Expert-Aware Causal Tracing of Factual Recall in Sparse MoE Language Models

Authors: Yuetian Lu, Ali Modarressi, Yihong Liu, Hinrich Schütze (LMU Munich, TU Darmstadt, MCML)

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Summary (Overview)

• Novel protocol for expert-level causal tracing: The paper introduces a two-stage expert-aware causal tracing protocol specifically designed for sparse Mixture-of-Experts (MoE) language models, moving beyond layer-level analysis to individual routed expert contributions.
• Key finding on Qwen3-30B-A3B-BASE: Layer-level tracing selects and validates layer 44, and expert-level tracing identifies expert L44E069 as a recurrent expert whose held-out patch significantly outperforms other active same-layer experts (Specificity = +0.400).
• Contrasting finding on Mixtral-8X7B-V0.1: While layer 19 validates as a mid-layer signal, the selected singleton expert L19E006 underperforms active controls (Specificity = -0.175); instead, routed multi-expert coalitions recover the layer-level signal.
• Methodological contribution: Distinguishes three levels of factual-recall evidence: aggregate MoE-block rescue, single-expert localization, and multi-expert routed recovery.
• Key insight: Expert-level localization is model- and protocol-dependent rather than universal across MoE architectures.

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Introduction and Theoretical Foundation

Background

Factual recall in language models refers to the ability to assign high probability to correct objects given subject–relation prompts (e.g., "The capital of France is" → Paris). Causal tracing and activation patching are established techniques for understanding which internal components mediate this behavior by:

1. Corrupting a prediction (e.g., adding noise to embeddings)
2. Restoring internal components from a clean run
3. Measuring which components mediate recovery

The MoE Challenge

Sparse MoE language models introduce a critical granularity problem: a token is processed not by a single dense feed-forward module but by a small routed subset of experts. This means:

• A layer-level patch shows that an MoE block matters
• But the patched block is an aggregate over routed expert updates
• It does not answer which selected expert contributions support the factual prediction

Research Question

Can factual-recall causal tracing be made expert-aware in sparse MoE language models?

Theoretical Foundation

The paper builds on:

• COUNTERFACT facts (Meng et al., 2022) for controlled factual contrasts
• Causal tracing and activation patching paradigms (Vig et al., 2020; Wang et al., 2023)
• Feed-forward memory theories of factual knowledge (Geva et al., 2021; Dai et al., 2022)
• Prior MoE interpretability work on routing patterns and expert specialization

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Methodology

3.1 COUNTERFACT Factual Tracing Setup

For a prompt $x$, true object $a_t$, and foil object $a_f$, the factual preference is defined as the logit difference:

$$\Delta(x; a_t, a_f) = \ell_x(a_t) - \ell_x(a_f), \tag{1}$$

where $\ell_x(a)$ is the next-token logit for object token $a$. The object token is not included in the input; true and foil objects only define the next-token contrast.

3.2 Subject-Noise Corrupted Run

The corrupted run adds Gaussian noise to subject-token embeddings:

$$h_s^{\mathrm{noised}} = h_s + \epsilon, \quad \epsilon \sim \mathcal{N}(0, \sigma^2 I), \tag{2}$$

where $\sigma = 3.0 \times$ (embedding-matrix standard deviation). The subject-noise drop is:

$$\Delta_{\mathrm{clean}} - \Delta_{\mathrm{noised}}. \tag{3}$$

3.3 MoE-Block Output Patching

At layer $\ell$, the clean final-position MoE-block output is patched into the noised run. The rescue score is:

$$\mathrm{Rescue}_{\ell} = \Delta_{\mathrm{patched}, \ell} - \Delta_{\mathrm{noised}}. \tag{4}$$

Discovery/validation split: Layers are selected only on discovery cases, then evaluated as fixed hypotheses on validation cases.

3.4 Expert-Contribution Patching

At a selected MoE layer, for a clean-active expert $e$, its routed update is estimated by ablation difference:

$$c_e(x) = \mathrm{MoEOut}(x) - \mathrm{MoEOut}_{\backslash e}(x), \tag{5}$$

where $\mathrm{MoEOut}_{\backslash e}$ suppresses expert $e$'s routed contribution under the original top-k routing decision (no rerouting, no renormalization).

