Mixture-of-experts (MoE) models have become an important approach for scaling model parameters. Modern MoE architectures increasingly combine two design choices: fine-grained expert segmentation and shared experts. The former increases expressiveness by enabling more expert combinations at a fixed activation ratio, and the latter introduces experts that are active for every token. We identify an exploration dilemma between these designs: shared experts can make routing less exploratory by reducing the variability of token representations. This conflicts with the greater need for exploration induced by fine-grained expert segmentation due to the combinatorially enlarged routing space. Consequently, the additional expressiveness offered by fine-grained segmentation may not be fully realized in practice. MirrorMoE is proposed to reconcile this exploration dilemma by shrinking the exploration space through token-adaptive suppression of unnecessary experts. MirrorMoE consistently improves performance across model scales.
Figures & tables
Figure 1: Comparison of MoEs with and without shared experts (SE) and the proposed MirrorMoE. MirrorMoE consistently i) achieves the best performance, ii) realizes the expressiveness gains from larger K , and iii) enables shared-expert MoEs to outperform their non-shared counterparts.
Figure 2: Perplexity increase after ablating individual experts. In the right subplot, the two rightmost columns, separated by a solid line, correspond to shared experts.
Figure 3: Shared experts make MoE routing less exploratory.
Figure 4: Preview of how MirrorMoE in Alg. 1 actively suppresses experts on a 100M MoE model. The rebound in Keff results from annealing ρ .
Model
Experts
Depth
PPL ( ↓ )
iteration time (ms) ( ↓ )
Total-activated params.
K / R / S
Vanilla
MirrorMoE
Vanilla
MirrorMoE
MoE-100M-A38M
8/64/2
1D + 8S
54.78
51.77
7871.3 ± 65.9
7844.4 ± 85.6
MoE-498M-A121M
8/64/2
1D + 12S
28.31
27.36
13550.0 ± 63.0
13426.7 ± 83.3
MoE-625M-A100M
8/128/2
1D + 8S
28.46
27.84
9527.5 ± 45.4
9462.5 ± 61.2
MoE-2.4B-A270M
8/128/2
1D + 15S
21.17
20.50
25711.1 ± 176.2
25635.4 ± 109.4
Table 1: Pretraining performance of MirrorMoE across scales. D/S in the depth column denotes dense/sparse Transformer layers.
Model
Method
ARC-E
OBQA
HellaSwag
PIQA
BoolQ
SIQA
Avg ( ↑ )
MoE-100M-A38M
Vanilla
32.11
26.40
26.62
57.56
42.66
34.29
36.61
MirrorMoE
34.22
26.00
25.76
58.00
42.48
34.49
36.82
MoE-498M-A121M
Vanilla
39.44
26.80
29.87
61.43
58.65
36.69
42.15
MirrorMoE
41.04
27.80
30.33
64.31
59.20
36.95
43.27
MoE-625M-A100M
Vanilla
41.12
28.20
29.97
61.10
61.47
37.36
43.20
MirrorMoE
41.37
29.80
30.23
62.08
61.16
36.59
43.53
Table 2: Downstream performance of MoE models trained with MirrorMoE.
Figure 7
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Parameter
MoE-100M-A38M
MoE-498M-A121M
MoE-625M-A100M
MoE-2.4B-A270M
Dense / MoE layers
1 / 8
1 / 12
1 / 8
1 / 15
Layer layout
1D + 8S
1D + 12S
1D + 8S
1D + 15S
Hidden size ( dmodel )
256
512
512
768
Dense FFN hidden
1368
2736
2736
3648
MoE FFN hidden (per expert)
176
352
352
512
Shared expert FFN (2 × )
352
704
704
1024
Appendix
Table 4: Model configurations used in our experiments.
Figure 6: Router variance under different levels of Gumbel perturbation.
