From Observation to Intervention: A Causal Audit of Expert Importance in Mixture-of-Experts Models

Technical Summary: From Observation to Intervention

Problem Statement
Interpretability methods in machine learning frequently rely on a logical leap: treating population-level summary statistics of observed model behavior as valid predictors for the outcomes of targeted interventions. In the context of Mixture-of-Experts (MoE) models, this manifests in pruning pipelines where observational metrics—such as expert utilization rates, activation norms, and routing weight distributions—are used to rank experts for removal. The implicit assumption is that experts with higher observational scores perform more critical work, and thus, removing low-scoring experts will not degrade model functionality. However, as noted by prior work on attention weights (Jain & Wallace, 2019) and saliency maps (Adebayo et al., 2020), associational evidence (Pearl's "rung 1") does not automatically support interventional conclusions ("rung 2"). This paper investigates whether observational routing statistics in MoE models actually predict causal expert importance at the token level.

Methodology
The authors conduct a "causal audit" across three high-redundancy MoE architectures: OLMoE-1B-7B-0924, Qwen1.5-MoE-A2.7B, and DeepSeek-V2-Lite. These models span diverse design dimensions, including different load-balancing strategies, top-k activation ratios (6.7%–12.5%), and training paradigms (scratch vs. upcycled).

The audit protocol involves the following steps:

1. Metric Selection: Four canonical observational metrics are tested: utilization rate, activation norm, mean routing weight when active, and activation standard deviation.
2. Interventional Ground Truth: For each metric, the authors perform per-token ablation experiments. At 200 sampled token positions per layer, they identify the set of active experts, rank them by the target metric, and ablate (zero out) the highest-ranked and lowest-ranked experts.
3. Causal Measurement: The "functional importance" of an expert is measured by the change in loss ($\Delta L$) and the residual-stream displacement (gap norm) resulting from the ablation.
4. Statistical Testing: A paired t-test and Wilcoxon signed-rank test are used to determine if ablating high-ranked experts causes significantly larger loss changes than ablating low-ranked experts. Effect sizes are measured via Cohen's $d$.
5. Controls:
   • Multiple Comparison Correction: Bonferroni correction is applied across the 60 tested metric-layer combinations (4 metrics $\times$ 5 layers $\times$ 3 models).
   • Routing Weight Control: A parallel experiment uses per-token routing weights ($g_i(x_t)$) directly as the ranking criterion. This serves as an upper bound on predictive signal, as it is token-conditioned rather than population-averaged.
   • Progressive Ablation: An experiment on OLMoE removes $k$ highest-weight experts to assess the redundancy buffer in early layers.

Key Results
The study yields a "clean three-model null" regarding observational metrics:

• No Predictive Power: None of the four observational metrics reached Bonferroni-corrected significance ($p < 0.0025$) in any of the 60 metric-layer cells. Effect sizes remained below Cohen's $d = 0.17$ across all combinations.
• Inconsistent Signs: The direction of effects (positive or negative) was inconsistent across layers within the same metric, a pattern characteristic of null distributions rather than weak true effects.
• Routing Weight Control: The control experiment using direct per-token routing weights recovered a single Bonferroni-significant signal in OLMoE at the final MoE layer (Layer 15, $d = +0.231, p = 0.0013$). This indicates the experimental setup has sufficient power to detect signals, but such signals are absent for population-level statistics.
• Redundancy Regime: Progressive ablation on OLMoE revealed that in early layers (0–9), removing up to seven of eight active experts resulted in negligible loss changes. This confirms that early-layer redundancy renders most selection criteria interchangeable; pruning succeeds not because metrics identify dispensable experts, but because nearly all experts in these layers are dispensable.
• OLMoE Late-Layer Anomaly: The single significant signal in OLMoE Layer 15 coincides with a 41$\times$ increase in residual-stream displacement compared to early layers. However, this signal is unique to OLMoE and does not appear in Qwen or DeepSeek, suggesting it is not a general property of high-redundancy MoEs.

Significance and Claims
The paper makes a modest but rigorous claim: it provides an explicit counterexample to the common inferential step from population-level observational summaries to token-level interventional claims about expert importance.

• Failure of the Inference: The results demonstrate that observational routing statistics do not license token-level interventional predictions. The success of existing pruning methods is attributed to the structural redundancy of early layers rather than the validity of the metrics used to select experts.
• Causal Hierarchy: The work illustrates a failure at the boundary between Pearl's rung 1 (association) and rung 2 (intervention). Just as attention weights and saliency maps failed to predict intervention outcomes in prior studies, MoE routing statistics also fail to serve as valid proxies for causal importance.
• Scope Limitations: The authors clarify that the audit is token-level and single-ablation focused. It does not falsify the deployed pruning pipeline (which often involves fine-tuning), but it removes the per-token mechanistic justification that such pipelines assume. The findings are specific to high-redundancy architectures; the validity of metrics in low-redundancy models (e.g., Switch, Mixtral) remains an open question.

In conclusion, the paper argues that interpretability claims requiring generalization must be supported by interventional evidence, and in the specific case of MoE pruning, the standard observational proxies fail this test.