The expert patch vector is:

$$\delta_e = c_e(x_{\mathrm{clean}}) - c_e(x_{\mathrm{noised}}), \tag{6}$$

added to the noised MoE-block output at the final position.

Confound Controls

1. Recurrence-first selection: Experts must appear in at least half of discovery cases (64/128) to avoid single-case artifacts.
2. Specificity metric: Selected expert is compared against same-source active-random experts:

$$\mathrm{Spec} = \mathrm{Rescue}(e^\star) - \frac{1}{|\mathcal{R}|} \sum_{r \in \mathcal{R}} \mathrm{Rescue}(r), \tag{7}$$

where $e^\star$ is the selected expert and $\mathcal{R}$ is the active-random control set.

Models Evaluated

Data

• 256 usable COUNTERFACT cases per model (128 discovery + 128 validation)
• Model-specific filters for single-token true/foil objects and sufficient clean/noise margins

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Empirical Validation / Results

Layer-Level Tracing Results

Table 1: Main validation results on 128 held-out cases per model. Spec subtracts same-layer active-random rescue.

Key Findings

Qwen3-30B-A3B-Base

• Layer 44 strongly validates as a layer-level site
• Expert L44E069 validates with positive specificity (+0.400)
• The expert is not merely an arbitrary active layer-44 expert; its patch vector $\delta_e$ rescues more than active-random controls
• Multiple additional controls preserve this conclusion (Appendices C–E)

Mixtral-8X7B-V0.1

• Layer 19 validates, but nearby layers are comparable → interpreted as mid-layer transfer rather than sharp single-layer localization
• Selected expert L19E006 has negative specificity (-0.175)
• Coalition check: Clean top-2 and clean/noised routing-union coalitions recover rescue close to the L19 MoE-block effect
• Layer-level signal is better explained by routed expert coalitions than single-expert localization

Visual Summary (Figure 1)

Left panel: MoE-block rescue across layers — Qwen3 shows sharp L44 peak; Mixtral shows broader mid-layer band. Middle panel: Selected-expert specificity — Qwen3 L44E069 positive; Mixtral L19E006 negative. Right panel: Mixtral coalition patching — dashed line marks L19 MoE-block rescue; coalitions recover near-block-level rescue.

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Theoretical and Practical Implications

Methodological Implications

1. Block-level rescue ≠ expert-level evidence: MoE factual tracing should not stop at layer-level activation patching. A clean MoE-block output can rescue a noised factual prompt, but this only localizes the signal to an aggregate routed block.

2. Router selection is not causal: An expert being selected by the router identifies candidates, but causal evidence requires patching the estimated expert update and comparing with active controls.

3. Three distinct levels of evidence:

   • Aggregate MoE-block rescue
   • Single-expert localization
   • Multi-expert routed recovery

Practical Implications

• Model debugging: More precise localization of factual behavior supports targeted model debugging and factual-behavior analysis.
• Dual-use risk: Precise localization could enable targeted manipulation, suppression, or editing of model outputs — such uses require careful evaluation before deployment.

Architectural Insights

• Qwen3 (128 experts, top-8): Factual recall can concentrate in a recurrent expert (L44E069)
• Mixtral (8 experts, top-2): Factual recall remains distributed across routed expert coalitions

The asymmetry suggests that expert specialization for factual recall is not universal and depends on architecture, routing design, and training.

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Conclusion

The paper introduces expert-aware causal tracing for sparse MoE factual-recall diagnostics, with two controlled case studies:

1. Qwen3-30B-A3B-Base: Layer-level site (L44) further localized to a robust routed expert contribution, L44E069, with positive specificity across held-out cases.

2. Mixtral-8X7B-V0.1: Layer-level rescue transfers (L19 band), but the signal is better recovered by routed expert coalitions than by the selected single expert.

Future Directions

• Extension to more datasets and MoE backbones
• Multi-token objects
• Subject/relation-position interventions
• Systematic coalition analyses across layers and models
• The relaxed-filter 512-case check preserves the main pattern, but the filtering funnel may bias retained cases

Limitations

• Controlled diagnostic rather than full account of natural factual recall
• Expert contributions estimated by ablation difference under fixed routing (not a complete subject-to-answer circuit)
• Two-stage design decomposes the selected layer only — useful experts outside the selected layer may be missed
• Model contrast treated as two case studies, not a broad survey
• Nontrivial compute requirements for reproduction