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Mar 11

COMET: Learning Cardinality Constrained Mixture of Experts with Trees and Local Search

The sparse Mixture-of-Experts (Sparse-MoE) framework efficiently scales up model capacity in various domains, such as natural language processing and vision. Sparse-MoEs select a subset of the "experts" (thus, only a portion of the overall network) for each input sample using a sparse, trainable gate. Existing sparse gates are prone to convergence and performance issues when training with first-order optimization methods. In this paper, we introduce two improvements to current MoE approaches. First, we propose a new sparse gate: COMET, which relies on a novel tree-based mechanism. COMET is differentiable, can exploit sparsity to speed up computation, and outperforms state-of-the-art gates. Second, due to the challenging combinatorial nature of sparse expert selection, first-order methods are typically prone to low-quality solutions. To deal with this challenge, we propose a novel, permutation-based local search method that can complement first-order methods in training any sparse gate, e.g., Hash routing, Top-k, DSelect-k, and COMET. We show that local search can help networks escape bad initializations or solutions. We performed large-scale experiments on various domains, including recommender systems, vision, and natural language processing. On standard vision and recommender systems benchmarks, COMET+ (COMET with local search) achieves up to 13% improvement in ROC AUC over popular gates, e.g., Hash routing and Top-k, and up to 9% over prior differentiable gates e.g., DSelect-k. When Top-k and Hash gates are combined with local search, we see up to 100times reduction in the budget needed for hyperparameter tuning. Moreover, for language modeling, our approach improves over the state-of-the-art MoEBERT model for distilling BERT on 5/7 GLUE benchmarks as well as SQuAD dataset.

GraphHash: Graph Clustering Enables Parameter Efficiency in Recommender Systems

Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques are often employed to map multiple entities to the same embedding and thus reduce the size of the embedding tables. Concurrently, graph-based collaborative signals have emerged as powerful tools in recommender systems, yet their potential for optimizing embedding table reduction remains unexplored. This paper introduces GraphHash, the first graph-based approach that leverages modularity-based bipartite graph clustering on user-item interaction graphs to reduce embedding table sizes. We demonstrate that the modularity objective has a theoretical connection to message-passing, which provides a foundation for our method. By employing fast clustering algorithms, GraphHash serves as a computationally efficient proxy for message-passing during preprocessing and a plug-and-play graph-based alternative to traditional ID hashing. Extensive experiments show that GraphHash substantially outperforms diverse hashing baselines on both retrieval and click-through-rate prediction tasks. In particular, GraphHash achieves on average a 101.52% improvement in recall when reducing the embedding table size by more than 75%, highlighting the value of graph-based collaborative information for model reduction. Our code is available at https://github.com/snap-research/GraphHash.

Deep Multi-View Enhancement Hashing for Image Retrieval

Hashing is an efficient method for nearest neighbor search in large-scale data space by embedding high-dimensional feature descriptors into a similarity preserving Hamming space with a low dimension. However, large-scale high-speed retrieval through binary code has a certain degree of reduction in retrieval accuracy compared to traditional retrieval methods. We have noticed that multi-view methods can well preserve the diverse characteristics of data. Therefore, we try to introduce the multi-view deep neural network into the hash learning field, and design an efficient and innovative retrieval model, which has achieved a significant improvement in retrieval performance. In this paper, we propose a supervised multi-view hash model which can enhance the multi-view information through neural networks. This is a completely new hash learning method that combines multi-view and deep learning methods. The proposed method utilizes an effective view stability evaluation method to actively explore the relationship among views, which will affect the optimization direction of the entire network. We have also designed a variety of multi-data fusion methods in the Hamming space to preserve the advantages of both convolution and multi-view. In order to avoid excessive computing resources on the enhancement procedure during retrieval, we set up a separate structure called memory network which participates in training together. The proposed method is systematically evaluated on the CIFAR-10, NUS-WIDE and MS-COCO datasets, and the results show that our method significantly outperforms the state-of-the-art single-view and multi-view hashing methods.

