Daily Papers

The task of multimodal learning has seen a growing interest recently as it allows for training neural architectures based on different modalities such as vision, text, and audio. One challenge in training such models is that they need to jointly learn semantic concepts and their relationships across different input representations. Capsule networks have been shown to perform well in context of capturing the relation between low-level input features and higher-level concepts. However, capsules have so far mainly been used only in small-scale fully supervised settings due to the resource demand of conventional routing algorithms. We present a new multimodal capsule network that allows us to leverage the strength of capsules in the context of a multimodal learning framework on large amounts of video data. To adapt the capsules to large-scale input data, we propose a novel routing by self-attention mechanism that selects relevant capsules which are then used to generate a final joint multimodal feature representation. This allows not only for robust training with noisy video data, but also to scale up the size of the capsule network compared to traditional routing methods while still being computationally efficient. We evaluate the proposed architecture by pretraining it on a large-scale multimodal video dataset and applying it on four datasets in two challenging downstream tasks. Results show that the proposed multimodal capsule network is not only able to improve results compared to other routing techniques, but also achieves competitive performance on the task of multimodal learning.

Information retrieval methods often rely on a single embedding model trained on large, general-domain datasets like MSMARCO. While this approach can produce a retriever with reasonable overall performance, models trained on domain-specific data often yield better results within their respective domains. While prior work in information retrieval has tackled this through multi-task training, the topic of combining multiple domain-specific expert retrievers remains unexplored, despite its popularity in language model generation. In this work, we introduce RouterRetriever, a retrieval model that leverages multiple domain-specific experts along with a routing mechanism to select the most appropriate expert for each query. It is lightweight and allows easy addition or removal of experts without additional training. Evaluation on the BEIR benchmark demonstrates that RouterRetriever outperforms both MSMARCO-trained (+2.1 absolute nDCG@10) and multi-task trained (+3.2) models. This is achieved by employing our routing mechanism, which surpasses other routing techniques (+1.8 on average) commonly used in language modeling. Furthermore, the benefit generalizes well to other datasets, even in the absence of a specific expert on the dataset. To our knowledge, RouterRetriever is the first work to demonstrate the advantages of using multiple domain-specific expert embedding models with effective routing over a single, general-purpose embedding model in retrieval tasks.

The Mixture-of-Experts (MoE) models have gained significant attention in deep learning due to their dynamic resource allocation and superior performance across diverse tasks. However, efficiently training these models remains challenging. The MoE upcycling technique has been proposed to reuse and improve existing model components, thereby minimizing training overhead. Despite this, simple routers, such as linear routers, often struggle with complex routing tasks within MoE upcycling. In response, we propose a novel routing technique called Router Upcycling to enhance the performance of MoE upcycling models. Our approach initializes multiple routers from the attention heads of preceding attention layers during upcycling. These routers collaboratively assign tokens to specialized experts in an attention-like manner. Each token is processed into diverse queries and aligned with the experts' features (serving as keys). Experimental results demonstrate that our method achieves state-of-the-art (SOTA) performance, outperforming other upcycling baselines.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

In LLM serving, reusing the KV cache of prompts across requests is critical for reducing TTFT and serving costs. Cache-affinity scheduling, which co-locates requests with the same prompt prefix to maximize KV cache reuse, often conflicts with load-balancing scheduling that distributes requests evenly across compute instances. Existing schedulers fail to reconcile this trade-off as they operate within a single mapping space, typically applying cache-affinity routing to a subset of requests and load-balanced routing to the rest, without a unified solution to achieve both goals. To address this limitation, we propose DualMap, a dual-mapping scheduling strategy for distributed LLM serving that achieves both cache affinity and load balancing. Its key idea is to map each request to two candidate instances via two independent hash functions based on the request prompt, then intelligently select the better candidate based on current system states. This design increases the likelihood that requests with shared prefixes are co-located, while evenly dispersing distinct prefixes across the cluster via ``the power of two choices''. To make DualMap robust under dynamic and skewed real-world workloads, we incorporate three techniques: 1) SLO-aware request routing, which prioritizes cache affinity but switches to load-aware scheduling when TTFT exceeds the SLO, enhancing load balance without sacrificing cache reuse; 2) hotspot-aware rebalancing, which dynamically migrates requests from overloaded to underloaded instances, mitigating hotspots and rebalancing the system; 3) lightweight dual-hash-ring scaling, which leverages a dual-hash-ring mapping to support fast and low-overhead instance scaling without costly global remapping. Experiments on real-world workloads show that DualMap improves effective request capacity by up to 2.25times under the same TTFT SLO constraints compared with SOTA work.

We present Nucleus-Image, a text-to-image generation model that establishes a new Pareto frontier in quality-versus-efficiency by matching or exceeding leading models on GenEval, DPG-Bench, and OneIG-Bench while activating only approximately 2B parameters per forward pass. Nucleus-Image employs a sparse mixture-of-experts (MoE) diffusion transformer architecture with Expert-Choice Routing that scales total model capacity to 17B parameters across 64 routed experts per layer. We adopt a streamlined architecture optimized for inference efficiency by excluding text tokens from the transformer backbone entirely and using joint attention that enables text KV sharing across timesteps. To improve routing stability when using timestep modulation, we introduce a decoupled routing design that separates timestep-aware expert assignment from timestep-conditioned expert computation. We construct a large-scale training corpus of 1.5B high-quality training pairs spanning 700M unique images through multi-stage filtering, deduplication, aesthetic tiering, and caption curation. Training follows a progressive resolution curriculum (256 to 512 to 1024) with multi-aspect-ratio bucketing at every stage, coupled with progressive sparsification of the expert capacity factor. We adopt the Muon optimizer and share our parameter grouping recipe tailored for diffusion models with timestep modulation. Nucleus-Image demonstrates that sparse MoE scaling is a highly effective path to high-quality image generation, reaching the performance of models with significantly larger active parameter budgets at a fraction of the inference cost. These results are achieved without post-training optimization of any kind: no reinforcement learning, no direct preference optimization, and no human preference tuning. We release the training recipe, making Nucleus-Image the first fully open-source MoE diffusion model at this quality.

Upcycling pre-trained dense language models into sparse mixture-of-experts (MoE) models is an efficient approach to increase the model capacity of already trained models. However, optimal techniques for upcycling at scale remain unclear. In this work, we conduct an extensive study of upcycling methods and hyperparameters for billion-parameter scale language models. We propose a novel "virtual group" initialization scheme and weight scaling approach to enable upcycling into fine-grained MoE architectures. Through ablations, we find that upcycling outperforms continued dense model training. In addition, we show that softmax-then-topK expert routing improves over topK-then-softmax approach and higher granularity MoEs can help improve accuracy. Finally, we upcycled Nemotron-4 15B on 1T tokens and compared it to a continuously trained version of the same model on the same 1T tokens: the continuous trained model achieved 65.3% MMLU, whereas the upcycled model achieved 67.6%. Our results offer insights and best practices to effectively leverage upcycling for building MoE language models.

To address overfitting and enhance model generalization in gastroenterological polyp size assessment, our study introduces Feature-Selection Gates (FSG) or Hard-Attention Gates (HAG) alongside Gradient Routing (GR) for dynamic feature selection. This technique aims to boost Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) by promoting sparse connectivity, thereby reducing overfitting and enhancing generalization. HAG achieves this through sparsification with learnable weights, serving as a regularization strategy. GR further refines this process by optimizing HAG parameters via dual forward passes, independently from the main model, to improve feature re-weighting. Our evaluation spanned multiple datasets, including CIFAR-100 for a broad impact assessment and specialized endoscopic datasets (REAL-Colon, Misawa, and SUN) focusing on polyp size estimation, covering over 200 polyps in more than 370,000 frames. The findings indicate that our HAG-enhanced networks substantially enhance performance in both binary and triclass classification tasks related to polyp sizing. Specifically, CNNs experienced an F1 Score improvement to 87.8% in binary classification, while in triclass classification, the ViT-T model reached an F1 Score of 76.5%, outperforming traditional CNNs and ViT-T models. To facilitate further research, we are releasing our codebase, which includes implementations for CNNs, multistream CNNs, ViT, and HAG-augmented variants. This resource aims to standardize the use of endoscopic datasets, providing public training-validation-testing splits for reliable and comparable research in gastroenterological polyp size estimation. The codebase is available at github.com/cosmoimd/feature-selection-gates.

Large language models' significant advances in capabilities are accompanied by significant increases in inference costs. Model routing is a simple technique for reducing inference cost, wherein one maintains a pool of candidate LLMs, and learns to route each prompt to the smallest feasible LLM. Existing works focus on learning a router for a fixed pool of LLMs. In this paper, we consider the problem of dynamic routing, where new, previously unobserved LLMs are available at test time. We propose a new approach to this problem that relies on representing each LLM as a feature vector, derived based on predictions on a set of representative prompts. Based on this, we detail two effective strategies, relying on cluster-based routing and a learned cluster map respectively. We prove that these strategies are estimates of a theoretically optimal routing rule, and provide an excess risk bound to quantify their errors. Experiments on a range of public benchmarks show the effectiveness of the proposed strategies in routing amongst more than 30 unseen LLMs.

The Mixture-of-Experts (MoE) technique can scale up the model size of Transformers with an affordable computational overhead. We point out that existing learning-to-route MoE methods suffer from the routing fluctuation issue, i.e., the target expert of the same input may change along with training, but only one expert will be activated for the input during inference. The routing fluctuation tends to harm sample efficiency because the same input updates different experts but only one is finally used. In this paper, we propose StableMoE with two training stages to address the routing fluctuation problem. In the first training stage, we learn a balanced and cohesive routing strategy and distill it into a lightweight router decoupled from the backbone model. In the second training stage, we utilize the distilled router to determine the token-to-expert assignment and freeze it for a stable routing strategy. We validate our method on language modeling and multilingual machine translation. The results show that StableMoE outperforms existing MoE methods in terms of both convergence speed and performance.

Mixture of Experts (MoE) architectures have become a key approach for scaling large language models, with growing interest in extending them to multimodal tasks. Existing methods to build multimodal MoE models either incur high training costs or suffer from degraded language capabilities when adapting pretrained models. To address this, we propose Soft ModalityAware Routing (SMAR), a novel regularization technique that uses Kullback Leibler divergence to control routing probability distributions across modalities, encouraging expert specialization without modifying model architecture or heavily relying on textual data. Experiments on visual instruction tuning show that SMAR preserves language ability at 86.6% retention with only 2.5% pure text, outperforming baselines while maintaining strong multimodal performance. Our approach offers a practical and efficient solution to balance modality differentiation and language capabilities in multimodal MoE models.

Diffusion models are well known for their ability to generate a high-fidelity image for an input prompt through an iterative denoising process. Unfortunately, the high fidelity also comes at a high computational cost due the inherently sequential generative process. In this work, we seek to optimally balance quality and computational cost, and propose a framework to allow the amount of computation to vary for each prompt, depending on its complexity. Each prompt is automatically routed to the most appropriate text-to-image generation function, which may correspond to a distinct number of denoising steps of a diffusion model, or a disparate, independent text-to-image model. Unlike uniform cost reduction techniques (e.g., distillation, model quantization), our approach achieves the optimal trade-off by learning to reserve expensive choices (e.g., 100+ denoising steps) only for a few complex prompts, and employ more economical choices (e.g., small distilled model) for less sophisticated prompts. We empirically demonstrate on COCO and DiffusionDB that by learning to route to nine already-trained text-to-image models, our approach is able to deliver an average quality that is higher than that achievable by any of these models alone.

Multi-model routing has evolved from an engineering technique into essential infrastructure, yet existing work lacks a systematic, reproducible benchmark for evaluating vision-language models (VLMs). We present VL-RouterBench to assess the overall capability of VLM routing systems systematically. The benchmark is grounded in raw inference and scoring logs from VLMs and constructs quality and cost matrices over sample-model pairs. In scale, VL-RouterBench covers 14 datasets across 3 task groups, totaling 30,540 samples, and includes 15 open-source models and 2 API models, yielding 519,180 sample-model pairs and a total input-output token volume of 34,494,977. The evaluation protocol jointly measures average accuracy, average cost, and throughput, and builds a ranking score from the harmonic mean of normalized cost and accuracy to enable comparison across router configurations and cost budgets. On this benchmark, we evaluate 10 routing methods and baselines and observe a significant routability gain, while the best current routers still show a clear gap to the ideal Oracle, indicating considerable room for improvement in router architecture through finer visual cues and modeling of textual structure. We will open-source the complete data construction and evaluation toolchain to promote comparability, reproducibility, and practical deployment in multimodal routing research.

