) requires manual derivation of new inverse functions.
• Approximation Error: The method relies on first-order linearization. It may lose accuracy in regions of high curvature or where components interact via highly coupled, non-linear synergies (second-order effects).
• Logit vs. Probability: DPA traces attribution to the target logit, not the final post-softmax probability. It may miss indirect effects where a token's probability increases due to the suppression of competing logits.

Conclusion

Dual Path Attribution represents a significant leap forward in mechanistic interpretability. By leveraging the specific bilinear structure of SwiGLU transformers, it bridges the gap between the high faithfulness of causal interventions and the efficiency of gradient-based methods, offering a scalable tool for understanding the "black box" of modern LLMs.