Real-Time Community Detection in Large Social Networks on a Laptop

For a broad range of research, governmental and commercial applications it is important to understand the allegiances, communities and structure of key players in society. One promising direction towards extracting this information is to exploit the rich relational data in digital social networks (the social graph). As social media data sets are very large, most approaches make use of distributed computing systems for this purpose. Distributing graph processing requires solving many difficult engineering problems, which has lead some researchers to look at single-machine solutions that are faster and easier to maintain. In this article, we present a single-machine real-time system for large-scale graph processing that allows analysts to interactively explore graph structures. The key idea is that the aggregate actions of large numbers of users can be compressed into a data structure that encapsulates user similarities while being robust to noise and queryable in real-time. We achieve single machine real-time performance by compressing the neighbourhood of each vertex using minhash signatures and facilitate rapid queries through Locality Sensitive Hashing. These techniques reduce query times from hours using industrial desktop machines operating on the full graph to milliseconds on standard laptops. Our method allows exploration of strongly associated regions (i.e. communities) of large graphs in real-time on a laptop. It has been deployed in software that is actively used by social network analysts and offers another channel for media owners to monetise their data, helping them to continue to provide free services that are valued by billions of people globally.

Multi-Head Adapter Routing for Cross-Task Generalization

Parameter-efficient fine-tuning (PEFT) for cross-task generalization consists in pre-training adapters on a multi-task training set before few-shot adaptation to test tasks. Polytropon [Ponti et al., 2023] (Poly) jointly learns an inventory of adapters and a routing function that selects a (variable-size) subset of adapters for each task during both pre-training and few-shot adaptation. In this paper, we investigate the role that adapter routing plays in its success and design new variants based on our findings. First, we build on the intuition that finer-grained routing provides more expressivity. Hence, we propose MHR (Multi-Head Routing), which combines subsets of adapter parameters and outperforms Poly under a comparable parameter budget; by only fine-tuning the routing function and not the adapters (MHR-z), we achieve competitive performance with extreme parameter efficiency. Second, we find that Poly/MHR performance is a result of better multi-task optimization, rather than modular inductive biases that facilitate adapter recombination and local adaptation, as previously hypothesized. In fact, we find that MHR exhibits higher gradient alignment between tasks than any other method. Since this implies that routing is only crucial during multi-task pre-training, we propose MHR-mu, which discards routing and fine-tunes the average of the pre-trained adapters during few-shot adaptation. This establishes MHR-mu as an effective method for single-adapter fine-tuning.

Deep Lifelong Cross-modal Hashing

Hashing methods have made significant progress in cross-modal retrieval tasks with fast query speed and low storage cost. Among them, deep learning-based hashing achieves better performance on large-scale data due to its excellent extraction and representation ability for nonlinear heterogeneous features. However, there are still two main challenges in catastrophic forgetting when data with new categories arrive continuously, and time-consuming for non-continuous hashing retrieval to retrain for updating. To this end, we, in this paper, propose a novel deep lifelong cross-modal hashing to achieve lifelong hashing retrieval instead of re-training hash function repeatedly when new data arrive. Specifically, we design lifelong learning strategy to update hash functions by directly training the incremental data instead of retraining new hash functions using all the accumulated data, which significantly reduce training time. Then, we propose lifelong hashing loss to enable original hash codes participate in lifelong learning but remain invariant, and further preserve the similarity and dis-similarity among original and incremental hash codes to maintain performance. Additionally, considering distribution heterogeneity when new data arriving continuously, we introduce multi-label semantic similarity to supervise hash learning, and it has been proven that the similarity improves performance with detailed analysis. Experimental results on benchmark datasets show that the proposed methods achieves comparative performance comparing with recent state-of-the-art cross-modal hashing methods, and it yields substantial average increments over 20\% in retrieval accuracy and almost reduces over 80\% training time when new data arrives continuously.

Unified Functional Hashing in Automatic Machine Learning

The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an evolutionary search method, which samples multiple candidate solutions from a large space and evaluates the quality of each candidate through a long training process. As a result, the search tends to be slow. In this paper, we show that large efficiency gains can be obtained by employing a fast unified functional hash, especially through the functional equivalence caching technique, which we also present. The central idea is to detect by hashing when the search method produces equivalent candidates, which occurs very frequently, and this way avoid their costly re-evaluation. Our hash is "functional" in that it identifies equivalent candidates even if they were represented or coded differently, and it is "unified" in that the same algorithm can hash arbitrary representations; e.g. compute graphs, imperative code, or lambda functions. As evidence, we show dramatic improvements on multiple AutoML domains, including neural architecture search and algorithm discovery. Finally, we consider the effect of hash collisions, evaluation noise, and search distribution through empirical analysis. Altogether, we hope this paper may serve as a guide to hashing techniques in AutoML.