The mixture of experts (MoE) model is a sparse variant of large language models (LLMs), designed to hold a better balance between intelligent capability and computational overhead. Despite its benefits, MoE is still too expensive to deploy on resource-constrained edge devices, especially with the demands of on-device inference services. Recent research efforts often apply model compression techniques, such as quantization, pruning and merging, to restrict MoE complexity. Unfortunately, due to their predefined static model optimization strategies, they cannot always achieve the desired quality-overhead trade-off when handling multiple requests, finally degrading the on-device quality of service. These limitations motivate us to propose the D^2MoE, an algorithm-system co-design framework that matches diverse task requirements by dynamically allocating the most proper bit-width to each expert. Specifically, inspired by the nested structure of matryoshka dolls, we propose the matryoshka weight quantization (MWQ) to progressively compress expert weights in a bit-nested manner and reduce the required runtime memory. On top of it, we further optimize the I/O-computation pipeline and design a heuristic scheduling algorithm following our hottest-expert-bit-first (HEBF) principle, which maximizes the expert parallelism between I/O and computation queue under constrained memory budgets, thus significantly reducing the idle temporal bubbles waiting for the experts to load. Evaluations on real edge devices show that D^2MoE improves the overall inference throughput by up to 1.39times and reduces the peak memory footprint by up to 53% over the latest on-device inference frameworks, while still preserving comparable serving accuracy as its INT8 counterparts.

Low-rank adapters (LoRAs) are a parameter-efficient finetuning technique that injects trainable low-rank matrices into pretrained models to adapt them to new tasks. Mixture-of-LoRAs models expand neural networks efficiently by routing each layer input to a small subset of specialized LoRAs of the layer. Existing Mixture-of-LoRAs routers assign a learned routing weight to each LoRA to enable end-to-end training of the router. Despite their empirical promise, we observe that the routing weights are typically extremely imbalanced across LoRAs in practice, where only one or two LoRAs often dominate the routing weights. This essentially limits the number of effective LoRAs and thus severely hinders the expressive power of existing Mixture-of-LoRAs models. In this work, we attribute this weakness to the nature of learnable routing weights and rethink the fundamental design of the router. To address this critical issue, we propose a new router designed that we call Reinforcement Routing for Mixture-of-LoRAs (ReMix). Our key idea is using non-learnable routing weights to ensure all active LoRAs to be equally effective, with no LoRA dominating the routing weights. However, our routers cannot be trained directly via gradient descent due to our non-learnable routing weights. Hence, we further propose an unbiased gradient estimator for the router by employing the reinforce leave-one-out (RLOO) technique, where we regard the supervision loss as the reward and the router as the policy in reinforcement learning. Our gradient estimator also enables to scale up training compute to boost the predictive performance of our ReMix. Extensive experiments demonstrate that our proposed ReMix significantly outperform state-of-the-art parameter-efficient finetuning methods under a comparable number of activated parameters.

Scaling the size of a model enhances its capabilities but significantly increases computation complexity. Mixture-of-Experts models (MoE) address the issue by allowing model size to scale up without substantially increasing training or inference costs. Despite their promising results, MoE models encounter several challenges. Primarily, for dynamic routing methods, the dispersion of training tokens across multiple experts can lead to underfitting, particularly for infrequent tokens. Additionally, while fixed routing methods can mitigate that issue, they compromise on the diversity of representations. In this paper, we propose MaskMoE, a method designed to enhance token-level learning by employing a routing masking technique within the Mixture-of-Experts model. MaskMoE is capable of maintaining representation diversity while achieving more comprehensive training. Experimental results demonstrate that our method outperforms previous dominant Mixture-of-Experts models in terms of both perplexity (PPL) and downstream task performance.

The complementary potential of Large Language Models (LLM) assumes off-the-shelf LLMs have heterogeneous expertise in a wide range of domains and tasks so that an ensemble of LLMs can achieve consistently better performance. Existing ensemble methods for LLMs mainly focus on reward model ranking of outputs, leading to significant computation overhead. To combat this issue, we revisit the complementary potential of LLMs and further elaborate it by mining latent expertise with off-the-shelf reward models. We propose Zooter, a reward-guided routing method distilling rewards on training queries to train a routing function, which can precisely distribute each query to the LLM with expertise about it. We also integrate a tag-based label enhancement to mitigate noise from uncertainty when using rewards as silver supervision. Zooter shows computation efficiency in inference as it introduces only a minor computation overhead of a routing function compared with reward model ranking methods. We evaluate Zooter on a comprehensive benchmark collection with 26 subsets on different domains and tasks. Zooter outperforms the best single model on average and ranks first on 44% of tasks, even surpassing multiple reward model ranking methods.

This paper introduces RouteFinder, a comprehensive foundation model framework to tackle different Vehicle Routing Problem (VRP) variants. Our core idea is that a foundation model for VRPs should be able to represent variants by treating each as a subset of a generalized problem equipped with different attributes. We propose a unified VRP environment capable of efficiently handling any attribute combination. The RouteFinder model leverages a modern transformer-based encoder and global attribute embeddings to improve task representation. Additionally, we introduce two reinforcement learning techniques to enhance multi-task performance: mixed batch training, which enables training on different variants at once, and multi-variant reward normalization to balance different reward scales. Finally, we propose efficient adapter layers that enable fine-tuning for new variants with unseen attributes. Extensive experiments on 48 VRP variants show RouteFinder outperforms recent state-of-the-art learning methods. Code: https://github.com/ai4co/routefinder.

Large language models (LLMs) have demonstrated exceptional performance across a wide range of natural language tasks. However, selecting the optimal LLM to respond to a user query often necessitates a delicate balance between performance and cost. While powerful models deliver better results, they come at a high cost, whereas smaller models are more cost-effective but less capable. To address this trade-off, we propose IRT-Router, a multi-LLM routing framework that efficiently routes user queries to the most suitable LLM. Inspired by Item Response Theory (IRT), a psychological measurement methodology, IRT-Router explicitly models the relationship between LLM capabilities and user query attributes. This not only enables accurate prediction of response performance but also provides interpretable insights, such as LLM abilities and query difficulty. Additionally, we design an online query warm-up technique based on semantic similarity, further enhancing the online generalization capability of IRT-Router. Extensive experiments on 20 LLMs and 12 datasets demonstrate that IRT-Router outperforms most baseline methods in terms of effectiveness and interpretability. Its superior performance in cold-start scenarios further confirms the reliability and practicality of IRT-Router in real-world applications. Code is available at https://github.com/Mercidaiha/IRT-Router.

Diffusion models generate highly realistic images through learning a multi-step denoising process, naturally embodying the principles of multi-task learning (MTL). Despite the inherent connection between diffusion models and MTL, there remains an unexplored area in designing neural architectures that explicitly incorporate MTL into the framework of diffusion models. In this paper, we present Denoising Task Routing (DTR), a simple add-on strategy for existing diffusion model architectures to establish distinct information pathways for individual tasks within a single architecture by selectively activating subsets of channels in the model. What makes DTR particularly compelling is its seamless integration of prior knowledge of denoising tasks into the framework: (1) Task Affinity: DTR activates similar channels for tasks at adjacent timesteps and shifts activated channels as sliding windows through timesteps, capitalizing on the inherent strong affinity between tasks at adjacent timesteps. (2) Task Weights: During the early stages (higher timesteps) of the denoising process, DTR assigns a greater number of task-specific channels, leveraging the insight that diffusion models prioritize reconstructing global structure and perceptually rich contents in earlier stages, and focus on simple noise removal in later stages. Our experiments demonstrate that DTR consistently enhances the performance of diffusion models across various evaluation protocols, all without introducing additional parameters. Furthermore, DTR contributes to accelerating convergence during training. Finally, we show the complementarity between our architectural approach and existing MTL optimization techniques, providing a more complete view of MTL within the context of diffusion training.

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to a particular domain or task. Model MoErging methods aim to recycle expert models to create an aggregate system with improved performance or generalization. A key component of MoErging methods is the creation of a router that decides which expert model(s) to use for a particular input or application. The promise, effectiveness, and large design space of MoErging has spurred the development of many new methods over the past few years. This rapid pace of development has made it challenging to compare different MoErging methods, which are rarely compared to one another and are often validated in different experimental setups. To remedy such gaps, we present a comprehensive survey of MoErging methods that includes a novel taxonomy for cataloging key design choices and clarifying suitable applications for each method. Apart from surveying MoErging research, we inventory software tools and applications that make use of MoErging. We additionally discuss related fields of study such as model merging, multitask learning, and mixture-of-experts models. Taken as a whole, our survey provides a unified overview of existing MoErging methods and creates a solid foundation for future work in this burgeoning field.

With the rapid proliferation of large language models (LLMs) -- each optimized for different strengths, style, or latency/cost profile -- routing has become an essential technique to operationalize the use of different models. However, existing LLM routing approaches are limited in two key ways: they evaluate performance using benchmarks that often fail to capture human preferences driven by subjective evaluation criteria, and they typically select from a limited pool of models. In this work, we propose a preference-aligned routing framework that guides model selection by matching queries to user-defined domains (e.g., travel) or action types (e.g., image editing) -- offering a practical mechanism to encode preferences in routing decisions. Specifically, we introduce Arch-Router, a compact 1.5B model that learns to map queries to domain-action preferences for model routing decisions. Our approach also supports seamlessly adding new models for routing without requiring retraining or architectural modifications. Experiments on conversational datasets demonstrate that our approach achieves state-of-the-art (SOTA) results in matching queries with human preferences, outperforming top proprietary models. Our approach captures subjective evaluation criteria and makes routing decisions more transparent and flexible. Our model is available at: https://huggingface.co/katanemo/Arch-Router-1.5B.

Diffusion models have emerged as mainstream framework in visual generation. Building upon this success, the integration of Mixture of Experts (MoE) methods has shown promise in enhancing model scalability and performance. In this paper, we introduce Race-DiT, a novel MoE model for diffusion transformers with a flexible routing strategy, Expert Race. By allowing tokens and experts to compete together and select the top candidates, the model learns to dynamically assign experts to critical tokens. Additionally, we propose per-layer regularization to address challenges in shallow layer learning, and router similarity loss to prevent mode collapse, ensuring better expert utilization. Extensive experiments on ImageNet validate the effectiveness of our approach, showcasing significant performance gains while promising scaling properties.

The rapid advancement of large language models (LLMs) has created a vibrant ecosystem of diverse architectures, each with unique strengths due to differences in design, training data, and objectives. However, most applications still rely on a single backend model, limiting coverage of capabilities and leading to inefficiencies in performance and token cost when tackling complex tasks. We highlight an underexploited opportunity: LLM routing data, produced when hosting platforms route diverse queries to different models, which can reveal comparative strengths across tasks. To address this, we propose FusionBench, a comprehensive routing benchmark covering 14 tasks across five domains with 20 open-source LLMs (8B to 671B parameters), capturing 103M tokens and summarizing reusable thought templates from top models. Building on this, we introduce FusionFactory, a systematic fusion framework with three levels: (1) query-level fusion, tailoring routers for each query using both direct responses and reasoning-augmented outputs; (2) thought-level fusion, leveraging abstract templates derived from top-performing LLMs' answers to similar queries; and (3) model-level fusion, transferring capabilities between models via distillation, using top responses or highest judge scores as training data. Experiments show FusionFactory consistently outperforms the best individual LLM across all 14 benchmarks, with optimal fusion configurations varying by benchmark, demonstrating the value of systematic LLM fusion in harnessing complementary strengths and improving overall performance.

