Mixture-of-Experts Interpretability

Multimodal Mixture-of-Experts (MoE) reasoning models rely on long chain-of-thought (CoT) for complex tasks, yet often overthink easy inputs, increasing token cost and latency, and sometimes degrading accuracy. Existing methods optimize reasoning length during training or impose external control at inference, but leave the underlying reasoning mechanism a black box. We find that fast and slow thinking exhibit distinct expert-routing patterns: holding the input fixed and varying only the prompted reasoning tempo produces stable routing shifts. Suppressing slow-thinking experts shortens the reasoning chain, whereas suppressing fast-thinking experts lengthens it, providing causal evidence that these experts influence reasoning depth. Based on this finding, we propose TempoMoE, a training-free, two-stage framework. It identifies fast- and slow-thinking experts via tempo-contrastive routing analysis and redistributes routing weights within the original top-k set according to sample difficulty. It amplifies fast-thinking experts and suppresses slow-thinking experts on easy inputs and reverses this adjustment on hard ones, enabling difficulty-adaptive control over reasoning depth. We evaluate TempoMoE on Kimi-VL, Qwen3-VL, and ERNIE-4.5-VL across six benchmarks. Compared with Vanilla, TempoMoE consistently improves accuracy while reducing output tokens, with accuracy gains of up to 2.6 points and token reductions of up to 35.4%.

Sparse Mixture of Experts (MoE) models scale more efficiently than dense models by routing tokens to modular expert networks that are only active for processing a fraction of tokens. A leading hypothesis for the performance of MoE models is that each expert specialises in a single, coherent domain. However, interpretability efforts that assume this hypothesis have generally been unsuccessful. We propose and present evidence for an alternative account that we call the Superposed Specialisation Hypothesis (SSH): experts specialise in a disjoint union of fine-grained features rather than one broad domain. Leveraging the SSH, we introduce RouterInterp, a method for interpreting expert routing that identifies Sparse Autoencoder features most predictive of routing decisions and produces unified natural language explanations. On gpt-oss-20b, RouterInterp explains expert routing with ${\sim}65\%$ higher detection accuracy than prior token statistics based methods. This work provides a scalable method for generating more accurate explanations of expert routing and increases our understanding of a previously uninterpretable component of foundation models.

Neural models, including dense retrievers, have been widely adopted in Information Retrieval (IR), often delivering state-of-the-art performance. Despite their effectiveness, these models operate as black boxes, limiting the interpretability of their ranking decisions. Existing post-hoc explainability methods for neural rankers primarily focus on feature-level attributions, which can be insufficient to capture the complexity of learned embedding spaces. In this work, we propose ExpertLens, a post-hoc explainability framework for Mixture-of-Experts (MoE)-enhanced dense retrievers that shifts focus from local scalar feature importance to representation-level global interpretability. ExpertLens leverages discriminative embedding space visualizations jointly with automatically extracted Concept Activation Vectors to reveal how expert routing drives embedding space formulation and retrieval effectiveness. Experiments across five IR benchmarks and two MoE-enhanced dense retrievers show that expert routing consistently improves embedding space structure, positioning queries and their relevant documents into better-defined geometric neighborhoods. Analysis of expert subspaces further reveals general-purpose dominant experts, along with minority experts exhibiting distinct linguistic specialization, with subspaces arranged according to multi-semantic concept similarity. Our code is publicly available.

Mixture-of-Experts (MoE) models provide a flexible framework for partitioning complex prediction problems into simpler local learning tasks through an input-dependent gating mechanism. Existing interpretable MoE approaches, such as Mixture of Decision Trees (MoDT), achieve transparency by employing homogeneous decision-tree experts, but this restricts the model to a single inductive bias across all regions of the feature space. We extend the MoDT framework by introducing heterogeneous expert families comprising decision trees, linear support vector machines, and quadratic discriminant analysis under a common probabilistic gating mechanism. To ensure coherent likelihood-based inference, non-probabilistic experts are calibrated to produce conditional class probabilities, allowing parameter estimation within the generalized Expectation-Maximization framework of MoDT. We further establish theoretical monotone ascent guarantees for the proposed heterogeneous gating updates, providing a justification for the optimization procedure. Experiments on a diverse collection of synthetic and real-world benchmark datasets demonstrate that the proposed framework adaptively specializes experts according to local data geometry, yielding interpretable expert assignments while achieving predictive performance competitive with homogeneous MoDT and Random Forests. The proposed approach combines interpretability, adaptive inductive bias selection, and probabilistic coherence within a unified mixture-of-experts framework.