Neural Locality Sensitive Hashing for Entity Blocking

Locality-sensitive hashing (LSH) is a fundamental algorithmic technique widely employed in large-scale data processing applications, such as nearest-neighbor search, entity resolution, and clustering. However, its applicability in some real-world scenarios is limited due to the need for careful design of hashing functions that align with specific metrics. Existing LSH-based Entity Blocking solutions primarily rely on generic similarity metrics such as Jaccard similarity, whereas practical use cases often demand complex and customized similarity rules surpassing the capabilities of generic similarity metrics. Consequently, designing LSH functions for these customized similarity rules presents considerable challenges. In this research, we propose a neuralization approach to enhance locality-sensitive hashing by training deep neural networks to serve as hashing functions for complex metrics. We assess the effectiveness of this approach within the context of the entity resolution problem, which frequently involves the use of task-specific metrics in real-world applications. Specifically, we introduce NLSHBlock (Neural-LSH Block), a novel blocking methodology that leverages pre-trained language models, fine-tuned with a novel LSH-based loss function. Through extensive evaluations conducted on a diverse range of real-world datasets, we demonstrate the superiority of NLSHBlock over existing methods, exhibiting significant performance improvements. Furthermore, we showcase the efficacy of NLSHBlock in enhancing the performance of the entity matching phase, particularly within the semi-supervised setting.

All You Need Is Hashing: Defending Against Data Reconstruction Attack in Vertical Federated Learning

Vertical federated learning is a trending solution for multi-party collaboration in training machine learning models. Industrial frameworks adopt secure multi-party computation methods such as homomorphic encryption to guarantee data security and privacy. However, a line of work has revealed that there are still leakage risks in VFL. The leakage is caused by the correlation between the intermediate representations and the raw data. Due to the powerful approximation ability of deep neural networks, an adversary can capture the correlation precisely and reconstruct the data. To deal with the threat of the data reconstruction attack, we propose a hashing-based VFL framework, called HashVFL, to cut off the reversibility directly. The one-way nature of hashing allows our framework to block all attempts to recover data from hash codes. However, integrating hashing also brings some challenges, e.g., the loss of information. This paper proposes and addresses three challenges to integrating hashing: learnability, bit balance, and consistency. Experimental results demonstrate HashVFL's efficiency in keeping the main task's performance and defending against data reconstruction attacks. Furthermore, we also analyze its potential value in detecting abnormal inputs. In addition, we conduct extensive experiments to prove HashVFL's generalization in various settings. In summary, HashVFL provides a new perspective on protecting multi-party's data security and privacy in VFL. We hope our study can attract more researchers to expand the application domains of HashVFL.

Sampling Is All You Need on Modeling Long-Term User Behaviors for CTR Prediction

Rich user behavior data has been proven to be of great value for Click-Through Rate (CTR) prediction applications, especially in industrial recommender, search, or advertising systems. However, it's non-trivial for real-world systems to make full use of long-term user behaviors due to the strict requirements of online serving time. Most previous works adopt the retrieval-based strategy, where a small number of user behaviors are retrieved first for subsequent attention. However, the retrieval-based methods are sub-optimal and would cause more or less information losses, and it's difficult to balance the effectiveness and efficiency of the retrieval algorithm. In this paper, we propose SDIM (Sampling-based Deep Interest Modeling), a simple yet effective sampling-based end-to-end approach for modeling long-term user behaviors. We sample from multiple hash functions to generate hash signatures of the candidate item and each item in the user behavior sequence, and obtain the user interest by directly gathering behavior items associated with the candidate item with the same hash signature. We show theoretically and experimentally that the proposed method performs on par with standard attention-based models on modeling long-term user behaviors, while being sizable times faster. We also introduce the deployment of SDIM in our system. Specifically, we decouple the behavior sequence hashing, which is the most time-consuming part, from the CTR model by designing a separate module named BSE (behavior Sequence Encoding). BSE is latency-free for the CTR server, enabling us to model extremely long user behaviors. Both offline and online experiments are conducted to demonstrate the effectiveness of SDIM. SDIM now has been deployed online in the search system of Meituan APP.