The recent success of specialized Large Language Models (LLMs) in domains such as mathematical reasoning and coding has led to growing interest in methods for merging these expert LLMs into a unified Mixture-of-Experts (MoE) model, with the goal of enhancing performance in each domain while retaining effectiveness on general tasks. However, the effective merging of expert models remains an open challenge, especially for models with highly divergent weight parameters or different architectures. State-of-the-art MoE merging methods only work with homogeneous model architectures and rely on simple unweighted averaging to merge expert layers, which does not address parameter interference and requires extensive fine-tuning of the merged MoE to restore performance. To address these limitations, this paper introduces new MoE merging techniques, including strategies to mitigate parameter interference, routing heuristics to reduce the need for MoE fine-tuning, and a novel method for merging experts with different architectures. Extensive experiments across multiple domains demonstrate the effectiveness of our proposed methods, reducing fine-tuning costs, improving performance over state-of-the-art methods, and expanding the applicability of MoE merging.

The emergence of large-scale Mixture of Experts (MoE) models has marked a significant advancement in artificial intelligence, offering enhanced model capacity and computational efficiency through conditional computation. However, the deployment and inference of these models present substantial challenges in terms of computational resources, latency, and energy efficiency. This comprehensive survey systematically analyzes the current landscape of inference optimization techniques for MoE models across the entire system stack. We first establish a taxonomical framework that categorizes optimization approaches into model-level, system-level, and hardware-level optimizations. At the model level, we examine architectural innovations including efficient expert design, attention mechanisms, various compression techniques such as pruning, quantization, and knowledge distillation, as well as algorithm improvement including dynamic routing strategies and expert merging methods. At the system level, we investigate distributed computing approaches, load balancing mechanisms, and efficient scheduling algorithms that enable scalable deployment. Furthermore, we delve into hardware-specific optimizations and co-design strategies that maximize throughput and energy efficiency. This survey not only provides a structured overview of existing solutions but also identifies key challenges and promising research directions in MoE inference optimization. Our comprehensive analysis serves as a valuable resource for researchers and practitioners working on large-scale deployment of MoE models in resource-constrained environments. To facilitate ongoing updates and the sharing of cutting-edge advances in MoE inference optimization research, we have established a repository accessible at https://github.com/MoE-Inf/awesome-moe-inference/.

Inventory Routing Problem (IRP) is a crucial challenge in supply chain management as it involves optimizing efficient route selection while considering the uncertainty of inventory demand planning. To solve IRPs, usually a two-stage approach is employed, where demand is predicted using machine learning techniques first, and then an optimization algorithm is used to minimize routing costs. Our experiment shows machine learning models fall short of achieving perfect accuracy because inventory levels are influenced by the dynamic business environment, which, in turn, affects the optimization problem in the next stage, resulting in sub-optimal decisions. In this paper, we formulate and propose a decision-focused learning-based approach to solving real-world IRPs. This approach directly integrates inventory prediction and routing optimization within an end-to-end system potentially ensuring a robust supply chain strategy.

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.

Network-on-Chip (NoC) is widely used to facilitate communication between components in sophisticated System-on-Chip (SoC) designs. Security of the on-chip communication is crucial because exploiting any vulnerability in shared NoC would be a goldmine for an attacker that puts the entire computing infrastructure at risk. NoC security relies on effective countermeasures against diverse attacks, including attacks on anonymity. We investigate the security strength of existing anonymous routing protocols in NoC architectures. Specifically, this paper makes two important contributions. We show that the existing anonymous routing is vulnerable to machine learning (ML) based flow correlation attacks on NoCs. We propose lightweight anonymous routing with traffic obfuscation techniques to defend against ML-based flow correlation attacks. Experimental studies using both real and synthetic traffic reveal that our proposed attack is successful against state-of-the-art anonymous routing in NoC architectures with high accuracy (up to 99%) for diverse traffic patterns, while our lightweight countermeasure can defend against ML-based attacks with minor hardware and performance overhead.

Underwater acoustic target recognition is a difficult task owing to the intricate nature of underwater acoustic signals. The complex underwater environments, unpredictable transmission channels, and dynamic motion states greatly impact the real-world underwater acoustic signals, and may even obscure the intrinsic characteristics related to targets. Consequently, the data distribution of underwater acoustic signals exhibits high intra-class diversity, thereby compromising the accuracy and robustness of recognition systems.To address these issues, this work proposes a convolution-based mixture of experts (CMoE) that recognizes underwater targets in a fine-grained manner. The proposed technique introduces multiple expert layers as independent learners, along with a routing layer that determines the assignment of experts according to the characteristics of inputs. This design allows the model to utilize independent parameter spaces, facilitating the learning of complex underwater signals with high intra-class diversity. Furthermore, this work optimizes the CMoE structure by balancing regularization and an optional residual module. To validate the efficacy of our proposed techniques, we conducted detailed experiments and visualization analyses on three underwater acoustic databases across several acoustic features. The experimental results demonstrate that our CMoE consistently achieves significant performance improvements, delivering superior recognition accuracy when compared to existing advanced methods.

Transformer-based architectures have become the prevailing backbone of large language models. However, the quadratic time and memory complexity of self-attention remains a fundamental obstacle to efficient long-context modeling. To address this limitation, recent research has introduced two principal categories of efficient attention mechanisms. Linear attention methods achieve linear complexity through kernel approximations, recurrent formulations, or fastweight dynamics, thereby enabling scalable inference with reduced computational overhead. Sparse attention techniques, in contrast, limit attention computation to selected subsets of tokens based on fixed patterns, block-wise routing, or clustering strategies, enhancing efficiency while preserving contextual coverage. This survey provides a systematic and comprehensive overview of these developments, integrating both algorithmic innovations and hardware-level considerations. In addition, we analyze the incorporation of efficient attention into largescale pre-trained language models, including both architectures built entirely on efficient attention and hybrid designs that combine local and global components. By aligning theoretical foundations with practical deployment strategies, this work aims to serve as a foundational reference for advancing the design of scalable and efficient language models.

Many data have an underlying dependence on spatial location; it may be weather on the Earth, a simulation on a mesh, or a registered image. Yet this feature is rarely taken advantage of, and violates common assumptions made by many neural network layers, such as translation equivariance. Further, many works that do incorporate locality fail to capture fine-grained structure. To address this, we introduce the Spatial Mixture-of-Experts (SMoE) layer, a sparsely-gated layer that learns spatial structure in the input domain and routes experts at a fine-grained level to utilize it. We also develop new techniques to train SMoEs, including a self-supervised routing loss and damping expert errors. Finally, we show strong results for SMoEs on numerous tasks, and set new state-of-the-art results for medium-range weather prediction and post-processing ensemble weather forecasts.

In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, and timetabling optimization problems providing optimized business solutions for industry sectors such as manufacturing, agriculture, defence, healthcare, medicine, energy, finance, and transportation. Despite the numerous real-life Combinatorial Optimization Problems found and solved and millions yet to be discovered and formulated, the number of types of constraints (the building blocks of a MILP) is relatively small. In the search for a suitable machine-readable knowledge representation structure for MILPs, we propose an optimization modelling tree built based upon an MILP model ontology that can be used as a guide for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems. Our ultimate aim is to develop a machine-readable knowledge representation for MILP that allows us to map an end-user's natural language description of the business optimization problem to an MILP formal specification as a first step towards automated mathematical modelling.

3D field-programmable gate arrays (FPGAs) promise higher performance through vertical integration. However, existing placement tools, largely inherited from 2D frameworks, fail to capture the unique delay characteristics and optimization dynamics of 3D fabrics. We introduce a 3D FPGA placement flow that integrates partitioning-based initialization, adaptive cost scheduling, refined delay estimation, and a simulated annealing move set -- all targeted at 3D FPGA architecture. Together, these enhancements improve timing estimates and the exploration of layer assignments during placement. Compared to Verilog-To-Routing (VTR), our experiments show geometric-mean (max) critical-path delay reductions of ~3% (~7%), ~2% (~4%), ~3% (~8%), and ~6% (~18%) for four 3D architectures: 3D CB, 3D CB-O, 3D CB-I, and 3D SB, respectively. We also achieve geometric-mean (max) routed wirelength reductions of ~1% (~3%), ~2% (~8%), < 1% (~5%), and ~5% (~10%), respectively. Our work will be permissively open-sourced on GitHub.

General-purpose pre-trained models ("foundation models") have enabled practitioners to produce generalizable solutions for individual machine learning problems with datasets that are significantly smaller than those required for learning from scratch. Such models are typically trained on large and diverse datasets with weak supervision, consuming much more training data than is available for any individual downstream application. In this paper, we describe the Visual Navigation Transformer (ViNT), a foundation model that aims to bring the success of general-purpose pre-trained models to vision-based robotic navigation. ViNT is trained with a general goal-reaching objective that can be used with any navigation dataset, and employs a flexible Transformer-based architecture to learn navigational affordances and enable efficient adaptation to a variety of downstream navigational tasks. ViNT is trained on a number of existing navigation datasets, comprising hundreds of hours of robotic navigation from a variety of different robotic platforms, and exhibits positive transfer, outperforming specialist models trained on singular datasets. ViNT can be augmented with diffusion-based subgoal proposals to explore novel environments, and can solve kilometer-scale navigation problems when equipped with long-range heuristics. ViNT can also be adapted to novel task specifications with a technique inspired by prompt-tuning, where the goal encoder is replaced by an encoding of another task modality (e.g., GPS waypoints or routing commands) embedded into the same space of goal tokens. This flexibility and ability to accommodate a variety of downstream problem domains establishes ViNT as an effective foundation model for mobile robotics. For videos, code, and model checkpoints, see our project page at https://visualnav-transformer.github.io.

This technical report presents Yi-Lightning, our latest flagship large language model (LLM). It achieves exceptional performance, ranking 6th overall on Chatbot Arena, with particularly strong results (2nd to 4th place) in specialized categories including Chinese, Math, Coding, and Hard Prompts. Yi-Lightning leverages an enhanced Mixture-of-Experts (MoE) architecture, featuring advanced expert segmentation and routing mechanisms coupled with optimized KV-caching techniques. Our development process encompasses comprehensive pre-training, supervised fine-tuning (SFT), and reinforcement learning from human feedback (RLHF), where we devise deliberate strategies for multi-stage training, synthetic data construction, and reward modeling. Furthermore, we implement RAISE (Responsible AI Safety Engine), a four-component framework to address safety issues across pre-training, post-training, and serving phases. Empowered by our scalable super-computing infrastructure, all these innovations substantially reduce training, deployment and inference costs while maintaining high-performance standards. With further evaluations on public academic benchmarks, Yi-Lightning demonstrates competitive performance against top-tier LLMs, while we observe a notable disparity between traditional, static benchmark results and real-world, dynamic human preferences. This observation prompts a critical reassessment of conventional benchmarks' utility in guiding the development of more intelligent and powerful AI systems for practical applications. Yi-Lightning is now available through our developer platform at https://platform.lingyiwanwu.com.

Upcycling pre-trained dense models into sparse Mixture-of-Experts (MoEs) efficiently increases model capacity but often suffers from poor expert specialization due to naive weight replication. Our analysis reveals that upcycled MoEs, even with conventional regularization, exhibit low-confidence, weakly differentiated routing, hindering performance. We introduce Dirichlet-Prior Shaping Loss (DPSL), a novel router regularization technique that directly shapes routing probability distributions by matching expert assignments to a target Dirichlet prior. DPSL offers fine-grained control over expert balance and specialization, and enables encoding of inductive biases such as encouraging experts to focus on specific modalities or tasks, without requiring manual intervention; notably, DPSL is a general tool applicable to any module that outputs categorical probability distributions, extending its utility beyond MoE training. Experiments on upcycled MoE vision-language models (with Qwen2, Phi3, Llama3.2 LLM backbones) show DPSL consistently outperforms upcycling strategies and regularization techniques across standard vision-language benchmarks, addressing the critical issue of poor specialization and fostering more adaptive, higher-performing models.

This paper proposes a novel formulation for reinforcement learning (RL) with large language models, explaining why and under what conditions the true sequence-level reward can be optimized via a surrogate token-level objective in policy gradient methods such as REINFORCE. Specifically, through a first-order approximation, we show that this surrogate becomes increasingly valid only when both the training-inference discrepancy and policy staleness are minimized. This insight provides a principled explanation for the crucial role of several widely adopted techniques in stabilizing RL training, including importance sampling correction, clipping, and particularly Routing Replay for Mixture-of-Experts (MoE) models. Through extensive experiments with a 30B MoE model totaling hundreds of thousands of GPU hours, we show that for on-policy training, the basic policy gradient algorithm with importance sampling correction achieves the highest training stability. When off-policy updates are introduced to accelerate convergence, combining clipping and Routing Replay becomes essential to mitigate the instability caused by policy staleness. Notably, once training is stabilized, prolonged optimization consistently yields comparable final performance regardless of cold-start initialization. We hope that the shared insights and the developed recipes for stable RL training will facilitate future research.