What a reasoning model writes is only a partial record of the process that produces it. We introduce a two-level internal readout for mixture-of-experts reasoning. We first distill vocabulary-scale J-space into J64, a 64-axis semantic frame learned from the model's own reasoning states. J64 reveals readable process state that the emitted trace does not show: it separates inference effort from problem-induced strain. It also adds 0.096 to 0.135 held-out AUC over a baseline that reads the same rollout as token occupancy and aggregates it in exactly the same way. We then reconstruct J64 from native expert-routing statistics. The result is R64, a low-overhead proxy: its median per-axis correlation with J64 is 0.69 to 0.86 across three models and two families, and on gpt-oss-20b it preserves 95 to 100% of J64's predictive gain. The readout supports test-time decisions at two temporal resolutions. Over completed candidate sets, J64 and R64 improve single-branch selection, and R64-weighted voting improves plain majority voting in seven of eight settings. During generation, rolling readout windows drive a cumulative stop-and-resample policy whose operating point is fixed on training questions alone. J64 improves accuracy by 1.1 to 5.9 points over a sibling-permuted control, and the routing-only R64 proxy retains 0.9 to 3.2 of those points. Finally, router edits aimed at the mechanism J64 names induce the predicted reasoning behaviors and shift a diagnosed stall from numerical guessing toward exact symbolic execution. Together, J64 makes latent process state readable, while routing makes it deployable and actionable.

Reward models are central to learning from human preferences, yet identifying what drives their predictions remains challenging. Recent sparse Mixture-of-Experts (MoE) reward models seek to improve interpretability by routing prompts to specialized experts and characterizing experts through examples with high routing weights. However, routing weights only reveal which prompts an expert $\textit{receives}$, not how it $\textit{judges}$ responses, providing only a partial account of expert behavior. We therefore propose $\textbf{Co}$ntribution-$\textbf{Co}$ntrast ($\textbf{CoCo}$) response-level interpretation, which faithfully characterizes experts' roles using chosen-rejected response pairs with the largest contribution contrasts, jointly capturing routing and preference behavior. Across automatic and human evaluations, CoCo yields more coherent, faithful, and specialized interpretations than router-based, score-based, and sparse autoencoder-based alternatives while maintaining competitive reward modeling accuracy. To the best of our knowledge, this is the first systematic study of interpretation methods for MoE reward models.

Sparse mixture-of-experts (MoE) language models route each token to multiple experts, suggesting a geometric account of their benefit: co-selected experts should contribute distinct representation directions. Existing evidence often conflates route coherence, candidate quality, and candidate-by-context interaction. We distinguish these quantities using an Expert Subspace Separation Index (ESSI), matched-route residuals, and a prefix-controlled $2\times2$ factorial; frozen-route interventions and a controlled Top-$k$ study assess functional value. Three paired contrasts organize the findings. First, across six MoE architectures, expert subspaces overlap substantially, yet actual routes explain token representations better than matched alternatives. Second, across the 39 factorial cells in OLMoE, Mixtral, and DeepSeek, the selected candidate explains more of the residual representation than the strongest unselected rival in every cell, yet the actual prefix narrows this advantage throughout: all interactions are negative, and every 95% confidence interval lies below zero. Third, this geometric narrowing does not imply functional redundancy: adding later experts improves next-token prediction in 24 of 39 frozen-route comparisons, while the other 15 estimates are inconclusive; a controlled training study also favors Top-2 over Top-1 in all three seeds. We call this joint pattern coherent overlap: routing selects token-relevant experts from a shared geometric neighborhood, while useful multi-expert computation persists without disjoint linear coverage. Separating these quantities clarifies why geometric similarity alone cannot determine redundancy or pruning value.