Secure and Privacy-Preserving Authentication Protocols for Wireless Mesh Networks

Wireless mesh networks (WMNs) have emerged as a promising concept to meet the challenges in next-generation wireless networks such as providing flexible, adaptive, and reconfigurable architecture while offering cost-effective solutions to service providers. As WMNs become an increasingly popular replacement technology for last-mile connectivity to the home networking, community and neighborhood networking, it is imperative to design efficient and secure communication protocols for these networks. However, several vulnerabilities exist in currently existing protocols for WMNs. These security loopholes can be exploited by potential attackers to launch attack on WMNs. The absence of a central point of administration makes securing WMNs even more challenging. The broadcast nature of transmission and the dependency on the intermediate nodes for multi-hop communications lead to several security vulnerabilities in WMNs. The attacks can be external as well as internal in nature. External attacks are launched by intruders who are not authorized users of the network. For example, an intruding node may eavesdrop on the packets and replay those packets at a later point of time to gain access to the network resources. On the other hand, the internal attacks are launched by the nodes that are part of the WMN. On example of such attack is an intermediate node dropping packets which it was supposed to forward. This chapter presents a comprehensive discussion on the current authentication and privacy protection schemes for WMN. In addition, it proposes a novel security protocol for node authentication and message confidentiality and an anonymization scheme for privacy protection of users in WMNs.

Duo-LLM: A Framework for Studying Adaptive Computation in Large Language Models

Large Language Models (LLMs) typically generate outputs token by token using a fixed compute budget, leading to inefficient resource utilization. To address this shortcoming, recent advancements in mixture of expert (MoE) models, speculative decoding, and early exit strategies leverage the insight that computational demands can vary significantly based on the complexity and nature of the input. However, identifying optimal routing patterns for dynamic execution remains an open challenge, limiting the full potential of these adaptive methods. To address this need, we study adaptive computation in LLMs more systematically. We propose a novel framework that integrates smaller auxiliary modules within each Feed-Forward Network layer of the LLM. This design enables dynamic routing of tokens based on task complexity: tokens can be processed by either the small or big modules at each layer, or even bypass certain layers entirely. This allows us to introduce a novel notion of a token's difficulty, defined by its potential to benefit from additional computational resources. Importantly, by employing oracles to identify optimal patterns of adaptive computations, we gain valuable insights into the internal workings of LLMs and the routing processes in a simplified heterogeneous MoE setup. We show that trained routers operate differently from oracles and often yield suboptimal solutions. Notably, activating a large module in just one layer outperforms models that use large modules across all layers, underscoring the gap between practical implementations of routing in MoE models and theoretical optima for adaptive computation.

ExpertFlow: Optimized Expert Activation and Token Allocation for Efficient Mixture-of-Experts Inference

Sparse Mixture of Experts (MoE) models, while outperforming dense Large Language Models (LLMs) in terms of performance, face significant deployment challenges during inference due to their high memory demands. Existing offloading techniques, which involve swapping activated and idle experts between the GPU and CPU, often suffer from rigid expert caching mechanisms. These mechanisms fail to adapt to dynamic routing, leading to inefficient cache utilization, or incur prohibitive costs for prediction training. To tackle these inference-specific challenges, we introduce ExpertFlow, a comprehensive system specifically designed to enhance inference efficiency by accommodating flexible routing and enabling efficient expert scheduling between CPU and GPU. This reduces overhead and boosts system performance. Central to our approach is a predictive routing path-based offloading mechanism that utilizes a lightweight predictor to accurately forecast routing paths before computation begins. This proactive strategy allows for real-time error correction in expert caching, significantly increasing cache hit ratios and reducing the frequency of expert transfers, thereby minimizing I/O overhead. Additionally, we implement a dynamic token scheduling strategy that optimizes MoE inference by rearranging input tokens across different batches. This method not only reduces the number of activated experts per batch but also improves computational efficiency. Our extensive experiments demonstrate that ExpertFlow achieves up to 93.72\% GPU memory savings and enhances inference speed by 2 to 10 times compared to baseline methods, highlighting its effectiveness and utility as a robust solution for resource-constrained inference scenarios.