Sparsely gated Mixture of Experts (MoE) models have been shown to be a compute-efficient method to scale model capacity for multilingual machine translation. However, for low-resource tasks, MoE models severely over-fit. We show effective regularization strategies, namely dropout techniques for MoE layers in EOM and FOM, Conditional MoE Routing and Curriculum Learning methods that prevent over-fitting and improve the performance of MoE models on low-resource tasks without adversely affecting high-resource tasks. On a massively multilingual machine translation benchmark, our strategies result in about +1 chrF++ improvement in very low resource language pairs. We perform an extensive analysis of the learned MoE routing to better understand the impact of our regularization methods and how we can improve them.

Large Language Models increasingly possess capabilities that carry dual-use risks. While data filtering has emerged as a pretraining-time mitigation, it faces significant challenges: labeling whether data is harmful is expensive at scale, and given improving sample efficiency with larger models, even small amounts of mislabeled content could give rise to dangerous capabilities. To address risks associated with mislabeled harmful content, prior work proposed Gradient Routing (Cloud et al., 2024) -- a technique that localizes target knowledge into a dedicated subset of model parameters so they can later be removed. We explore an improved variant of Gradient Routing, which we call Selective GradienT Masking (SGTM), with particular focus on evaluating its robustness to label noise. SGTM zero-masks selected gradients such that target domain examples only update their dedicated parameters. We test SGTM's effectiveness in two applications: removing knowledge of one language from a model trained on a bilingual synthetic dataset, and removing biology knowledge from a model trained on English Wikipedia. In both cases SGTM provides better retain/forget trade-off in the presence of labeling errors compared to both data filtering and a previously proposed instantiation of Gradient Routing. Unlike shallow unlearning approaches that can be quickly undone through fine-tuning, SGTM exhibits strong robustness to adversarial fine-tuning, requiring seven times more fine-tuning steps to reach baseline performance on the forget set compared to a finetuning-based unlearning method (RMU). Our results suggest SGTM provides a promising pretraining-time complement to existing safety mitigations, particularly in settings where label noise is unavoidable.

The growing number of parameter-efficient adaptations of a base large language model (LLM) calls for studying whether we can reuse such trained adapters to improve performance for new tasks. We study how to best build a library of adapters given multi-task data and devise techniques for both zero-shot and supervised task generalization through routing in such library. We benchmark existing approaches to build this library and introduce model-based clustering, MBC, a method that groups tasks based on the similarity of their adapter parameters, indirectly optimizing for transfer across the multi-task dataset. To re-use the library, we present a novel zero-shot routing mechanism, Arrow, which enables dynamic selection of the most relevant adapters for new inputs without the need for retraining. We experiment with several LLMs, such as Phi-2 and Mistral, on a wide array of held-out tasks, verifying that MBC-based adapters and Arrow routing lead to superior generalization to new tasks. We make steps towards creating modular, adaptable LLMs that can match or outperform traditional joint training.

While Mixture-of-Experts (MoE) scales model capacity without proportionally increasing computation, its massive total parameter footprint creates significant storage and memory-access bottlenecks, which hinder efficient end-side deployment that simultaneously requires high performance, low computational cost, and small storage overhead. To achieve these properties, we present DECO, a sparse MoE architecture designed to match the performance of dense Transformers under identical total parameter budgets and training tokens. DECO utilizes the differentiable and flexible ReLU-based routing enhanced by learnable expert-wise scaling, which adaptively balances the contributions of routed and shared experts. Furthermore, we introduce NormSiLU, an activation function that normalizes inputs prior to SiLU operators, producing a more stable trend of routed-expert activation ratio and a higher intrinsic sparsity level. We also identify an empirical advantage in using non-gated MLP experts with ReLU-based routing, indicating the possibility of MoE architecture simplification. Experiments demonstrate that DECO, activating only 20% of experts, matches dense performance and outperforms established MoE baselines. Our specialized acceleration kernel delivers a 3.00times speedup on real hardware compared with dense inference. Codes and checkpoints will be released.

Mixture-of-Experts (MoE) models have emerged as a cornerstone of large-scale deep learning by efficiently distributing computation and enhancing performance. However, their unique architecture-characterized by sparse expert activation and dynamic routing mechanisms-introduces inherent complexities that challenge conventional quantization techniques. Existing post-training quantization (PTQ) methods struggle to address activation outliers, router consistency and sparse expert calibration, leading to significant performance degradation. To bridge this gap, we propose EAQuant, a novel PTQ framework tailored for MoE architectures. Our method systematically tackles these challenges through three key innovations: (1) expert-aware smoothing aggregation to suppress activation outliers and stabilize quantization, (2) router logits distribution alignment to preserve expert selection consistency post-quantization, and (3) expert-level calibration data balance to optimize sparsely activated experts. Extensive experiments across W4A4 and extreme W3A4 quantization configurations demonstrate that EAQuant significantly outperforms existing methods, achieving average score improvements of 1.15 - 2.28% across three diverse MoE architectures, with particularly pronounced gains in reasoning tasks and robust performance retention under aggressive quantization. By integrating these innovations, EAQuant establishes a new state-of-the-art for high-precision, efficient MoE model compression. Our code is available at https://github.com/darren-fzq/EAQuant.

In this paper, we introduce Hunyuan-Large, which is currently the largest open-source Transformer-based mixture of experts model, with a total of 389 billion parameters and 52 billion activation parameters, capable of handling up to 256K tokens. We conduct a thorough evaluation of Hunyuan-Large's superior performance across various benchmarks including language understanding and generation, logical reasoning, mathematical problem-solving, coding, long-context, and aggregated tasks, where it outperforms LLama3.1-70B and exhibits comparable performance when compared to the significantly larger LLama3.1-405B model. Key practice of Hunyuan-Large include large-scale synthetic data that is orders larger than in previous literature, a mixed expert routing strategy, a key-value cache compression technique, and an expert-specific learning rate strategy. Additionally, we also investigate the scaling laws and learning rate schedule of mixture of experts models, providing valuable insights and guidances for future model development and optimization. The code and checkpoints of Hunyuan-Large are released to facilitate future innovations and applications. Codes: https://github.com/Tencent/Hunyuan-Large Models: https://huggingface.co/tencent/Tencent-Hunyuan-Large

Autoregressive video generation aims at real-time, open-ended synthesis. Yet, cinematic storytelling is not merely the endless extension of a single scene; it requires progressing through evolving events, viewpoint shifts, and discrete shot boundaries. Existing autoregressive models often struggle in this setting. Trained primarily for short-horizon continuation, they treat long sequences as extended single shots, inevitably suffering from motion stagnation and semantic drift during long rollouts. To bridge this gap, we introduce CausalCine, an interactive autoregressive framework that transforms multi-shot video generation into an online directing process. CausalCine generates causally across shot changes, accepts dynamic prompts on the fly, and reuses context without regenerating previous shots. To achieve this, we first train a causal base model on native multi-shot sequences to learn complex shot transitions prior to acceleration. We then propose Content-Aware Memory Routing (CAMR), which dynamically retrieves historical KV entries according to attention-based relevance scores rather than temporal proximity, preserving cross-shot coherence under bounded active memory. Finally, we distill the causal base model into a few-step generator for real-time interactive generation. Extensive experiments demonstrate that CausalCine significantly outperforms autoregressive baselines and approaches the capability of bidirectional models while unlocking the streaming interactivity of causal generation. Demo available at https://yihao-meng.github.io/CausalCine/

Scaling up the number of parameters of language models has proven to be an effective approach to improve performance. For dense models, increasing model size proportionally increases the model's computation footprint. In this work, we seek to aggressively decouple learning capacity and FLOPs through Mixture-of-Experts (MoE) style models with large knowledge-rich vocabulary based routing functions and experts. Our proposed approach, dubbed Mixture of Word Experts (MoWE), can be seen as a memory augmented model, where a large set of word-specific experts play the role of a sparse memory. We demonstrate that MoWE performs significantly better than the T5 family of models with similar number of FLOPs in a variety of NLP tasks. Additionally, MoWE outperforms regular MoE models on knowledge intensive tasks and has similar performance to more complex memory augmented approaches that often require to invoke custom mechanisms to search the sparse memory.

Large language models (LLMs) require continual knowledge updates to stay abreast of the ever-changing world facts, prompting the formulation of lifelong model editing task. While recent years have witnessed the development of various techniques for single and batch editing, these methods either fail to apply or perform sub-optimally when faced with lifelong editing. In this paper, we introduce LEMoE, an advanced Mixture of Experts (MoE) adaptor for lifelong model editing. We first analyze the factors influencing the effectiveness of conventional MoE adaptor in lifelong editing, including catastrophic forgetting, inconsistent routing and order sensitivity. Based on these insights, we propose a tailored module insertion method to achieve lifelong editing, incorporating a novel KV anchor routing to enhance routing consistency between training and inference stage, along with a concise yet effective clustering-based editing order planning. Experimental results demonstrate the effectiveness of our method in lifelong editing, surpassing previous model editing techniques while maintaining outstanding performance in batch editing task. Our code will be available.

Retrieval-Augmented Generation (RAG) has emerged as a powerful technique for enhancing the quality of responses in Question-Answering (QA) tasks. However, existing approaches often struggle with retrieving contextually relevant information, leading to incomplete or suboptimal answers. In this paper, we introduce Structured-Semantic RAG (SSRAG), a hybrid architecture that enhances QA quality by integrating query augmentation, agentic routing, and a structured retrieval mechanism combining vector and graph based techniques with context unification. By refining retrieval processes and improving contextual grounding, our approach improves both answer accuracy and informativeness. We conduct extensive evaluations on three popular QA datasets, TruthfulQA, SQuAD and WikiQA, across five Large Language Models (LLMs), demonstrating that our proposed approach consistently improves response quality over standard RAG implementations.

Training large language models (LLMs) with increasingly long and varying sequence lengths introduces severe load imbalance challenges in large-scale data-parallel training. Recent frameworks attempt to mitigate these issues through data reorganization or hybrid parallel strategies. However, they often overlook how computational and communication costs scale with sequence length, resulting in suboptimal performance. We identify three critical challenges: (1) varying computation-to-communication ratios across sequences of different lengths in distributed attention, (2) mismatch between static NIC-GPU affinity and dynamic parallel workloads, and (3) distinct optimal partitioning strategies required for quadratic attention versus linear components. To address these challenges, we present Zeppelin, a novel training system that integrates three key techniques: (1) a hierarchical sequence partitioning method for the attention module that reduces communication overhead and balances computation, supported by an efficient attention engine that applies divergent parallel strategies; (2) a routing layer that orchestrates inter-node transfers to fully utilize NIC bandwidth; and (3) a remapping layer that transforms sequence layouts between attention and linear modules, ensuring high computational efficiency across both. Comprehensive evaluations across diverse configurations show that Zeppelin delivers an average 2.80x speedup over state-of-the-art methods.

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

By routing input tokens to only a few split experts, Sparse Mixture-of-Experts has enabled efficient training of large language models. Recent findings suggest that fixing the routers can achieve competitive performance by alleviating the collapsing problem, where all experts eventually learn similar representations. However, this strategy has two key limitations: (i) the policy derived from random routers might be sub-optimal, and (ii) it requires extensive resources during training and evaluation, leading to limited efficiency gains. This work introduces \HyperRout, which dynamically generates the router's parameters through a fixed hypernetwork and trainable embeddings to achieve a balance between training the routers and freezing them to learn an improved routing policy. Extensive experiments across a wide range of tasks demonstrate the superior performance and efficiency gains of \HyperRouter compared to existing routing methods. Our implementation is publicly available at {{https://github.com/giangdip2410/HyperRouter}}.