We study interaction-aware mixture-of-experts for post-stroke rigidity prediction using multi-level views of structured health records. Despite minimal performance gains, routing attribution reveals systematic importance differences across views, underscoring view construction as key to interpretability.

Mixture-of-Experts (MoE) architectures have recently been extended with role-based mechanisms for interpretability. This is typically done by assigning semantic roles to individual expert components, for example roles like synergy, redundancy, and uniqueness in multimodal settings. However, whether such structural role decomposition preserves explanation faithfulness of the overall architecture remains largely underexplored. We hypothesize that inter-expert representation overlap weakens effective role separation and degrades attribution-based faithfulness, even when semantic roles are explicitly defined. To address this limitation, we introduce representation-level decorrelation regularization to explicitly reduce inter-expert similarity in latent space. Using representation decorrelation objectives, we encourage clearer specialization among experts by minimizing representation overlap. Our experiments show that across multiple multimodal benchmarks, this separation consistently improves explanation faithfulness, as measured by comprehensiveness, sufficiency, and their Area Over the Perturbation Curve (AOPC) summaries, while preserving task performance. We further show that these improvements are not limited to role-based architectures such as Interpretable Multimodal Interaction-aware MoE (I2MoE). Similar trends are observed in a standard sparse MoE baseline, suggesting that representation-level separation may provide a more general mechanism for enhancing explanation faithfulness in MoE systems. Overall, our findings suggest that structural role decomposition alone may be insufficient to guarantee faithful explanations and that representation-level separation helps improve explanation faithfulness. To support reproducibility, the source code and supplementary material are publicly available at https://github.com/dut0817/FL-I2MoE_Decor.

Sparse Mixture-of-Experts (MoE) models route each token to a few of many experts, inviting the hypothesis that experts form functional modules tied to capabilities or languages. We test this causally on Command A+, a frontier open-weights MoE (218B total / 25B active; 128 experts, 8 active, +1 shared). We build a routing-mass atlas, pre-register six family-to-axis hypotheses before any intervention, and ablate each family at inference time against a size-matched random-expert null, measuring whether it selectively breaks its own axis (worst off-target effect at most one third of on-target). Crucially, we test the same families under four metrics and a held-out, independent-corpus run with bootstrap confidence intervals. Our finding is cautionary: robust functional modularity is rare and measurement-dependent. Of six pre-registered families, only one, the Arabic-language family, is a clean selective module that survives an independent corpus and a conservative statistical bar (1/6; a more permissive pre-registered point rule admits 3/6, but that count is threshold-sensitive). Every other family has a real causal effect yet fails selectivity, and its apparent modularity flips with the measurement: with the corpus, the metric, and the statistical bar. A positive control on Qwen3-30B-A3B recovers its published disjoint structure, confirming the method detects modularity when present. The verdict reproduces on the un-quantized BF16 model, ruling out a 4-bit quantization artifact. We conclude that ablation-based modularity verdicts are not safe unless the corpus, metric, and statistical bar are controlled. We release the atlas and ablation data.

Interpretability methods routinely use population-level summary statistics over observed model behaviour to license claims about the effects of targeted interventions on specific computations; in Pearl's terms, they treat rung-1 associational evidence as if it supported rung-2 interventional conclusions, a move whose validity is rarely tested. We examine one concrete instance: the use of routing statistics in Mixture-of-Experts (MoE) pruning, where utilization rates, activation norms, and routing weight distributions are treated as predictors of which experts can be removed without functional cost. A token-level interventional audit across three high-redundancy MoE architectures (OLMoE-1B-7B-0924, Qwen1.5-MoE-A2.7B, DeepSeek-V2-Lite) finds no observational metric predicts causal expert importance in any model: across all 60 metric-layer combinations effect sizes stay below Cohen's $d = 0.23$, and no metric is reliably positive under our corrected, dual-test criterion. A per-token routing weight control, run with identical $n$, rules out insufficient power, recovering a signal whose CI excludes zero at OLMoE's final MoE layer ($d = +0.231$, 95% CI $[+0.09, +0.37]$, $p = 0.0013$). Existing pruning methods succeed in this regime not by identifying dispensable experts but because early-layer redundancy renders most selection criteria interchangeable. Our results provide an explicit counterexample to the common inferential step from population-level observational summaries to token-level interventional claims about expert importance, and illustrate how interventional audits can calibrate the evidential standards for interpretability claims.

