The capacity of a neural network to absorb information is limited by the number of its parameters, and as a consequence, finding more effective ways to increase model parameters has become a trend in deep learning research. Mixture-of-experts (MoE), a type of conditional computation where parts of the network are activated on a per-example basis, has been proposed as a way of dramatically increasing model capacity without a proportional increase in computation. In sparsely-activated variants of MoE models (e.g., Switch Transformer, GLaM, V-MoE), a subset of experts is selected on a per-token or per-example basis, thus creating sparsity in the network. Such models have demonstrated better scaling in multiple domains and better retention capability in a continual learning setting (e.g., Expert Gate). However, a poor expert routing strategy can cause certain experts to be under-trained, leading to an expert being under or over-specialized.

MoE operates by adopting a number of experts, each as a sub-network, and activating only one or a few experts for each input token. A gating network must be chosen and optimized in order to route each token to the most suited expert(s). Depending on how tokens are mapped to experts, MoE can be sparse or dense. Sparse MoE only selects a subset of experts when routing each token, reducing computational cost as compared to a dense MoE. For example, recent work has implemented sparse routing via k-means clustering, linear assignment to maximize token-expert affinities, or hashing. Google also recently announced GLaM and V-MoE, both of which advance the state of the art in natural language processing and computer vision via sparsely gated MoE with top-k token routing, demonstrating better performance scaling with sparsely activated MoE layers. Many of these prior works used a token choice routing strategy in which the routing algorithm picks the best one or two experts for each token.

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In addition to load imbalance, most prior works allocate a fixed number of experts to each token using a top-k function, regardless of the relative importance of different tokens. We argue that different tokens should be received by a variable number of experts, conditioned on token importance or difficulty.

To address the above issues, we propose a heterogeneous MoE that employs the expert choice routing method illustrated below. Instead of having tokens select the top-k experts, the experts with predetermined buffer capacity are assigned to the top-k tokens. This method guarantees even load balancing, allows a variable number of experts for each token, and achieves substantial gains in training efficiency and downstream performance. EC routing speeds up training convergence by over 2x in an 8B/64E (8 billion activated parameters, 64 experts) model, compared to the top-1 and top-2 gating counterparts in Switch Transformer, GShard, and GLaM.

In EC routing, we set expert capacity k as the average tokens per expert in a batch of input sequences multiplied by a capacity factor, which determines the average number of experts that can be received by each token. To learn the token-to-expert affinity, our method produces a token-to-expert score matrix that is used to make routing decisions. The score matrix indicates the likelihood of a given token in a batch of input sequences being routed to a given expert.

Similar to Switch Transformer and GShard, we apply an MoE and gating function in the dense feedforward (FFN) layer, as it is the most computationally expensive part of a Transformer-based network. After producing the token-to-expert score matrix, a top-k function is applied along the token dimension for each expert to pick the most relevant tokens. A permutation function is then applied based on the generated indexes of the token, to create a hidden value with an additional expert dimension. The data is split across multiple experts such that all experts can execute the same computational kernel concurrently on a subset of tokens. Because a fixed expert capacity can be determined, we no longer overprovision expert capacity due to load imbalancing, thus significantly reducing training and inference step time by around 20% compared to GLaM.

Our empirical results indicate that capping the number of experts for each token hurts the fine-tuning score by 1 point on average. This study confirms that allowing a variable number of experts per token is indeed helpful. On the other hand, we compute statistics on token-to-expert routing, particularly on the ratio of tokens that have been routed to a certain number of experts. We find that a majority of tokens have been routed to one or two experts while 23% have been routed to three or four experts and only about 3% tokens have been routed to more than four experts, thus verifying our hypothesis that expert choice routing learns to allocate a variable number of experts to tokens.

We propose a new routing method for sparsely activated mixture-of-experts models. This method addresses load imbalance and under-utilization of experts in conventional MoE methods, and enables the selection of different numbers of experts for each token. Our model demonstrates more than 2x training efficiency improvement when compared to the state-of-the-art GShard and Switch Transformer models, and achieves strong gains when fine-tuning on 11 datasets in the GLUE and SuperGLUE benchmark.

Our approach for expert choice routing enables heterogeneous MoE with straightforward algorithmic innovations. We hope that this may lead to more advances in this space at both the application and system levels.

Experts-Choice Decal Film is available in both clear and white one and three sheet packs. With Experts-Choice plain decal film you can use your own color ink jet or laser printer to make home made decals. You can also use a color photo copier to reproduce any decal of your choice. This material allows you to use existing artwork from books, magazines, computer clip art, or your own original art to create any decal. The standard 8 1/2 X 11 sheets work perfectly with any copier or printer.

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That's strange: expert's choice decals paper is IMHO very thin, so much that I'm always very careful with it as the risk of major disaster is always present. It also has no visible film at all if applied following the usual procedure. The model shown here has all the black markings printed with an inkjet on this same paper. The model is not great, but the decals look like painted on

Instead of choosing the top-k experts for each token, you choose the top-k tokens per expert. Seems to work even better. I actually started coding this independently last month (scooped!), and the subtleties are: 1) it makes your routing function super cheap, which is great, but 2) you end up summing different numbers of activation tensors for each token, which is hard to make efficient. You can embedding_bag this, but even constructing the indices is a pain.

Supports designing efficient discrete choice experiments (DCEs). Experimental designs can be formed on the basis of orthogonal arrays or search methods for optimal designs (Federov or mixed integer programs). Various methods for converting these experimental designs into a discrete choice experiment. Many efficiency measures! Draws from literature of Kuhfeld (2010) and Street et. al (2005) .

Sparsely-activated Mixture-of-experts (MoE) models allow the number of parameters to greatly increase while keeping the amount of computation for a given token or a given sample unchanged. However, a poor expert routing strategy (e.g. one resulting in load imbalance) can cause certain experts to be under-trained, leading to an expert being under or over-specialized. Prior work allocates a fixed number of experts to each token using a top-k function regardless of the relative importance of different tokens. To address this, we propose a heterogeneous mixture-of-experts employing an expert choice method. Instead of letting tokens select the top-k experts, we have experts selecting the top-k tokens. As a result, each token can be routed to a variable number of experts and each expert can have a fixed bucket size. We systematically study pre-training speedups using the same computational resources of the Switch Transformer top-1 and GShard top-2 gating of prior work and find that our method improves training convergence time by more than 2x. For the same computational cost, our method demonstrates higher performance in fine-tuning 11 selected tasks in the GLUE and SuperGLUE benchmarks. For a smaller activation cost, our method outperforms the T5 dense model in 7 out of the 11 tasks.

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