Large language model (LLM) routers improve the efficiency of multi-model systems by directing each query to the most appropriate model while leveraging the diverse strengths of heterogeneous LLMs. Most existing approaches frame routing as a classification problem based solely on the input query. While this reduces overhead by avoiding inference across all models, it overlooks valuable information that could be gleaned from potential outputs and fails to capture implicit intent or contextual nuances that often emerge only during response generation. These limitations can result in suboptimal routing decisions, particularly for complex or ambiguous queries that require deeper semantic understanding. To address this challenge, we propose Lookahead, a routing framework that "foresees" potential model outputs by predicting their latent representations and uses these predictions to guide model selection, thus enabling more informed routing without full inference. Within this framework, we implement two approaches based on causal and masked language models. Empirical evaluations across seven public benchmarks - spanning instruction following, mathematical reasoning, and code generation - show that Lookahead consistently outperforms existing routing baselines, achieving an average performance gain of 7.7% over the state-of-the-art. Our code is available at https://github.com/huangcb01/lookahead-routing.

This paper proposes a novel admission and routing scheme which takes into account arbitrarily assigned priorities for network flows. The presented approach leverages the centralized Software Defined Networking (SDN) capabilities in order to do so. Exact and heuristic approaches to the stated Priority Flow Admission and Routing (PFAR) problem are provided. The exact approach which provides an optimal solution is based on Integer Linear Programming (ILP). Given the potentially long running time required to find an exact and optimal solution, a heuristic approach is proposed; this approach is based on Genetic Algorithms (GAs). In order to effectively estimate the performance of the proposed approaches, a simulator that is capable of generating semi-random network topologies and flows has been developed. Experimental results for large problem instances (up 50 network nodes and thousands of network flows), show that: i) an optimal solution can be often found in few seconds (even milliseconds), and ii) the heuristic approach yields close-to-optimal solutions (approximately 95\% of the optimal) in a fixed amount of time; these experimental results demonstrate the pertinence of the proposed approaches.

Recent works show that assembling multiple off-the-shelf large language models (LLMs) can harness their complementary abilities. To achieve this, routing is a promising method, which learns a router to select the most suitable LLM for each query. However, existing routing models are ineffective when multiple LLMs perform well for a query. To address this problem, in this paper, we propose a method called query-based Router by Dual Contrastive learning (RouterDC). The RouterDC model consists of an encoder and LLM embeddings, and we propose two contrastive learning losses to train the RouterDC model. Experimental results show that RouterDC is effective in assembling LLMs and largely outperforms individual top-performing LLMs as well as existing routing methods on both in-distribution (+2.76\%) and out-of-distribution (+1.90\%) tasks. Source code is available at https://github.com/shuhao02/RouterDC.

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.

Multi-Agent Systems(MAS) have become a powerful paradigm for building high performance intelligent applications. Within these systems, the router responsible for determining which expert agents should handle a given query plays a crucial role in overall performance. Existing routing strategies generally fall into two categories: performance routing, which balances latency and cost across models of different sizes, and task routing, which assigns queries to domain-specific experts to improve accuracy. In real-world enterprise applications, task routing is more suitable; however, most existing approaches rely on static single-label decisions, which introduce two major limitations: (i) difficulty in seamlessly integrating new agents as business domains expand, and (ii) routing conflicts caused by overlapping agent capabilities, ultimately degrading accuracy and robustness.To address these challenges, we propose TCAndon-Router(TCAR): an adaptive reasoning router for multi-agent collaboration. Unlike traditional routers, TCAR supports dynamic agent onboarding and first generates a natural-language reasoning chain before predicting a set of candidate agents capable of handling the query. In addition, we design a collaborative execution pipeline in which selected agents independently produce responses, which are then aggregated and refined into a single high-quality response by a dedicated Refining Agent.Experiments on public datasets and real enterprise data demonstrate that TCAR significantly improves routing accuracy, reduces routing conflicts, and remains robust in ambiguous scenarios. We have released TCAR at https://huggingface.co/tencent/TCAndon-Router to support future research on explainable and collaborative multi-agent routing.

For pre-training of MoE (Mixture-of-Experts) models, one of the main issues is unbalanced expert loads, which may cause routing collapse or increased computational overhead. Existing methods contain the Loss-Controlled method and the Loss-Free method, where both the unbalanced degrees at first several training steps are still high and decrease slowly. In this work, we propose BIP-Based Balancing, an expert load balancing algorithm based on binary integer programming (BIP). The algorithm maintains an additional vector q on each MoE layer that can help change the top-K order of s by solving a binary integer programming with very small time costs. We implement the algorithm on two MoE language models: 16-expert (0.3B) and 64-expert (1.1B). The experimental results show that on both models comparing with the Loss-Controlled method and the Loss-Free method, our algorithm trains models with the lowest perplexities, while saves at least 13% of pre-training time compared with the Loss-Controlled method. Within our current knowledge, this is the first routing algorithm that achieves maintaining load balance status on every expert in every MoE layer from the first step to the last step during the whole pre-training process, while the trained MoE models also perform well. The code material of this work is available at https://github.com/sunyuanLLM/bip_routing_algorithm.

As the range of applications for Large Language Models (LLMs) continues to grow, the demand for effective serving solutions becomes increasingly critical. Despite the versatility of LLMs, no single model can optimally address all tasks and applications, particularly when balancing performance with cost. This limitation has led to the development of LLM routing systems, which combine the strengths of various models to overcome the constraints of individual LLMs. Yet, the absence of a standardized benchmark for evaluating the performance of LLM routers hinders progress in this area. To bridge this gap, we present RouterBench, a novel evaluation framework designed to systematically assess the efficacy of LLM routing systems, along with a comprehensive dataset comprising over 405k inference outcomes from representative LLMs to support the development of routing strategies. We further propose a theoretical framework for LLM routing, and deliver a comparative analysis of various routing approaches through RouterBench, highlighting their potentials and limitations within our evaluation framework. This work not only formalizes and advances the development of LLM routing systems but also sets a standard for their assessment, paving the way for more accessible and economically viable LLM deployments. The code and data are available at https://github.com/withmartian/routerbench.

A mobile ad hoc network (MANET) is a collection of autonomous nodes that communicate with each other by forming a multi-hop radio network and maintaining connections in a decentralized manner. Security remains a major challenge for these networks due to their features of open medium, dynamically changing topologies, reliance on cooperative algorithms, absence of centralized monitoring points, and lack of clear lines of defense. Protecting the network layer of a MANET from malicious attacks is an important and challenging security issue, since most of the routing protocols for MANETs are vulnerable to various types of attacks. Ad hoc on-demand distance vector routing (AODV) is a very popular routing algorithm. However, it is vulnerable to the well-known black hole attack, where a malicious node falsely advertises good paths to a destination node during the route discovery process but drops all packets in the data forwarding phase. This attack becomes more severe when a group of malicious nodes cooperate each other. The proposed mechanism does not apply any cryptographic primitives on the routing messages. Instead, it protects the network by detecting and reacting to malicious activities of the nodes. Simulation results show that the scheme has a significantly high detection rate with moderate network traffic overhead and computation overhead in the nodes.

Sparse Mixture-of-Experts (MoE) architectures employ increasingly sophisticated routing mechanisms -- learned routers, multi-hop trajectories, token-dependent gating. We ask: does routing topology actually determine language modeling quality? We build a geometric MoE (ST-MoE) using cosine-similarity routing against learned centroids in a low-dimensional space (d_{space} = 64), requiring 80% fewer routing parameters than standard linear routers. Through 62 controlled experiments on WikiText-103 at 76--84M parameters trained to convergence (50K steps, 1.64B tokens), we find that routing topology does not determine asymptotic perplexity (PPL): five cosine-routing variants are statistically equivalent within a 1-PPL margin (Two One-Sided Tests [TOST], p < 0.05 for all 10 pairwise comparisons; 15 runs across 3 seeds, observed range 33.93--34.72). The finding extends to hash, random-fixed, and top-1 routing (single-seed; graceful 1.1--2.2 PPL degradation) and replicates on OpenWebText (0.03 PPL gap, 6 runs, 3 seeds each). A standard linear router with 5.3times more routing parameters reaches PPL 32.76, but iso-parameter cosine routing closes 67% of this gap -- the true mechanism advantage is sim1.2%. The mechanistic explanation is convergent redundancy: multi-hop updates are collinear (cos(Δh_0, Δh_1) = 0.805), implementing magnitude amplification rather than compositional reasoning; a single learnable scalar replicates multi-hop performance. As a practical payoff, zero-shot relative-norm halting saves 25% of MoE FLOPs at +0.12% PPL. Expert-level specialization and causal controllability -- which coexist with topology-level equifinality -- are explored in a companion paper.

The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to solve this problem setting, like epsilon-greedy, Upper confident bound (UCB) and Thompson Sampling (TS). We are showing here how this algorithms were adapted to solve the different problems of exploration exploitation.

Large Language Model (LLM)-driven Multi-Agent Systems (MAS) have demonstrated strong capability in complex reasoning and tool use, and heterogeneous agent pools further broaden the quality--cost trade-off space. Despite these advances, real-world deployment is often constrained by high inference cost, latency, and limited transparency, which hinders scalable and efficient routing. Existing routing strategies typically rely on expensive LLM-based selectors or static policies, and offer limited controllability for semantic-aware routing under dynamic loads and mixed intents, often resulting in unstable performance and inefficient resource utilization. To address these limitations, we propose AMRO-S, an efficient and interpretable routing framework for Multi-Agent Systems (MAS). AMRO-S models MAS routing as a semantic-conditioned path selection problem, enhancing routing performance through three key mechanisms: First, it leverages a supervised fine-tuned (SFT) small language model for intent inference, providing a low-overhead semantic interface for each query; second, it decomposes routing memory into task-specific pheromone specialists, reducing cross-task interference and optimizing path selection under mixed workloads; finally, it employs a quality-gated asynchronous update mechanism to decouple inference from learning, optimizing routing without increasing latency. Extensive experiments on five public benchmarks and high-concurrency stress tests demonstrate that AMRO-S consistently improves the quality--cost trade-off over strong routing baselines, while providing traceable routing evidence through structured pheromone patterns.

Large language models (LLMs) often exhibit complementary strengths. Model routing harnesses these strengths by dynamically directing each query to the most suitable model, given a candidate model pool. However, routing performance relies on accurate model representations, and adding new models typically requires retraining, limiting scalability. To address these challenges, we propose a novel routing method using in-context vectors to represent model capabilities. The method proceeds in two stages. First, queries are embedded and projected into vectors, with a projector and LLM-based router trained to reconstruct the original queries, aligning vector representations with the router's semantic space. Second, each candidate model is profiled on a query set, and the router learns -- based on in-context vectors of query and model performance -- to predict whether each model can correctly answer new queries. Extensive experiments demonstrate that our method achieves state-of-the-art routing performance in both in-distribution and out-of-distribution tasks. Moreover, our method allows for seamless integration of new models without retraining the router. The code is available at https://github.com/lalalamdbf/ICL-Router.

Modeling networks as different graph types and researching on route finding strategies, to avoid congestion in dense subnetworks via graph-theoretic approaches, contributes to overall blocking probability reduction in networks. Our main focus is to study methods for modeling congested subnetworks and graph density measures, in order to identify routes that avoid dense subgraphs for global congestion avoidance, along with covering related algorithmic issues.

Large language models (LLMs) are increasingly used in applications where LLM inputs may span many different tasks. Recent work has found that the choice of LLM is consequential, and different LLMs may be good for different input samples. Prior approaches have thus explored how engineers might select an LLM to use for each sample (i.e. routing). While existing routing methods mostly require training auxiliary models on human-annotated data, our work explores whether it is possible to perform unsupervised routing. We propose Smoothie, a weak supervision-inspired routing approach that requires no labeled data. Given a set of outputs from different LLMs, Smoothie constructs a latent variable graphical model over embedding representations of observable LLM outputs and unknown "true" outputs. Using this graphical model, we estimate sample-dependent quality scores for each LLM, and route each sample to the LLM with the highest corresponding score. We find that Smoothie's LLM quality-scores correlate with ground-truth model quality (correctly identifying the optimal model on 9/14 tasks), and that Smoothie outperforms baselines for routing by up to 10 points accuracy.