An LLM's residual stream is both state and instruction: it encodes the current context and determines the next transformation. We introduce a parameter-free decomposition for Mixture-of-Experts models that splits each layer's hidden state into a control signal that causally drives routing and an orthogonal content channel invisible to the router. Across six MoE architectures, we find that models preserve surface-level features (language, token identity, position) in the content channel, while the control signal encodes an abstract function that rotates from layer to layer. Because each routing decision is low-bandwidth, this hand-off forces compositional specialization across layers. While individual experts remain polysemantic, expert paths become monosemantic, clustering tokens by semantic function across languages and surface forms. The same token (e.g., ":") follows distinct trajectories depending on whether it serves as a type annotation, an introductory colon, or a time separator. Our decomposition identifies the source of this structure: clusters in the control subspace are substantially more monosemantic than those in the full representation. As a result, the natural unit of interpretability in MoEs is not the expert but the trajectory.

Sparse Mixture-of-Experts (MoE) models scale parameters while fixing active computation per token, but the specialization of individual experts remains opaque. In a companion paper we showed that routing topology is quality-neutral: five structurally different configurations converge to statistically equivalent language modeling quality. Here we show that expert identity is nonetheless causally meaningful: individual rank-1 experts are monosemantic by construction, and cosine-similarity routing in a low-dimensional metric space makes their specialization directly inspectable. We present four lines of evidence. First, projecting expert output vectors through the unembedding matrix yields a Semantic Dictionary: 15% of experts are monosemantic specialists spanning 10 categories (temporal, geographic, cardinal, discourse, emotional, financial, military, scientific). Second, routing exhibits a frequency-to-syntax gradient: early layers separate tokens by word frequency, deeper layers by syntactic class (Zipf-confound controls, all $p < 0.001$). Third, causal interventions confirm these labels: steering toward a temporal expert's centroid increases P(temporal) by +321% (median across 44 prompts); suppressing a geographic expert drops P(geographic) by -23%; rewriting an expert's output vector halves target-category probability, and effects compose additively across layers. Fourth, the interventions are not unique to cosine routing: linear routers support comparable steering, but only cosine routing provides geometric transparency -- expert specialization is readable directly from the centroid matrix. MoE expert-level specialization is a first-class interpretability primitive: architecturally monosemantic, causally validated, and controllable at inference with zero overhead.

Mixture-of-Experts (MoE) architectures have become the dominant choice for scaling Large Language Models (LLMs), activating only a subset of parameters per token. While MoE architectures are primarily adopted for computational efficiency, it remains an open question whether their sparsity makes them inherently easier to interpret than dense feed-forward networks (FFNs). We compare MoE experts and dense FFNs using $k$-sparse probing and find that expert neurons are consistently less polysemantic, with the gap widening as routing becomes sparser. This suggests that sparsity pressures both individual neurons and entire experts toward monosemanticity. Leveraging this finding, we zoom out from the neuron to the expert level as a more effective unit of analysis. We validate this approach by automatically interpreting hundreds of experts. This analysis allows us to resolve the debate on specialization: experts are neither broad domain specialists (e.g., biology) nor simple token-level processors. Instead, they function as fine-grained task experts, specializing in linguistic operations or semantic tasks (e.g., closing brackets in $\LaTeX{}$). Our findings suggest that MoEs are inherently interpretable at the expert level, providing a clearer path toward large-scale model interpretability. Code is available at: https://github.com/jerryy33/MoE_analysis.

