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RouterInterp: Understanding Superposed Specialisation in Mixture of Experts Routing

Ilya Lasy, Nora Yinuo Cai, Kola Ayonrinde

arXiv:2610.11775v1cs.AIcs.CLcs.LG

TL;DR

MoE interpretability has struggled to recover clear expert-specialisation patterns, motivating a distinction between coherent-domain specialisation and experts responding to disjoint micro-domains. RouterInterp uses predictive SAE features to produce unified natural-language explanations of routing. On gpt-oss-20b and OLMoE-1B-7B, its explanations score 0.49 / 0.60, outperforming direct-text and unigram explanations.

  • Problem

    Interpretability studies have struggled to recover clear expert-specialisation patterns, while the Specialisation Hypothesis may describe either coherent domains or disjoint micro-domains.

    Source: §1 · p. 2

  • Method

    RouterInterp identifies sparse autoencoder features predictive of expert selection and aggregates their explanations into unified natural-language descriptions.

    Source: §7 · p. 12

  • Results

    On gpt-oss-20b and OLMoE-1B-7B, RouterInterp achieves explanation scores of 0.49 / 0.60, outperforming direct-text and unigram explanations.

    Source: §7 · p. 12

  • Takeaways & Limitations

    The findings support the SSH account that experts often span disjoint concepts rather than specialising in a single monosemantic domain.

    Source: §5 · p. 10

    Evaluation covered two models in the 1B–20B parameter range; scaling to frontier architectures, shared experts, and other routing methods remains future work.

    Source: §5.1 · p. 11

Abstract

from arXiv · show

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.

1 INTRODUCTION

Sparse MoE models use expert specialisation to process inputs with only a subset of parameters, but prior analyses struggled to find clear expert patterns. The paper distinguishes coherent-domain specialisation from superposed specialisation and introduces RouterInterp to explain routing through predictive SAE features.

1 INTRODUCTION

  • MoE expert specialisation is a proposed explanation for efficiency: each input can use only selected parameters when experts handle subsets of inputs or computations.The introduction notes that sparse MoE models can activate only 2–15% of parameters per input.Source: §1 · p. 1

Alternative Specialisation Hypotheses

  • The SSH proposes that experts specialise in disjoint collections of features spanning semantically unrelated micro-domains, unlike the DSH’s coherent-domain clusters.Real-world data contains more fine-grained categories than a layer has experts, so multiple micro-domains must share an expert.Source: Alternative Specialisation Hypotheses · p. 2, §1 · p. 2
  • SAE latents serve as feature-level proxies for micro-domains and predict gpt-oss-20b expert selection with macro-F1 0.73.The paper reports better routing prediction than token co-occurrence statistics or sparse linear probes.Source: Alternative Specialisation Hypotheses · p. 2
  • The authors suggest that unrelated micro-domains coactivate less often, producing less interference when assigned to one expert than semantically similar domains would.They connect this proposed mechanism to superposition theory.Source: Alternative Specialisation Hypotheses · p. 2
  • RouterInterp achieves a 0.49 explanation score on gpt-oss-20b, outperforming token-expert co-occurrence explanations at 0.30.It selects SAE latents predictive of routing, gathers inputs where those features and an expert are jointly active, and explains the expert in natural language.Source: Alternative Specialisation Hypotheses · p. 2

2 BACKGROUND

The background describes sparse autoencoders as a way to represent activations with sparse latents and reconstruct them, then outlines how MoE routers select experts and combine their outputs.

2.1 SPARSE AUTOENCODERS (SAE)

  • An SAE encodes activations into a sparse latent representation and decodes those latents to reconstruct the original activation.The described Top-K approach retains the s largest activations per input, and training optimises reconstruction fidelity.Source: §2.1 · p. 3

2.2 MIXTURE OF EXPERTS (MOE)

  • An MoE router computes routing logits from each token representation, converts them to expert probabilities, and selects the top-k experts.The layer output is a weighted sum of the selected experts’ outputs.Source: §2.2 · p. 3
  • MoE training commonly uses auxiliary load-balancing losses to encourage uniform expert utilisation.Without intervention, models can collapse to using only a few experts, leaving others undertrained.Source: §2.2 · p. 3

3 SPECIALISATION HYPOTHESES

The section contrasts coherent-domain routing with the Superposed Specialisation Hypothesis (SSH), in which experts combine semantically disjoint micro-domains. The reported clustering evidence favors SSH while indicating some thematic coherence.