As large language models (LLMs) grow in scale and specialization, routing--selecting the best model for a given input--has become essential for efficient and effective deployment. While recent methods rely on complex learned routing strategies, their dependence on disparate training data and evaluation setups makes comparison and generalization difficult. In this work, we revisit LLM routing through the lens of simplicity. We show that a well-tuned k-Nearest Neighbors (kNN) approach not only matches but often outperforms state-of-the-art learned routers across diverse tasks. To support systematic evaluation, we introduce a suite of standardized routing benchmarks spanning instruction-following, question-answering, and reasoning tasks, as well as the first multi-modal routing dataset involving visual inputs. Our findings reveal that the locality properties of model performance in embedding space enable simple non-parametric methods to achieve strong routing decisions with lower sample complexity than parametric approaches. This challenges the prevailing trend toward sophisticated architectures and highlights the importance of thoroughly evaluating simple baselines before investing in complex solutions. To support reproducibility and further exploration, we will release all benchmarks and code upon publication.

As LLM agent ecosystems grow, the number of available skills (tools, plugins) has reached tens of thousands, making it infeasible to inject all skills into an agent's context. This creates a need for skill routing -- retrieving the most relevant skills from a large pool given a user task. The problem is compounded by pervasive functional overlap in community skill repositories, where many skills share similar names and purposes yet differ in implementation details. Despite its practical importance, skill routing remains under-explored. Current agent architectures adopt a progressive disclosure design -- exposing only skill names and descriptions to the agent while keeping the full implementation body hidden -- implicitly treating metadata as sufficient for selection. We challenge this assumption through a systematic empirical study on a benchmark of ~$80K skills and 75 expert-verified queries. Our key finding is that the skill body (full implementation text) is the decisive signal: removing it causes 29--44 percentage point degradation across all retrieval methods, and cross-encoder attention analysis reveals 91.7% of attention concentrating on the body field. Motivated by this finding, we propose SkillRouter, a two-stage retrieve-and-rerank pipeline totaling only 1.2B parameters (0.6B encoder + 0.6B reranker). SkillRouter achieves 74.0% top-1 routing accuracy and delivers the strongest average result among the compact and zero-shot baselines we evaluate, while remaining deployable on consumer hardware.

Traditional Mixture-of-Experts (MoE) training typically proceeds without any structural priors, effectively requiring the model to simultaneously train expert weights while searching for an optimal routing policy within a vast combinatorial space. This entanglement often leads to sluggish convergence and training instabilities. This paper introduces Grouter, a preemptive routing method that by distilling high-quality structures from fully-trained MoE models and serving as a fixed router for target models. By decoupling structural optimization from weight updates, Grouter significantly accelerates both the speed and quality of model convergence. To ensure the framework's versatility, we also introduce expert folding to adapt Grouter across varying model configurations and expert tuning to rebalance workloads across different data distributions. Furthermore, by leveraging the structural priors provided by preemptive routing, we can implement targeted optimizations to further enhance training throughput. Experiments demonstrate that Grouter achieves superior performance and efficiency which boosts pre-training data utilization by 4.28x and achieves up to 33.5% throughput acceleration, establishing preemptive routing as a fundamental paradigm for scalable MoE training.

The sparsely-activated models have achieved great success in natural language processing through large-scale parameters and relatively low computational cost, and gradually become a feasible technique for training and implementing extremely large models. Due to the limit of communication cost, activating multiple experts is hardly affordable during training and inference. Therefore, previous work usually activate just one expert at a time to alleviate additional communication cost. Such routing mechanism limits the upper bound of model performance. In this paper, we first investigate a phenomenon that increasing the number of activated experts can boost the model performance with higher sparse ratio. To increase the number of activated experts without an increase in computational cost, we propose SAM (Switch and Mixture) routing, an efficient hierarchical routing mechanism that activates multiple experts in a same device (GPU). Our methods shed light on the training of extremely large sparse models and experiments prove that our models can achieve significant performance gain with great efficiency improvement.

We present ACAR (Adaptive Complexity and Attribution Routing), a measurement framework for studying multi-model orchestration under auditable conditions. ACAR uses self-consistency variance (sigma) computed from N=3 probe samples to route tasks across single-model, two-model, and three-model execution modes. The system is implemented on top of TEAMLLM, a deterministic execution substrate with immutable artifacts and complete decision traces. We evaluate ACAR on 1,510 tasks spanning four benchmarks: MathArena, Reasoning Gym, LiveCodeBench, and SuperGPQA, using Claude Sonnet 4, GPT-4o, and Gemini 2.0 Flash, producing more than 7,550 auditable runs. Results show that sigma-based routing achieves 55.6 percent accuracy, exceeding the two-model baseline of 54.4 percent while avoiding full ensembling on 54.2 percent of tasks. The routing mechanism is model-agnostic and requires no learned components. We also document negative results. First, retrieval augmentation reduced accuracy by 3.4 percentage points, as median retrieval similarity was only 0.167, demonstrating that experience injection without semantic alignment introduces noise rather than grounding. Second, when models agree on incorrect answers (sigma equals zero), no downstream ensemble can recover; this agreement-but-wrong failure mode is intrinsic to self-consistency and bounds achievable accuracy at approximately eight percentage points below full ensembling. Third, attribution estimates based on proxy signals such as response similarity and entropy showed weak correlation with ground-truth leave-one-out values, indicating that practical attribution requires explicit counterfactual computation. This work documents which assumptions fail in practice and provides falsifiable baselines for future research on routing, retrieval, and multi-model attribution.

Mixture-of-Experts (MoE) layers increase model capacity by activating only a small subset of experts per token, and typically rely on a learned router to map hidden states to expert assignments. In this work, we ask whether a dedicated learned router is strictly necessary in the MoE settings we study. We propose Self-Routing, a parameter-free routing mechanism that uses a designated subspace of the token hidden state directly as expert logits, eliminating the router projection entirely while leaving the rest of the MoE layer unchanged. We evaluate Self-Routing on GPT-2-scale language modeling and ImageNet-1K classification by comparing it against a standard learned router, random-routing baselines, and dense non-MoE baselines. Our results show that Self-Routing remains competitive with the learned-router baseline while removing all dedicated routing parameters, and yields more balanced expert utilization, with about 17 % higher average normalized routing entropy and no explicit load-balancing loss. On ImageNet-1K with DeiT-S/16, Self-Routing also slightly improves over the corresponding learned-router MoE. These findings suggest that effective MoE routing can emerge from the hidden representation itself without requiring a separate learned router module.

Multi-agent systems (MAS) powered by Large Language Models (LLMs) have been demonstrated to push the boundaries of LLM capabilities, yet they often incur significant costs and face challenges in dynamic LLM selection. Current LLM routing methods effectively reduce overhead in single-agent scenarios by customizing LLM selection for each query, but they overlook the critical decisions regarding collaboration modes and agent roles in MAS. In response to this challenge, we first introduce the problem of Multi-Agent System Routing (MASR), which integrates all components of MAS into a unified routing framework. Toward this goal, we propose MasRouter, the first high-performing, cost-effective, and inductive MASR solution. MasRouter employs collaboration mode determination, role allocation, and LLM routing through a cascaded controller network, progressively constructing a MAS that balances effectiveness and efficiency. Extensive experiments demonstrate that MasRouter is (1) high-performing, achieving a 1.8%sim8.2% improvement over the state-of-the-art method on MBPP; (2) economical, reducing overhead by up to 52.07% compared to SOTA methods on HumanEval; and (3) plug-and-play, seamlessly integrating with mainstream MAS frameworks, reducing overhead by 17.21%sim28.17% via customized routing. The code is available at https://github.com/yanweiyue/masrouter.

Supervised fine-tuning (SFT) is a milestone in aligning large language models with human instructions and adapting them to downstream tasks. In particular, Low-Rank Adaptation (LoRA) has gained widespread attention due to its parameter efficiency. However, its impact on improving the performance of large models remains limited. Recent studies suggest that combining LoRA with Mixture-of-Experts (MoE) can significantly enhance fine-tuning performance. MoE adapts to the diversity and complexity of datasets by dynamically selecting the most suitable experts, thereby improving task accuracy and efficiency. Despite impressive results, recent studies reveal issues in the MoE routing mechanism, such as incorrect assignments and imbalanced expert allocation. Inspired by the principles of Redundancy and Fault Tolerance Theory. We innovatively integrate the concept of Mixture of Experts into the routing mechanism and propose an efficient fine-tuning method called Mixture of Routers (MoR). It employs multiple sub-routers for joint selection and uses a learnable main router to determine the weights of the sub-routers. The results show that MoR outperforms baseline models on most tasks, achieving an average performance improvement of 1%. MoR can serve as a plug-and-play, parameter-efficient fine-tuning method suitable for a wide range of applications. Our code is available here: https://anonymous.4open.science/r/MoR-DFC6.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

Large language models (LLMs) are powerful tools but are often expensive to deploy at scale. LLM query routing mitigates this by dynamically assigning queries to models of varying cost and quality to obtain a desired trade-off. Prior query routing approaches generate only one response from the selected model and a single response from a small (inexpensive) model was often not good enough to beat a response from a large (expensive) model due to which they end up overusing the large model and missing out on potential cost savings. However, it is well known that for small models, generating multiple responses and selecting the best can enhance quality while remaining cheaper than a single large-model response. We leverage this idea to propose BEST-Route, a novel routing framework that chooses a model and the number of responses to sample from it based on query difficulty and the quality thresholds. Experiments on real-world datasets demonstrate that our method reduces costs by up to 60% with less than 1% performance drop.

Large Language Models (LLM)-based systems, i.e. interconnected elements that include an LLM as a central component (e.g., conversational agents), are typically monolithic static architectures that rely on a single LLM for all user queries. However, they often require different preprocessing strategies, levels of reasoning, or knowledge. Generalist LLMs (i.e. GPT-4), trained on very large multi-topic corpora, can perform well in a variety of tasks. However, they require significant financial, energy, and hardware resources that may not be justified for basic tasks. This implies potentially investing in unnecessary costs for a given query. To overcome this problem, a routing mechanism routes user queries to the most suitable components, such as smaller LLMs or experts in specific topics. This approach may improve response quality while minimising costs. Routing can be expanded to other components of the conversational agent architecture, such as the selection of optimal embedding strategies. This paper explores key considerations for integrating routing into LLM-based systems, focusing on resource management, cost definition, and strategy selection. Our main contributions include a formalisation of the problem, a novel taxonomy of existing approaches emphasising relevance and resource efficiency, and a comparative analysis of these strategies in relation to industry practices. Finally, we identify critical challenges and directions for future research.

Cost-aware routing dynamically dispatches user queries to models of varying capability to balance performance and inference cost. However, the routing strategy introduces a new security concern that adversaries may manipulate the router to consistently select expensive high-capability models. Existing routing attacks depend on either white-box access or heuristic prompts, rendering them ineffective in real-world black-box scenarios. In this work, we propose R^2A, which aims to mislead black-box LLM routers to expensive models via adversarial suffix optimization. Specifically, R^2A deploys a hybrid ensemble surrogate router to mimic the black-box router. A suffix optimization algorithm is further adapted for the ensemble-based surrogate. Extensive experiments on multiple open-source and commercial routing systems demonstrate that {R^2A} significantly increases the routing rate to expensive models on queries of different distributions. Code and examples: https://github.com/thcxiker/R2A-Attack.

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.

Prompt routing dynamically selects the most appropriate large language model from a pool of candidates for each query, optimizing performance while managing costs. As model pools scale to include dozens of frontier models with narrow performance gaps, existing approaches face significant challenges: manually defined task taxonomies cannot capture fine-grained capability distinctions, while monolithic routers struggle to differentiate subtle differences across diverse tasks. We propose a two-stage routing architecture that addresses these limitations through automated fine-grained task discovery and task-aware quality estimation. Our first stage employs graph-based clustering to discover latent task types and trains a classifier to assign prompts to discovered tasks. The second stage uses a mixture-of-experts architecture with task-specific prediction heads for specialized quality estimates. At inference, we aggregate predictions from both stages to balance task-level stability with prompt-specific adaptability. Evaluated on 10 benchmarks with 11 frontier models, our method consistently outperforms existing baselines and surpasses the strongest individual model while incurring less than half its cost.