Sparse Mixture-of-Experts (MoE) architectures enable efficient scaling of large language models through conditional computation, yet the routing mechanisms responsible for expert selection remain poorly understood. In this work, we introduce routing signatures, a vector representation summarizing expert activation patterns across layers for a given prompt, and use them to study whether MoE routing exhibits task-conditioned structure. Using OLMoE-1B-7B-0125-Instruct as an empirical testbed, we show that prompts from the same task category induce highly similar routing signatures, while prompts from different categories exhibit substantially lower similarity. Within-category routing similarity (0.8435 +/- 0.0879) significantly exceeds across-category similarity (0.6225 +/- 0.1687), corresponding to Cohen's d = 1.44. A logistic regression classifier trained solely on routing signatures achieves 92.5% +/- 6.1% cross-validated accuracy on four-way task classification. To ensure statistical validity, we introduce permutation and load-balancing baselines and show that the observed separation is not explained by sparsity or balancing constraints alone. We further analyze layer-wise signal strength and low-dimensional projections of routing signatures, finding that task structure becomes increasingly apparent in deeper layers. These results suggest that routing in sparse transformers is not merely a balancing mechanism, but a measurable task-sensitive component of conditional computation. We release MOE-XRAY, a lightweight toolkit for routing telemetry and analysis.

Mixture of Experts (MoE) models enable parameter-efficient scaling through sparse expert activations, yet optimizing their inference and memory costs remains challenging due to limited understanding of their specialization behavior. We present a systematic analysis of expert specialization in MoEs through two complementary approaches: domain-specific routing patterns and an early decoding framework that tracks expert contributions to output representations. Our analysis of the DeepSeekMoE model reveals that despite having 64 routed experts with 6 active for each layer's computation, the model predominantly relies on a few specialized experts, with the top-weighted expert's output closely approximating the full ensemble prediction. We quantitatively validate these findings through a systematic analysis of the token routing distribution, demonstrating that very few experts handle over 50% of routing decisions across different specialized domains. Hidden state similarity between single and ensemble experts for every layer is extremely high, with some layers having cosine similarity as high as 0.95 and perplexity increasing by only 5% when using a single expert across all three domains. Our results indicate that Mixture of Experts models exhibit concentrated expertise highlighting potential opportunities for inference optimization through targeted expert pruning while maintaining model performance and opening avenues towards studying localization of learned knowledge in these models.

Mixture of Experts (MoE) achieve parameter-efficient scaling through sparse expert routing, yet their internal representations remain poorly understood compared to dense models. We present a systematic comparison of MoE and dense model internals using crosscoders, a variant of sparse autoencoders, that jointly models multiple activation spaces. We train 5-layer dense and MoEs (equal active parameters) on 1B tokens across code, scientific text, and english stories. Using BatchTopK crosscoders with explicitly designated shared features, we achieve $\sim 87\%$ fractional variance explained and uncover concrete differences in feature organization. The MoE learns significantly fewer unique features compared to the dense model. MoE-specific features also exhibit higher activation density than shared features, whereas dense-specific features show lower density. Our analysis reveals that MoEs develop more specialized, focused representations while dense models distribute information across broader, more general-purpose features.

Mixture-of-Experts (MoE) offers flexible graph reasoning by combining multiple views of a graph through a learned router. We investigate routing-aware explanations for MoE graph models in malware detection using control flow graphs (CFGs). Our architecture builds diversity at two levels. At the node level, each layer computes multiple neighborhood statistics and fuses them with an MLP, guided by a degree reweighting factor rho and a pooling choice lambda in {mean, std, max}, producing distinct node representations that capture complementary structural cues in CFGs. At the readout level, six experts, each tied to a specific (rho, lambda) view, output graph-level logits that the router weights into a final prediction. Post-hoc explanations are generated with edge-level attributions per expert and aggregated using the router gates so the rationale reflects both what each expert highlights and how strongly it is selected. Evaluated against single-expert GNN baselines such as GCN, GIN, and GAT on the same CFG dataset, the proposed MoE achieves strong detection accuracy while yielding stable, faithful attributions under sparsity-based perturbations. The results indicate that making the router explicit and combining multi-statistic node encoding with expert-level diversity can improve the transparency of MoE decisions for malware analysis.