G-Rank: Unsupervised Continuous Learn-to-Rank for Edge Devices in a P2P Network

Ranking algorithms in traditional search engines are powered by enormous training data sets that are meticulously engineered and curated by a centralized entity. Decentralized peer-to-peer (p2p) networks such as torrenting applications and Web3 protocols deliberately eschew centralized databases and computational architectures when designing services and features. As such, robust search-and-rank algorithms designed for such domains must be engineered specifically for decentralized networks, and must be lightweight enough to operate on consumer-grade personal devices such as a smartphone or laptop computer. We introduce G-Rank, an unsupervised ranking algorithm designed exclusively for decentralized networks. We demonstrate that accurate, relevant ranking results can be achieved in fully decentralized networks without any centralized data aggregation, feature engineering, or model training. Furthermore, we show that such results are obtainable with minimal data preprocessing and computational overhead, and can still return highly relevant results even when a user's device is disconnected from the network. G-Rank is highly modular in design, is not limited to categorical data, and can be implemented in a variety of domains with minimal modification. The results herein show that unsupervised ranking models designed for decentralized p2p networks are not only viable, but worthy of further research.

Challenging the Need for Packet Spraying in Large-Scale Distributed Training

Large-scale distributed training in production datacenters constitutes a challenging workload bottlenecked by network communication. In response, both major industry players (e.g., Ultra Ethernet Consortium) and parts of academia have surprisingly, and almost unanimously, agreed that packet spraying is necessary to improve the performance of large-scale distributed training workloads. In this paper, we challenge this prevailing belief and pose the question: How close can a singlepath transport approach an optimal multipath transport? We demonstrate that singlepath transport (from a NIC's perspective) is sufficient and can perform nearly as well as an ideal multipath transport with packet spraying, particularly in the context of distributed training in leaf-spine topologies. Our assertion is based on four key observations about workloads driven by collective communication patterns: (i) flows within a collective start almost simultaneously, (ii) flow sizes are nearly equal, (iii) the completion time of a collective is more crucial than individual flow completion times, and (iv) flows can be split upon arrival. We analytically prove that singlepath transport, using minimal flow splitting (at the application layer), is equivalent to an ideal multipath transport with packet spraying in terms of maximum congestion. Our preliminary evaluations support our claims. This paper suggests an alternative agenda for developing next-generation transport protocols tailored for large-scale distributed training.

SeQUeNCe: A Customizable Discrete-Event Simulator of Quantum Networks

Recent advances in quantum information science enabled the development of quantum communication network prototypes and created an opportunity to study full-stack quantum network architectures. This work develops SeQUeNCe, a comprehensive, customizable quantum network simulator. Our simulator consists of five modules: Hardware models, Entanglement Management protocols, Resource Management, Network Management, and Application. This framework is suitable for simulation of quantum network prototypes that capture the breadth of current and future hardware technologies and protocols. We implement a comprehensive suite of network protocols and demonstrate the use of SeQUeNCe by simulating a photonic quantum network with nine routers equipped with quantum memories. The simulation capabilities are illustrated in three use cases. We show the dependence of quantum network throughput on several key hardware parameters and study the impact of classical control message latency. We also investigate quantum memory usage efficiency in routers and demonstrate that redistributing memory according to anticipated load increases network capacity by 69.1% and throughput by 6.8%. We design SeQUeNCe to enable comparisons of alternative quantum network technologies, experiment planning, and validation and to aid with new protocol design. We are releasing SeQUeNCe as an open source tool and aim to generate community interest in extending it.

RREH: Reconstruction Relations Embedded Hashing for Semi-Paired Cross-Modal Retrieval

Known for efficient computation and easy storage, hashing has been extensively explored in cross-modal retrieval. The majority of current hashing models are predicated on the premise of a direct one-to-one mapping between data points. However, in real practice, data correspondence across modalities may be partially provided. In this research, we introduce an innovative unsupervised hashing technique designed for semi-paired cross-modal retrieval tasks, named Reconstruction Relations Embedded Hashing (RREH). RREH assumes that multi-modal data share a common subspace. For paired data, RREH explores the latent consistent information of heterogeneous modalities by seeking a shared representation. For unpaired data, to effectively capture the latent discriminative features, the high-order relationships between unpaired data and anchors are embedded into the latent subspace, which are computed by efficient linear reconstruction. The anchors are sampled from paired data, which improves the efficiency of hash learning. The RREH trains the underlying features and the binary encodings in a unified framework with high-order reconstruction relations preserved. With the well devised objective function and discrete optimization algorithm, RREH is designed to be scalable, making it suitable for large-scale datasets and facilitating efficient cross-modal retrieval. In the evaluation process, the proposed is tested with partially paired data to establish its superiority over several existing methods.

