Sparse mixture-of-experts (MoE) models use an independently parameterized router at each sparse layer to select experts for every token. Prior work has shown that routing decisions across depth can often be predicted from earlier routing signals, suggesting that routing is not fully independent across layers. However, the structure behind this predictability remains unclear. In this work, we provide evidence that routing-relevant states across layers share a common geometric structure that is obscured by layer-specific coordinate systems. We isolate the control subspace of each router and align these spaces into a shared canonical representation using generalized orthogonal Procrustes analysis. After alignment, a single linear transition reaches $R^2=0.39$--$0.71$ and retains 79--90\% of the predictive power of separately fitted layer-specific dynamics, indicating that much of routing-state evolution follows a reusable process across depth. We then ask whether this shared dynamics is specific to routing or simply reflects the smooth evolution of hidden representations. A matched-rank comparison shows that residual representations are often easier to predict across layers, while router-control states preserve the model's expert choices much more faithfully. This separates generic cross-layer predictability from routing-specific information. Finally, we test whether the predicted canonical states remain meaningful when used in place of native routing states. The transported states preserve local routing behavior, while learned state evolution reduces $Δ\mathrm{NLL}$ relative to simple persistence by 15.7\% on OLMoE and 6.2\% over a 10-router horizon on Phi.
In large-scale pretraining, the algorithm, architecture, and systems decisions are conventionally made in disconnected stages. A scaling law stage selects an architecture and training recipe, optimizing loss under compute constraints, and a separate systems stage then optimizes the implementation for hardware efficiency. In this work, we develop MOSAIC, which formulates model architecture and systems co-design as an optimization problem. MOSAIC couples a predictive scaling law with a calibrated performance model that estimates Model FLOPs Utilization (MFU), communication cost, memory footprint, and the best parallel layout. We instantiate the framework for sparse Mixture-of-Experts (MoE) language models, where expert count, routing sparsity, and other MoE layer dimensions affect both the loss and systems efficiency. We fit a scaling law on sparse MoE models trained on text data, whose scaling dimensions include the sparsity factor, which is the fraction of model parameters inactive per token in a forward pass. The scaling law sweeps in our work span active parameters from $104$ million to $2.7$ billion and total model sizes reaching $79$ billion parameters. We show that, within the calibrated sparsity range, an efficiency-agnostic model-FLOPs budget admits no interior optimal sparsity. The fitted loss decreases monotonically with sparser models and the compute optimum lies at the upper boundary of the data support. An optimal sparsity in MoE models instead emerges under the cluster's systems constraints, as captured by MOSAIC. Our results argue for a shift towards unified architecture and systems co-design for frontier language model training.
Sparse Mixture-of-Experts (MoE) routers commonly use the same scores both to select experts and to weight their already-computed outputs. We study whether these two roles, dispatch and aggregation, should be coupled. On pretrained OLMoE-1B-7B, we keep selected Top-8 expert IDs, expert computation, and total selected router mass fixed and change only within-set aggregation. A structured oracle improves full-horizon cross-entropy by 0.0160 +/- 0.0039 across three seeds; the router's top-scored expert is the counterfactual-best vertex only 17.2% of the time, with router-utility Spearman 0.030. We therefore train Fixed-Dispatch Adaptive Aggregation (FDAA), a 301K-parameter post-compute head optimized directly with the language-modeling objective while freezing the backbone, router, and experts. On OLMoE, FDAA improves fresh WikiText-103 test by Delta CE = -0.1523 +/- 0.0031 across three seeds, and mixed-domain training gives robust gains on WikiText-103, C4, and held-out Penn Treebank under frozen confirmatory evaluation. We also replicate the fixed-dispatch audit on DeepSeek-V2-Lite, which uses Top-6 routed experts plus shared experts. Best-vertex headroom remains significant on WikiText and C4, while router Top1 identifies the best selected expert in only 12.5% and 16.7% of audited examples. In a one-seed mixed-domain replication, FDAA improves locked WikiText and PTB, while C4 is statistically neutral. These results support a cross-architecture distinction between expert selection and expert commitment.