Sparse Mixture of Experts (MoE) models are popular for training large language models due to their computational efficiency. However, the commonly used top-k routing mechanism suffers from redundancy computation and memory costs due to the unbalanced routing. Some experts are overflow, where the exceeding tokens are dropped. While some experts are vacant, which are padded with zeros, negatively impacting model performance. To address the dropped tokens and padding, we propose the Rectify-Router, comprising the Intra-GPU Rectification and the Fill-in Rectification. The Intra-GPU Rectification handles dropped tokens, efficiently routing them to experts within the GPU where they are located to avoid inter-GPU communication. The Fill-in Rectification addresses padding by replacing padding tokens with the tokens that have high routing scores. Our experimental results demonstrate that the Intra-GPU Rectification and the Fill-in Rectification effectively handle dropped tokens and padding, respectively. Furthermore, the combination of them achieves superior performance, surpassing the accuracy of the vanilla top-1 router by 4.7%.

The rapid growth of large language models (LLMs) with diverse capabilities, costs, and domains has created a critical need for intelligent model selection at inference time. While smaller models suffice for routine queries, complex tasks demand more capable models. However, static model deployment does not account for the complexity and domain of incoming queries, leading to suboptimal performance and increased costs. Dynamic routing systems that adaptively select models based on query characteristics have emerged as a solution to this challenge. We provide a systematic analysis of state-of-the-art multi-LLM routing and cascading approaches. In contrast to mixture-of-experts architectures, which route within a single model, we study routing across multiple independently trained LLMs. We cover diverse routing paradigms, including query difficulty, human preferences, clustering, uncertainty quantification, reinforcement learning, multimodality, and cascading. For each paradigm, we analyze representative methods and examine key trade-offs. Beyond taxonomy, we introduce a conceptual framework that characterizes routing systems along three dimensions: when decisions are made, what information is used, and how they are computed. This perspective highlights that practical systems are often compositional, integrating multiple paradigms under operational constraints. Our analysis demonstrates that effective multi-LLM routing requires balancing competing objectives. Choosing the optimal routing strategy depends on deployment and computational constraints. Well-designed routing systems can outperform even the most powerful individual models by strategically leveraging specialized capabilities across models while maximizing efficiency gains. Meanwhile, open challenges remain in developing routing mechanisms that generalize across diverse architectures, modalities, and applications.

Over the past year, the vLLM Semantic Router project has released a series of work spanning: (1) core routing mechanisms -- signal-driven routing, context-length pool routing, router performance engineering, policy conflict detection, low-latency embedding models, category-aware semantic caching, user-feedback-driven routing adaptation, hallucination detection, and hierarchical content-safety classification for privacy and jailbreak protection; (2) fleet optimization -- fleet provisioning and energy-efficiency analysis; (3) agentic and multimodal routing -- multimodal agent routing, tool selection, CUA security, and multi-turn context memory and safety; (4) governance and standards -- inference routing protocols and multi-provider API extensions. Each paper tackled a specific problem in LLM inference, but the problems are not independent; for example, fleet provisioning depends on the routing policy, which depends on the workload mix, shifting as organizations adopt agentic and multimodal workloads. This paper distills those results into the Workload-Router-Pool (WRP) architecture, a three-dimensional framework for LLM inference optimization. Workload characterizes what the fleet serves (chat vs. agent, single-turn vs. multi-turn, warm vs. cold, prefill-heavy vs. decode-heavy). Router determines how each request is dispatched (static semantic rules, online bandit adaptation, RL-based model selection, quality-aware cascading). Pool defines where inference runs (homogeneous vs. heterogeneous GPU, disaggregated prefill/decode, KV-cache topology). We map our prior work onto a 3x3 WRP interaction matrix, identify which cells we have covered and which remain open, and propose twenty-one concrete research directions at the intersections, each grounded in our prior measurements, tiered by maturity from engineering-ready to open research.

A mobile ad hoc network (MANET) is a collection of autonomous nodes that communicate with each other by forming a multi-hop radio network and maintaining connections in a decentralized manner. Security remains a major challenge for these networks due to their features of open medium, dynamically changing topologies, reliance on cooperative algorithms,absence of centralized monitoring points, and lack of clear lines of defense. Most of the routing protocols for MANETs are thus vulnerable to various types of attacks. Ad hoc on-demand distance vector routing (AODV) is a very popular routing algorithm. However, it is vulnerable to the well-known black hole attack, where a malicious node falsely advertises good paths to a destination node during the route discovery process. This attack becomes more sever when a group of malicious nodes cooperate each other. In this paper, a defense mechanism is presented against a coordinated attack by multiple black hole nodes in a MANET. The simulation carried out on the proposed scheme has produced results that demonstrate the effectiveness of the mechanism in detection of the attack while maintaining a reasonable level of throughput in the network.

We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released at https://github.com/pytorch/fairseq/

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

The Mixtures-of-Experts (MoE) model is a widespread distributed and integrated learning method for large language models (LLM), which is favored due to its ability to sparsify and expand models efficiently. However, the performance of MoE is limited by load imbalance and high latency of All-To-All communication, along with relatively redundant computation owing to large expert capacity. Load imbalance may result from existing routing policies that consistently tend to select certain experts. The frequent inter-node communication in the All-To-All procedure also significantly prolongs the training time. To alleviate the above performance problems, we propose a novel routing strategy that combines load balance and locality by converting partial inter-node communication to that of intra-node. Notably, we elucidate that there is a minimum threshold for expert capacity, calculated through the maximal angular deviation between the gating weights of the experts and the assigned tokens. We port these modifications on the PanGu-Sigma model based on the MindSpore framework with multi-level routing and conduct experiments on Ascend clusters. The experiment results demonstrate that the proposed LocMoE reduces training time per epoch by 12.68% to 22.24% compared to classical routers, such as hash router and switch router, without impacting the model accuracy.

Protecting the network layer from malicious attacks is an important and challenging security issue in mobile ad hoc networks (MANETs). In this paper, a security mechanism is proposed to defend against a cooperative gray hole attack on the well known AODV routing protocol in MANETs. A gray hole is a node that selectively drops and forwards data packets after it advertises itself as having the shortest path to the destination node in response to a route request message from a source node. The proposed mechanism does not apply any cryptographic primitives on the routing messages. Instead, it protects the network by detecting and reacting to malicious activities of any node. Simulation results show that the scheme has a significantly high detection rate with moderate network traffic overhead.

Large language model (LLM) routing assigns each query to the most suitable model from an ensemble. We introduce LLMRouterBench, a large-scale benchmark and unified framework for LLM routing. It comprises over 400K instances from 21 datasets and 33 models. Moreover, it provides comprehensive metrics for both performance-oriented routing and performance-cost trade-off routing, and integrates 10 representative routing baselines. Using LLMRouterBench, we systematically re-evaluate the field. While confirming strong model complementarity-the central premise of LLM routing-we find that many routing methods exhibit similar performance under unified evaluation, and several recent approaches, including commercial routers, fail to reliably outperform a simple baseline. Meanwhile, a substantial gap remains to the Oracle, driven primarily by persistent model-recall failures. We further show that backbone embedding models have limited impact, that larger ensembles exhibit diminishing returns compared to careful model curation, and that the benchmark also enables latency-aware analysis. All code and data are available at https://github.com/ynulihao/LLMRouterBench.

Compound AI systems promise capabilities beyond those of individual models, yet their success depends critically on effective orchestration. Existing routing approaches face two limitations: (1) input-level routers make coarse query-level decisions that ignore evolving task requirements; (2) RL-trained orchestrators are expensive to adapt and often suffer from routing collapse, repeatedly invoking one strong but costly option in multi-turn scenarios. We introduce SkillOrchestra, a framework for skill-aware orchestration. Instead of directly learning a routing policy end-to-end, SkillOrchestra learns fine-grained skills from execution experience and models agent-specific competence and cost under those skills. At deployment, the orchestrator infers the skill demands of the current interaction and selects agents that best satisfy them under an explicit performance-cost trade-off. Extensive experiments across ten benchmarks demonstrate that SkillOrchestra outperforms SoTA RL-based orchestrators by up to 22.5% with 700x and 300x learning cost reduction compared to Router-R1 and ToolOrchestra, respectively. These results show that explicit skill modeling enables scalable, interpretable, and sample-efficient orchestration, offering a principled alternative to data-intensive RL-based approaches. The code is available at: https://github.com/jiayuww/SkillOrchestra.

Long-context ability, has become one of the most important iteration direction of next-generation Large Language Models, particularly in semantic understanding/reasoning, code agentic intelligence and recommendation system. However, the standard softmax attention exhibits quadratic time complexity with respect to sequence length. As the sequence length increases, this incurs substantial overhead in long-context settings, leading the training and inference costs of extremely long sequences deteriorate rapidly. Existing solutions mitigate this issue through two technique routings: i) Reducing the KV cache per layer, such as from the head-level compression GQA, and the embedding dimension-level compression MLA, but the KV cache remains linearly dependent on the sequence length at a 1:1 ratio. ii) Interleaving with KV Cache friendly architecture, such as local attention SWA, linear kernel GDN, but often involve trade-offs among KV Cache and long-context modeling effectiveness. Besides the two technique routings, we argue that there exists an intermediate path not well explored: {Maintaining a linear relationship between the KV cache and sequence length, but performing semantic-level compression through a specific ratio k}. This O(n/k) path does not pursue a ``minimum KV cache'', but rather trades acceptable memory costs for complete, referential, and interpretable retention of long distant dependency. Motivated by this, we propose Kwai Summary Attention (KSA), a novel attention mechanism that reduces sequence modeling cost by compressing historical contexts into learnable summary tokens.

The rapid advancement of large language models (LLMs) and domain-specific AI agents has greatly expanded the ecosystem of AI-powered services. User queries, however, are highly diverse and often span multiple domains and task types, resulting in a complex and heterogeneous landscape. This diversity presents a fundamental routing challenge: how to accurately direct each query to an appropriate execution unit while optimizing both performance and efficiency. To address this, we propose MoMA (Mixture of Models and Agents), a generalized routing framework that integrates both LLM and agent-based routing. Built upon a deep understanding of model and agent capabilities, MoMA effectively handles diverse queries through precise intent recognition and adaptive routing strategies, achieving an optimal balance between efficiency and cost. Specifically, we construct a detailed training dataset to profile the capabilities of various LLMs under different routing model structures, identifying the most suitable tasks for each LLM. During inference, queries are dynamically routed to the LLM with the best cost-performance efficiency. We also introduce an efficient agent selection strategy based on a context-aware state machine and dynamic masking. Experimental results demonstrate that the MoMA router offers superior cost-efficiency and scalability compared to existing approaches.

Modern LLM deployments confront a widening cost-performance spectrum: premium models deliver strong reasoning but are expensive, while lightweight models are economical yet brittle on complex tasks. Static escalation rules and keyword heuristics under-utilize this spectrum and fail to adapt across task types. We present xRouter, a tool-calling-based routing system in which a learned router can either answer directly or invoke one or more external models. The router is trained end-to-end with reinforcement learning using an explicit, cost-aware reward that encodes cost-performance trade-offs, eliminating the need for hand-engineered routing rules. Our implementation encompasses the full reinforcement learning framework, including reward and cost accounting, as well as the deployment and evaluation pipelines. Across diverse benchmarks, xRouter achieves strong cost-performance trade-offs (e.g., substantial cost reductions at comparable task completion rates), and provides empirical insights into what reliably helps learned routing and what does not, ranging from model trainability to the difficulty of eliciting sophisticated orchestration behaviors in small open models. We hope these findings and our open implementation will serve as a practical substrate for advancing learned, cost-aware LLM orchestration.

As the large language model (LLM) ecosystem expands, individual models exhibit varying capabilities across queries, benchmarks, and domains, motivating the development of LLM routing. While prior work has largely focused on router mechanism design, LLM profiles, which capture model capabilities, remain underexplored. In this work, we ask: How does LLM profile design affect routing performance across different routers? Addressing this question helps clarify the role of profiles in routing, disentangle profile design from router design, and enable fairer comparison and more principled development of routing systems. To this end, we view LLM profiling as a structured information integration problem over heterogeneous interaction histories. We develop a general design space of LLM profiles, named RouteProfile, along four key dimensions: organizational form, representation type, aggregation depth, and learning configuration. Through systematic evaluation across three representative routers under both standard and new-LLM generalization settings, we show that: (1) structured profiles consistently outperform flat ones; (2) query-level signals are more reliable than coarse domain-level signals; and (3) generalization to newly introduced models benefits most from structured profiles under trainable configurations. Overall, our work highlights LLM profile design as an important direction for future routing research.