3 SPECIALISATION HYPOTHESES

  • The hypotheses treat routing as monosemantic or polysemantic, extending superposition theory to experts that may specialise in disjoint collections of domains.The section frames its formal predictions, theoretical motivations, and experiments around distinguishing these accounts.Source: §3 · p. 4

3.1 ALTERNATIVE SPECIALISATION HYPOTHESES

  • When micro-domains outnumber experts, DSH predicts that each expert groups similar micro-domains, whereas SSH predicts that experts combine dissimilar ones.DSH predicts a coherent domain; SSH predicts a polysemantic collection of concepts or domains.Source: §3.1 · pp. 4–5

3.2 MOTIVATION FOR SUPERPOSED SPECIALISATION

  • Low coactivation can reduce interference when sparse features share representational capacity, motivating experts to apply disjoint transforms to different input domains.The paper argues that this may let one expert perform Computation in Superposition.Source: §3.2 · p. 5
  • Load-balancing loss, especially with relatively small batches, may encourage routing dissimilar inputs to the same expert rather than keeping a macro-domain together.The paper reasons that batches contain few macro-domains, while the loss encourages distribution across experts.Source: §3.2 · p. 5

3.3 EMPIRICAL EVIDENCE FOR SUPERPOSED SPECIALISATION

  • The empirical test uses each expert’s most predictive SAE latents as micro-domain proxies and compares their semantic similarity or cluster diversity.SSH predicts mutually dissimilar latents; DSH predicts mutually similar latents, with G(Ei)=1 for DSH and G(Ei) approaching n for SSH.Source: §3.3 · pp. 5–6
  • Mean cluster counts were 11.3 for gpt-oss-20b (layer 20) and 10.8 for OLMoE-1B-7B (layer 15), far above the DSH prediction of G=1 and supporting SSH.Both means are out of an upper bound of n=20; the observed values remain slightly below random cluster assignment.Source: Figure 2 · p. 6, §3.3 · p. 6
  • Routing-prediction F1 generally falls as fewer SAE features remain active per token, while routing across Pile subsets stays near corpus-proportional.These findings suggest routing depends jointly on many features rather than one domain-level signal.Source: §3.3 · p. 6

4 ROUTERINTERP

RouterInterp uses SAE features to explain expert routing as a combination of fine-grained signals, building on evidence for the Superposed Specialisation Hypothesis. Its explanations outperform the evaluated routing-interpretation baselines on both tested models.

4.1 METHOD

  • The method selects features by approximating their ablation effect on expert selection, assigns each feature to at most one expert, and collects positive and negative activation windows.Positive windows contain a feature-active token routed to the target expert; negative windows contain a feature-active token not routed to it.Source: §4.1 · pp. 6–7

4.2 EVALUATION

  • The evaluation uses a language-model scorer to predict expert activation from explanations on held-out positive and negative windows, then reports binary-classification F1.A small-scale human evaluation found human–LLM agreement comparable to human–human agreement, supporting the scorer as a proxy for interpretability judgments.Source: §4.2 · pp. 7–8

4.3 EXPERIMENTAL SETUP

  • Experiments use OLMoE-1B-7B and gpt-oss-20b, with Pile activations for routing analysis and SAEs trained or selected at specified layers and sparsities.RouterInterp explanations use the top 45 gradient-attribution-selected features per expert; scoring uses 15 positive and 85 negative examples per expert.Source: §4.3 · p. 8

4.4 RESULTS

  • RouterInterp reaches mean F1 0.492 (s=128) on gpt-oss-20b and 0.602 on OLMoE-1B-7B, beating both baselines at every layer.Figure 4 reports gains of ∼65% / ∼76% mean F1 over Unigram Lookup on gpt-oss-20b / OLMoE-1B-7B, and ∼28% over Expert Impact AutoInterp on gpt-oss-20b.Source: Figure 4 · p. 9, §4.4 · p. 9