Most language-model access controls regulate behavior while leaving the same computation available to every request. We study a different systems question: can trusted authorization determine which newly trained parameters are reachable by the forward pass? Policy-Masked Private Experts freezes a pretrained sparse Mixture-of-Experts (MoE) model, trains a disjoint expert branch, and selects the public or private pool before top-k routing. The resulting claim is narrow but testable: under the declared trusted computing base (TCB), an unauthorized request executes no private expert. It does not imply that the public model lacks the same semantic capability. We test this separation between execution control and task utility in Qwen3-30B-A3B and DeepSeek-V2-Lite. Three Qwen BF16 seeds update all 32 private experts while the public fingerprint remains unchanged. Across 64 adversarial scenarios and 96 deny/fail-closed events, unauthorized private execution is zero; independent hooks exactly match 11,616 routed private rows and allow-deny-allow recovery is exact. On two prospectively frozen Qwen benchmarks, the private branch improves exact tool use by 5.0 percentage points (pp) (five versus zero discordances; one-sided Holm p = 0.03125, corresponding two-sided exact p = 0.0625) and 21.3 pp (percentile-bootstrap 95% CI [13.3, 29.3], Holm p = 0.000031). Three arm-blinded model evaluators retain a positive external effect of 18.7 pp (95% CI [9.3, 28.0]). A parameter-matched Lora has similar external utility, but a post-hoc request gate leaves 1,225 adapter calls under deny; the disjoint expert branch leaves none. DeepSeek reproduces the route invariant and gains 27.0 pp. A valid sealed evaluation is near-neutral. These results support auditable, reversible control over a trained parameter path, while showing that useful transfer remains distribution dependent.
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.
Sparsely activated Mixture-of-Experts (MoE) language models contain substantial structured redundancy among routed experts, but pruning them without downstream calibration data remains challenging. Existing expert-pruning methods typically rely on a single aggregated importance score, which can bias the retained set toward experts favored by dominant calibration patterns. We propose \textbf{Generic TB-Coverage}, a coverage-aware expert pruning method that uses only generic text corpora (WikiText2 and C4) for calibration. Instead of collapsing expert utility into one score, our method profiles per-expert utility separately on each corpus and enforces a fixed-budget coverage rule that preserves high-utility experts from each corpus before constructing the final pruning mask. Across Qwen1.5-MoE-A2.7B and DeepSeek-MoE-16B-Base at 25\%, 50\%, and 75\% retention budgets, our method improves average accuracy on six common zero-shot benchmarks over random pruning, REAP, and ExpertSparsity, while also reducing perplexity degradation on WikiText2 and C4. The gains are largest under aggressive pruning (25\% and 50\% retain), suggesting that preserving cross-corpus expert coverage is an effective generic-data prior for MoE pruning. Our improvements hold with fixed pruning budgets and no downstream calibration data.
Large-scale retail and industrial forecasting systems contain many heterogeneous time series whose lifecycle, sparsity, volatility, seasonality, spectral patterns, and contextual sensitivity differ substantially. A single forecasting model rarely performs well across all regimes, while dense ensembles increase inference cost and provide limited insight into expert suitability. This paper studies forecastability-aware expert routing: learning how data characteristics determine the suitability of forecasting experts. We propose \method{}, a sparse mixture-of-experts framework that represents each series with a multidimensional forecastability fingerprint, mines expert-suitability targets from validation performance, and trains a cost-aware sparse router to activate a small budgeted set of experts for each series. Using a production-scale vending-machine sales dataset from Shandong New Beiyang (SNBC), where the forecasting component has been integrated into the replenishment-planning pipeline, together with public retail benchmarks, we show that expert suitability varies systematically across data regimes. On the industrial dataset with 5,000+ machines and 60M+ transactions, \method{} Top-2 reduces MSE by 12.4\% over the strongest single expert, LightGBM, while executing 1.92 experts per series on average. The deployed component produces demand forecasts, while inventory-oriented gains are estimated by an offline replay simulator under a fixed replenishment policy rather than by online intervention. The framework turns heterogeneous sales forecasting from heuristic model selection into data mining of forecastability patterns and expert specialization. Code is available at https://github.com/hit636/FAME
Yuetian Lu, Ali Modarressi, Yihong Liu +1cs.CL cs.LG
Activation patching can identify a mixture-of-experts (MoE) block whose clean output restores a corrupted factual prediction. However, because the block output combines contributions from multiple routed experts, block-level rescue does not establish whether the recovery localizes to an individual expert or depends on the routed expert set. We study this question on single-token COUNTERFACT contrasts by corrupting subject-token embeddings, restoring clean block outputs, and then restoring clean-minus-noised expert updates under fixed routing. In Qwen3-30B-A3B-Base, a discovery sweep selects layer 44, and held-out analysis identifies L44E069 as a recurrent routed contributor with positive specificity over same-layer active experts. Its effect is fact-matched and improves true-token probability and rank, which explains part of the layer rescue. In Mixtral-8x7B-v0.1, the selected recurrent singleton is not specific; matched-size controls instead show specificity of the clean-routed top-2 set. These findings show that successful MoE-block restoration does not necessarily imply localization to a single expert.