Top- (K−S)
Sto- (K−S)
Top-2 with Sto- (K−S−2)
PPL
54.78
55.74
55.38
Appendix
Table 5: Intrinsic difficulty of increasing exploration
Figure 7: Effective experts vs. iterations plot by layers.
vanilla balancing loss
our load balancing loss ( 6 )
PPL
52.94
51.77
runtime
7727.1 ± 91.8
7844.4 ± 85.6
Appendix
Table 6: Comparison of different load balancing loss for MirrorMoE
Model
Experts
Depth
PPL ( ↓ )
Total-activated params
K / R / S
Vanilla
MirrorMoE
MoE-NS-97M-A36M
8/64/0
8S
52.01
51.23
MoE-NS-480M-A115M
8/64/0
12S
28.24
28.20
MoE-NS-614M-A95M
8/128/0
8S
28.42
28.49
MoE-NS-2.5B-A270M
8/128/0
16S
20.85
20.83
Appendix
Table 7: MirrorMoE has less gains when pretraining MoEs without shared experts.
Method
PPL ( ↓ )
# activated experts at first iteration
# activated experts at last iteration
Vanilla
54.78
8
8
MirrorMoE
51.77
8
8
Top- p , p=0.4
55.64
18.65
6.73
Top- p , p=0.6
54.09
29.46
10.79
Appendix
Table 8: Comparison with top- p routing. Activated experts are averaged over layers and tokens for top- p routing.
Mixture-of-experts models use input-dependent routing to activate specialized subnetworks, increasing model capacity without running every parameter for each input.
Standard Mixture-of-Experts (MoE) models rely on centralized routing mechanisms that introduce rigid inductive biases. We propose Routing-Free MoE which eliminates any hard-coded centralized designs including external routers, Softmax, Top-K and load balancing, instead encapsulating all activation functionalities within individual experts and directly optimized through continuous gradient flow, enabling each expert to determine its activation entirely on its own. We introduce a unified adaptive load-balancing framework to simultaneously optimize both expert-balancing and token-balancing objectives through a configurable interpolation, allowing flexible and customizable resource allocation. Extensive experiments show that Routing-Free MoE can consistently outperform baselines with better scalability and robustness. We analyze its behavior in detail and offer insights that may facilitate future MoE design ad optimization.
Yilun Liu, Jinru Han, Sikuan Yan +2
Ludwig Maximilian University of Munich · Munich Center for Machine Learning · University of California, Los Angeles
Mixture-of-experts (MoE) models enable scalable transformer architectures by activating only a subset of experts per token. Recent evidence suggests that performance improves with increasingly granular experts, i.e., many small experts instead of a few large ones. However, this regime substantially increases routing cost, which can dominate computation. We introduce adaptive inverted-index routing for MoE (AIR-MoE), an inverted-index-inspired routing architecture based on vector quantization (VQ). In a first stage, AIR-MoE performs coarse shortlisting by assigning tokens to VQ codewords to construct a candidate set of experts. In a second stage, fine scoring computes exact routing scores restricted to this shortlist. This two-stage procedure approximates true top-k routing while avoiding full expert scoring and, in contrast to prior work, imposing no structural constraints on expert parameters. AIR-MoE serves as a drop-in replacement for standard routers and requires no modifications to the model architecture or loss function. We further provide a lower bound on the mass recall achieved by AIR-MoE that yields insights into its inner workings. Empirically, we demonstrate that AIR-MoE achieves improved performance compared to existing routing approaches in granular MoE settings.
Klaus-Rudolf Kladny, Maximilian Mordig, Bernhard Schölkopf +1
Max Planck Institute for Intelligent Systems, Tübingen · Tübingen AI Center · ETH Zurich +1
Sparse Mixture-of-Experts (MoE) architectures route each token through a subset of experts at each layer independently. We propose viewing MoE computation through the lens of expert paths -- the sequence of expert selections a token makes across all layers. This perspective reveals that, despite NL possible paths for N experts across L layers, tokens in practice cluster into a small fraction of paths that align with linguistic function, yet the vast majority of paths remain unexplored, representing a statistical inefficiency. This motivates architectures that constrain the effective path space to amplify this natural concentration. As one instantiation, we introduce \pathmoe{}, which shares router parameters across blocks of consecutive layers. Analysis confirms that \pathmoe{} amplifies the emergent path structure: it produces more concentrated path clusters, better cross-layer consistency, and greater robustness to routing perturbations. Experiments on 0.9B and 16B parameter \pathmoe{} models demonstrate consistent improvements on perplexity and downstream tasks over independent routing, while eliminating the need for auxiliary losses. These results establish expert paths as a useful design axis for MoE architectures, complementary to existing work on independent routing mechanisms.