4.1 METHOD

  • RouterInterp selects top-45 attribution-ranked SAE features and contrasts routed with non-routed windows for each feature to cover an expert’s micro-domains.The method groups examples by feature, then prompts a language model to synthesize a unified description while keeping distinct activation cases separate.Source: §4.1 · p. 7, §4.4 · p. 9

4.4 RESULTS

  • On gpt-oss-20b, SAE-feature grouping improves precision and recall together (P 0.47 / R 0.64; 0.495 mean F1, s=64), versus 0.417 mean F1 for bigram and expert-activation explainers.Bigram descriptions have P 0.39 / R 0.59, while full-window descriptions have P 0.30 / R 0.81.Source: §4.4 · p. 10
  • Herbst et al. (2026) scores are not directly comparable because their evaluation uses maximum-activation examples, a balanced set, and a scorer that accepts rough target-token fit.In this evaluation, the method scores 0.383 versus 0.417 mean F1 for Expert Activations AutoInterp on gpt-oss-20b, and falls below Unigram Lookup on OLMoE-1B-7B (0.305 vs. 0.342).Source: §4.4 · p. 10

5 DISCUSSION

The discussion argues that experts are polysemantic, often combining disjoint feature domains, and suggests this helps explain why monosemantic interpretations have struggled. It also identifies methodological and evaluation boundaries for RouterInterp.

5 DISCUSSION

  • Experts’ predictive features often span disjoint concepts, supporting the SSH and suggesting why work assuming monosemantic experts struggled to explain routing.Automated interpretations frequently describe logical disjunctions of unrelated features.Source: §5 · p. 10
  • Apparently domain-specialised experts may participate in a language, task, or behaviour without doing so exclusively; each expert covers many semantic roles.The discussion notes that Spanish can be only a small fraction of an expert’s broader activity.Source: §5 · p. 10
  • Functional similarity may explain why experts group seemingly unrelated inputs that require similar downstream transformations, but the discussion leaves this hypothesis for future testing.The authors suggest that experts may perform Computation in Superposition.Source: §5 · pp. 10–11
  • Alternative routes to interpretability include increasing the number of experts or interpreting routing collections and paths rather than individual experts.The discussion notes that more experts may yield more monosemantic routing, while collections and paths offer combinatorially many units to analyze.Source: §5 · p. 11

5.1 LIMITATIONS

  • RouterInterp’s effectiveness depends on SAE and automated-explanation quality; higher SAE FVU correlates with weaker routing prediction across layers.The authors frame SAE-based interpretation as useful for discovery, while noting that other feature-manifold methods may suit cases without guaranteed linearity.Source: §5.1 · p. 11, §5 · p. 11
  • Evaluation covers OLMoE-1B-7B and gpt-oss-20b, leaving scaling to frontier architectures, shared experts, and Expert Choice routing for future work.Aggregated natural-language explanations also grow with the number of features, motivating possible compression or interactive presentation.Source: §5.1 · p. 11

6 RELATED WORK

Prior work has found expert-routing patterns difficult to interpret from token statistics, while RouterInterp uses SAE features to improve explanations. Related work also distinguishes expert-weight monosemanticity from the polysemanticity of routing decisions.

6 RELATED WORK

  • RouterInterp uses SAE features rather than tokens as its explanatory basis and reports more accurate explanations than unigram analysis.Earlier unigram analyses found variable specialization, making interpretation difficult.Source: §6 · p. 11
  • Large expert counts may make routing more interpretable, but the cited setting uses more experts than is compute-optimal or typical in high-performing open-source MoEs.Yang et al. (2025b) suggest interpretability with very large numbers of experts.Source: §6 · p. 11
  • Expert weights can be more monosemantic than dense-model weights in a toy setting, yet routing decisions may remain polysemantic because dissimilar, rarely co-occurring domains can share an expert.The cited analysis measures expert weight matrices, whereas this paper focuses on routing decisions.Source: §6 · p. 12

7 CONCLUSION

RouterInterp uses predictive SAE features to explain expert routing, and the results support the SSH account of experts combining unrelated feature domains. The paper presents this as a step toward more transparent and controllable routing while identifying further questions about specialization and its development.