MoS: Unleashing Parameter Efficiency of Low-Rank Adaptation with Mixture of Shards

The rapid scaling of large language models necessitates more lightweight finetuning methods to reduce the explosive GPU memory overhead when numerous customized models are served simultaneously. Targeting more parameter-efficient low-rank adaptation (LoRA), parameter sharing presents a promising solution. Empirically, our research into high-level sharing principles highlights the indispensable role of differentiation in reversing the detrimental effects of pure sharing. Guided by this finding, we propose Mixture of Shards (MoS), incorporating both inter-layer and intra-layer sharing schemes, and integrating four nearly cost-free differentiation strategies, namely subset selection, pair dissociation, vector sharding, and shard privatization. Briefly, it selects a designated number of shards from global pools with a Mixture-of-Experts (MoE)-like routing mechanism before sequentially concatenating them to low-rank matrices. Hence, it retains all the advantages of LoRA while offering enhanced parameter efficiency, and effectively circumvents the drawbacks of peer parameter-sharing methods. Our empirical experiments demonstrate approximately 8x parameter savings in a standard LoRA setting. The ablation study confirms the significance of each component. Our insights into parameter sharing and MoS method may illuminate future developments of more parameter-efficient finetuning methods.

Union of Experts: Adapting Hierarchical Routing to Equivalently Decomposed Transformer

Mixture-of-Experts (MoE) enhances model performance while maintaining computational efficiency, making it well-suited for large-scale applications. However, expert in exist MoE paradigm works as an individual, thereby lacking high-quality expert interactions. Moreover, they have not been effectively extended to attention block, which constrains further efficiency improvements. To tackle these issues, we propose Union-of-Experts (UoE), which decomposes transformer into an equitant group of experts, and then implement dynamic routing on input data and experts. Our approach advances MoE design with three key innovations: (1) We conducted equitant expert decomposition on both MLP blocks and attention blocks based on matrix partition in tensor parallelism. (2) We developed two routing paradigms: patch wise data selection and expert selection, to apply routing across different levels. (3) We design the architecture of UoE model, including Selective Multi-Head Attention (SMHA) and Union-of-MLP-Experts (UoME). (4) We develop parallel implementation of UoE's routing and computation operation, and optimize efficiency based on the hardware processing analysis. The experiments demonstrate that the model employed with UoE surpass Full Attention, state-of-art MoEs and efficient transformers in several tasks across image and natural language domains. The source codes are available at https://github.com/YujiaoYang-work/UoE.

FSMoE: A Flexible and Scalable Training System for Sparse Mixture-of-Experts Models

Recent large language models (LLMs) have tended to leverage sparsity to reduce computations, employing the sparsely activated mixture-of-experts (MoE) technique. MoE introduces four modules, including token routing, token communication, expert computation, and expert parallelism, that impact model quality and training efficiency. To enable versatile usage of MoE models, we introduce FSMoE, a flexible training system optimizing task scheduling with three novel techniques: 1) Unified abstraction and online profiling of MoE modules for task scheduling across various MoE implementations. 2) Co-scheduling intra-node and inter-node communications with computations to minimize communication overheads. 3) To support near-optimal task scheduling, we design an adaptive gradient partitioning method for gradient aggregation and a schedule to adaptively pipeline communications and computations. We conduct extensive experiments with configured MoE layers and real-world MoE models on two GPU clusters. Experimental results show that 1) our FSMoE supports four popular types of MoE routing functions and is more efficient than existing implementations (with up to a 1.42times speedup), and 2) FSMoE outperforms the state-of-the-art MoE training systems (DeepSpeed-MoE and Tutel) by 1.18times-1.22times on 1458 MoE layers and 1.19times-3.01times on real-world MoE models based on GPT-2 and Mixtral using a popular routing function.