7 CONCLUSION

  • 0.49 / 0.60 explanation score on gpt-oss-20b and OLMoE-1B-7B, versus 0.42 on gpt-oss-20b for direct text explanations and 0.30 / 0.34 for unigram explanations.RouterInterp aggregates explanations of SAE features most predictive of expert selection into natural-language descriptions.Source: §7 · p. 12
  • Experimental results support the SSH: experts’ most predictive SAE latents span unrelated micro-domains rather than one coherent domain.Automated interpretations frequently describe experts as activating on logical disjunctions of unrelated features.Source: §7 · p. 12
  • The mechanisms that produce particular feature combinations remain open questions, including whether load balancing or capacity constraints drive redundancy across experts.The authors also ask whether experts group inputs by semantic similarity or by required downstream transformations.Source: §7 · p. 12
  • Tracking routing across training checkpoints could reveal when specialization emerges and how early training shapes it.The authors point to developmental interpretability as a possible approach.Source: §7 · p. 12
  • RouterInterp is presented as a step toward making expert routing more transparent and controllable in foundation models.The paper connects this goal to scientific understanding and alignment with human intent.Source: §7 · p. 12

IMPACT STATEMENT

The paper presents RouterInterp as a tool for interpreting expert routing and situates SAE-based explanations within broader interpretability and modularity questions. It also notes the approach’s feature-representation caveats and the potential dual use of interpretability research.

IMPACT STATEMENT

  • RouterInterp interprets MoE expert routing and could complement methods for interpreting attention, MLPs, and intermediate representations.The authors anticipate applications including debugging, trustworthiness, fairness and bias evaluation, and risk mitigation, while acknowledging dual use.Source: IMPACT STATEMENT · p. 13

A.1 SPARSE FEATURE DECOMPOSITIONS FOR MODEL INTERPRETABILITY

  • SAEs rely on the Linear Representation Hypothesis, and the authors argue they suit routing because routing is usually performed by a linear map.The paper notes that the hypothesis is controversial in interpretability.Source: §A.1 · p. 20
  • SAEs can struggle with hierarchical or multidimensional features, cross-token relations, and relational composition.These are identified as limitations of SAE representations.Source: §A.1 · p. 20
  • The paper combines trained SAEs, an Ansatz about router weights, and AutoInterp for mathematical description, semantic description, and validation of routing explanations.The empirical success of this approach is presented as evidence for the Ansatz.Source: §A.1 · p. 21

A.2 ADAPTIVE COMPUTATION

  • Sparse MoE is an adaptive-computation approach that uses a subset of parameters; the authors suggest generalizing routing interpretation to early-exit models.The paper contrasts this with looping models that reuse parameters.Source: §A.2 · p. 21

A.3 MODULARITY IN NEURAL NETWORKS

  • Sparse MoE provides enforced modularity that the authors hope can help uncover latent modularity in dense neural networks.They point to specialization and reduced connection costs as pressures that may contribute to modularity.Source: §A.3 · p. 21

B SAE FEATURES AS ROUTING PREDICTORS

SAE latents predict expert routing more accurately than token co-occurrence baselines and matched-sparsity sparse probes. This advantage supports using SAE features as routing-specific signals for RouterInterp.

Routing Probes.

  • The routing probes train one logistic-regression classifier per expert on SAE representations from 1M tokens, predicting whether each expert is in the router’s top-k selection.The reported metric is macro-F1, the mean per-expert F1.Source: B SAE FEATURES AS ROUTING PREDICTORS · pp. 21–22

Baselines.

  • Baselines include token-level unigram and bigram co-occurrence counts plus sparse linear probes over neuron and PCA bases, with sparsity matched to the SAE probes.The neuron probe keeps the top-s residual neurons; the PCA probe sparsifies after projection onto leading components.Source: B SAE FEATURES AS ROUTING PREDICTORS · p. 22

SAE Latents Predict Expert Routing.

  • SAE latents outperform unigram and bigram baselines and matched-sparsity neuron- and PCA-basis probes on both OLMoE-1B-7B and gpt-oss-20b.The SAE-basis advantage also holds across multiple gpt-oss-20b layers and sparsity levels, beating the best neuron and PCA probe at four of five layers.Source: B SAE FEATURES AS ROUTING PREDICTORS · p. 22, Table 2 · p. 22

C.1 FEATURE SELECTION METHOD

The appendix describes gradient-based attribution for selecting routing-relevant SAE features and tests that criterion against alternatives. It also examines Pile-domain routing patterns and whether SAE routing-prediction gains persist across layers.

C.1 FEATURE SELECTION METHOD

  • The method estimates each active SAE feature’s effect on an expert’s routing margin, then assigns top-ranked features to non-overlapping expert sets.The margin is the expert’s logit gap above the threshold for entering the router’s top-k; positive attribution indicates support for selection.Source: §C.1 · pp. 22–23

C.2 SELECTION CRITERION AND SET SIZE

  • Gradient-based attribution outperforms ρ-usefulness and cosine similarity across five gpt-oss-20b layers, while mean F1 improves only gradually beyond ∼50 features.The comparison trains a linear probe using the top-n features per expert; Figure 5 reports the feature-selection comparison.Source: §C.2 · p. 24, Figure 5 · p. 24

D EXPERT ROUTING ACROSS PILE DOMAINS

  • Pile-subset routing preferences show little spread around corpus rates, providing evidence against expert domains aligned with those subsets but not against domains that cut across them.For most expert–subset pairs, subset tokens reach an expert at or below the corpus rate; syntax-defined domains remain possible.Source: D EXPERT ROUTING ACROSS PILE DOMAINS · p. 26

E ROUTING PREDICTION ACROSS LAYERS

F ROUTING DEPENDS ON MULTIPLE FEATURES

Routing prediction improves as more active SAE features are retained per token, consistent with expert routing depending on multiple distinct concepts rather than a single domain.

F ROUTING DEPENDS ON MULTIPLE FEATURES

G SAE SETUP AND RECONSTRUCTION QUALITY

The appendix reports SAE configurations and reconstruction quality for OLMoE-1B-7B and gpt-oss-20b. On gpt-oss-20b, reconstruction quality and routing-prediction performance vary together, especially at layer 16.

OLMoE-1B-7B

gpt-oss-20b

SAE reconstruction quality

  • At gpt-oss-20b layer 16, improving SAE reconstruction from FVU 0.232 to 0.191 corresponds to routing-prediction macro-F1 rising from 0.297 to 0.439.The passage notes that explanation scores do not show the same dependence and suggests poor reconstruction may bottleneck probe performance.Source: Table 6 · p. 27, G SAE SETUP AND RECONSTRUCTION QUALITY · p. 28

H HUMAN EVALUATION

Human evaluation supports the LLM scorer as a practical proxy for human judgments, while SAE probes recover router probability rankings across stronger-performing layers. The prompts specify how to form expert explanations from feature-grouped examples, and a worked example shows several distinct expert specialisations.

H HUMAN EVALUATION

  • Human–LLM agreement was comparable to human–human agreement on pooled agreement and Cohen’s κ, with no statistically significant difference.The evaluation used 150 examples across 25 experts from layer 12 of gpt-oss-20b.Source: H HUMAN EVALUATION · p. 28, Table 7 · p. 28

I SAE PROBES RECOVER ROUTER PROBABILITIES

  • Spearman ρ exceeded 0.7 at layers 8, 12, and 20, while calibration weakened at layers 4 and 16; MSE was ≈0.03 (RMSE ≈0.17).The probes were trained on top-k membership, not directly to recover the full router probability distribution.Source: I SAE PROBES RECOVER ROUTER… · p. 28, Table 8 · p. 29

J PROMPTS

  • RouterInterp groups activating examples by SAE feature and contrasts positives with hard negatives where the feature fires but the expert is not selected.Its prompt directs the explainer to merge similar groups and describe distinct contextual patterns rather than list tokens.Source: J PROMPTS · pp. 29–30
  • The explanation scorer assigns contextual match scores from 0 to 4 and treats scores ≥2 as positive, counting plausible incomplete matches but not superficial token overlap.The judge evaluates whether a highlighted token in its exact context matches a mode in the expert explanation.Source: J PROMPTS · pp. 31–32

K EXAMPLE EXPERT EXPLANATIONS

  • Expert 2’s layer-12 explanation links five attributed SAE features to distinct specialisations, including physical trauma, scientific notation, structured punctuation, brand suffixes, and electronic components.The five displayed features were selected by gradient-based attribution.Source: K EXAMPLE EXPERT EXPLANATIONS · p. 32, Table 9 · p. 33

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