Model routing chooses which language model to use for each query. By sending easy queries to cheaper models and hard queries to stronger ones, it can significantly reduce inference cost while maintaining high accuracy. However, most existing routers treat this as a fixed choice among a small set of models, which makes them hard to adapt to new models or changing budget constraints. In this paper, we propose SCOPE (Scalable and Controllable Outcome Performance Estimator), a routing framework that goes beyond model selection by predicting their cost and performance. Trained with reinforcement learning, SCOPE makes reasoning-based predictions by retrieving how models behave on similar problems, rather than relying on fixed model names, enabling it to work with new, unseen models. Moreover, by explicitly predicting how accurate and how expensive a model will be, it turns routing into a dynamic decision problem, allowing users to easily control the trade-off between accuracy and cost. Experiments show that SCOPE is more than just a cost-saving tool. It flexibly adapts to user needs: it can boost accuracy by up to 25.7% when performance is the priority, or cut costs by up to 95.1% when efficiency matters most.

Packaging has become a crucial process due to the paradigm shift of More than Moore. Addressing manufacturing and yield issues is a significant challenge for modern layout algorithms. We propose to use printed circuit board (PCB) placement as a benchmark for the packaging problem. A maximum-margin formulation is devised to improve the separation between nets. Our framework includes seed layout proposals, a coordinate descent-based procedure to optimize routability, and a mixed-integer linear programming method to legalize the layout. We perform an extensive study with 14 PCB designs and an open-source router. We show that the placements produced by NS-place improve routed wirelength by up to 25\%, reduce the number of vias by up to 50\%, and reduce the number of DRVs by 79\% compared to manual and wirelength-minimal placements.

As LLMs proliferate with diverse capabilities and costs, LLM routing has emerged by learning to predict each LLM's quality and cost for a given query, then selecting the one with high quality and low cost. However, existing routers implicitly assume a single fixed quality and cost per LLM for each query, ignoring that the same LLM's quality varies with its output length. This causes routers to exclude powerful LLMs when their estimated cost exceeds the budget, missing the opportunity that these LLMs could still deliver high quality at reduced cost with shorter outputs. To address this, we introduce R2-Router, which treats output length budget as a controllable variable and jointly selects the best LLM and length budget, enforcing the budget via length-constrained instructions. This enables R2-Router to discover that a powerful LLM with constrained output can outperform a weaker LLM at comparable cost-efficient configurations invisible to prior methods. Together with the router framework, we construct R2-Bench, the first routing dataset capturing LLM behavior across diverse output length budgets. Experiments show that R2-Router achieves state-of-the-art performance at 4-5x lower cost compared with existing routers. This work opens a new direction: routing as reasoning, where routers evolve from reactive selectors to deliberate reasoners that explore which LLM to use and at what cost budget.

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width. However, we argue that effective SMoE training remains challenging because of the suboptimal routing process where experts that perform computation do not directly contribute to the routing process. In this work, we propose competition, a novel mechanism to route tokens to experts with the highest neural response. Theoretically, we show that the competition mechanism enjoys a better sample efficiency than the traditional softmax routing. Furthermore, we develop CompeteSMoE, a simple yet effective algorithm to train large language models by deploying a router to learn the competition policy, thus enjoying strong performances at a low training overhead. Our extensive empirical evaluations on both the visual instruction tuning and language pre-training tasks demonstrate the efficacy, robustness, and scalability of CompeteSMoE compared to state-of-the-art SMoE strategies. We have made the implementation available at: https://github.com/Fsoft-AIC/CompeteSMoE. This work is an improved version of the previous study at arXiv:2402.02526

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to particular domains. This has enabled the creation of powerful and adaptive routing-based "Model MoErging" methods with the goal of using expert modules to create an aggregate system with improved performance or generalization. However, existing MoErging methods often prioritize generalization to unseen tasks at the expense of performance on held-in tasks, which limits its practical applicability in real-world deployment scenarios. We observe that current token-level routing mechanisms neglect the global semantic context of the input task. This token-wise independence hinders effective expert selection for held-in tasks, as routing decisions fail to incorporate the semantic properties of the task. To address this, we propose, Global and Local Instruction Driven Expert Router (GLIDER) that integrates a multi-scale routing mechanism, encompassing a semantic global router and a learned local router. The global router leverages LLM's advanced reasoning capabilities for semantic-related contexts to enhance expert selection. Given the input query and LLM, the router generates semantic task instructions that guide the retrieval of the most relevant experts across all layers. This global guidance is complemented by a local router that facilitates token-level routing decisions within each module, enabling finer control and enhanced performance on unseen tasks. Our experiments using T5-based models for T0 and FLAN tasks demonstrate that GLIDER achieves substantially improved held-in performance while maintaining strong generalization on held-out tasks. We also perform ablations experiments to dive deeper into the components of GLIDER. Our experiments highlight the importance of our multi-scale routing that leverages LLM-driven semantic reasoning for MoErging methods.

Mixture-of-Experts (MoE) architectures are often considered a natural fit for continual learning because sparse routing should localize updates and reduce interference, yet MoE Transformers still forget substantially even with sparse, well-balanced expert utilization. We attribute this gap to a pre-routing bottleneck: multi-head attention concatenates head-specific signals into a single post-attention router input, forcing routing to act on co-occurring feature compositions rather than separable head channels. We show that this router input simultaneously encodes multiple separately decodable semantic and structural factors with uneven head support, and that different feature compositions induce weakly aligned parameter-gradient directions; as a result, routing maps many distinct compositions to the same route. We quantify this collision effect via a route-wise effective composition number N_{eff} and find that higher N_{eff} is associated with larger old-task loss increases after continual training. Motivated by these findings, we propose MH-MoE, which performs head-wise routing over sub-representations to increase routing granularity and reduce composition collisions. On TRACE with Qwen3-0.6B/8B, MH-MoE effectively mitigates forgetting, reducing BWT on Qwen3-0.6B from 11.2% (LoRAMoE) to 4.5%.

Large language models (LLMs) achieve impressive performance by scaling model parameters, but this comes with significant inference overhead. Feed-forward networks (FFNs), which dominate LLM parameters, exhibit high activation sparsity in hidden neurons. To exploit this, researchers have proposed using a mixture-of-experts (MoE) architecture, where only a subset of parameters is activated. However, existing approaches often require extensive training data and resources, limiting their practicality. We propose CMoE (Carved MoE), a novel framework to efficiently carve MoE models from dense models. CMoE achieves remarkable performance through efficient expert grouping and lightweight adaptation. First, neurons are grouped into shared and routed experts based on activation rates. Next, we construct a routing mechanism without training from scratch, incorporating a differentiable routing process and load balancing. Using modest data, CMoE produces a well-designed, usable MoE from a 7B dense model within five minutes. With lightweight fine-tuning, it achieves high-performance recovery in under an hour. We make our code publicly available at https://github.com/JarvisPei/CMoE.

VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations. Initially before creating a route, each vehicle needs a group of delivery points that are not exceeding their maximum capacity. Drivers tend to deliver only to certain areas. Cluster-based is one of the approaches to give a basis for generating tighter routes. In this paper we propose new algorithms for producing such clusters/groups that do not exceed vehicles maximum capacity. Our basic assumptions are each vehicle originates from a depot, delivers the items to the customers and returns to the depot, also the vehicles are homogeneous. This methods are able to compact sub-areas in each cluster. Computational results demonstrate the effectiveness of our new procedures, which are able to assist users to plan service territories and vehicle routes more efficiently.

The deployment of large language models (LLMs) in real-world applications is increasingly limited by their high inference cost. While recent advances in dynamic token-level computation allocation attempt to improve efficiency by selectively activating model components per token, existing methods rely on greedy routing--a myopic execute-or-skip mechanism that often leads to irreversible information loss and suboptimal token selection. This paper introduces informed routing, a new paradigm that proactively addresses these issues. The key insight is to assess not only a token's immediate importance but also its recoverability, i.e., how well its transformation can be approximated. To this end, we propose the Lightweight Feature Forecaster (LFF), a small predictive module that estimates a unit's output before routing decisions are made. This enables a flexible execute-or-approximate policy that preserves model fidelity while drastically reducing computation. Extensive experiments on both language modeling and reasoning tasks show that informed routing achieves state-of-the-art efficiency-performance trade-offs across multiple sparsity levels. Notably, even without final LoRA fine-tuning, our method matches or surpasses strong baselines that require full fine-tuning, all while reducing training time by over 50%. The code is available at: https://github.com/EIT-NLP/informed-routing

Large Language Models (LLMs) process every token through all layers of a transformer stack, causing wasted computation on simple queries and insufficient flexibility for harder ones that need deeper reasoning. Adaptive-depth methods can improve efficiency, but prior approaches rely on costly inference-time search, architectural changes, or large-scale retraining, and in practice often degrade accuracy despite efficiency gains. We introduce Dr.LLM, Dynamic routing of Layers for LLMs, a retrofittable framework that equips pretrained models with lightweight per-layer routers deciding to skip, execute, or repeat a block. Routers are trained with explicit supervision: using Monte Carlo Tree Search (MCTS), we derive high-quality layer configurations that preserve or improve accuracy under a compute budget. Our design, windowed pooling for stable routing, focal loss with class balancing, and bottleneck MLP routers, ensures robustness under class imbalance and long sequences. On ARC (logic) and DART (math), Dr.LLM improves accuracy by up to +3.4%p while saving 5 layers per example on average. Routers generalize to out-of-domain tasks (MMLU, GSM8k, AIME, TruthfulQA, SQuADv2, GPQA, PIQA, AGIEval) with only 0.85% accuracy drop while retaining efficiency, and outperform prior routing methods by up to +7.7%p. Overall, Dr.LLM shows that explicitly supervised routers retrofit frozen LLMs for budget-aware, accuracy-driven inference without altering base weights.

Existing industrial-scale navigation applications contend with massive road networks, typically employing two main categories of approaches for route planning. The first relies on precomputed road costs for optimal routing and heuristic algorithms for generating alternatives, while the second, generative methods, has recently gained significant attention. However, the former struggles with personalization and route diversity, while the latter fails to meet the efficiency requirements of large-scale real-time scenarios. To address these limitations, we propose GenMRP, a generative framework for multi-route planning. To ensure generation efficiency, GenMRP first introduces a skeleton-to-capillary approach that dynamically constructs a relevant sub-network significantly smaller than the full road network. Within this sub-network, routes are generated iteratively. The first iteration identifies the optimal route, while the subsequent ones generate alternatives that balance quality and diversity using the newly proposed correctional boosting approach. Each iteration incorporates road features, user historical sequences, and previously generated routes into a Link Cost Model to update road costs, followed by route generation using the Dijkstra algorithm. Extensive experiments show that GenMRP achieves state-of-the-art performance with high efficiency in both offline and online environments. To facilitate further research, we have publicly released the training and evaluation dataset. GenMRP has been fully deployed in a real-world navigation app, demonstrating its effectiveness and benefits.

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.

Retrieval-Augmented Generation (RAG) systems typically rely on a single fixed retriever, despite growing evidence that no single retriever performs optimally across all query types. In this paper, we explore a query routing approach that dynamically selects from a pool of retrievers based on the query, using both train-free heuristics and learned routing models. We frame routing as a learning-to-rank (LTR) problem and introduce LTRR, a framework that learns to rank retrievers by their expected utility gain to downstream LLM performance. Our experiments, conducted on synthetic QA data with controlled query type variations, show that routing-based RAG systems can outperform the best single-retriever-based systems. Performance gains are especially pronounced in models trained with the Answer Correctness (AC) metric and with pairwise learning approaches, especially with XGBoost. We also observe improvements in generalization to out-of-distribution queries. As part of the SIGIR 2025 LiveRAG challenge, our submitted system demonstrated the practical viability of our approach, achieving competitive performance in both answer correctness and faithfulness. These findings highlight the importance of both training methodology and metric selection in query routing for RAG systems.

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.

The mixture of Expert (MoE) parallelism is a recent advancement that scales up the model size with constant computational cost. MoE selects different sets of parameters (i.e., experts) for each incoming token, resulting in a sparsely-activated model. Despite several successful applications of MoE, its training efficiency degrades significantly as the number of experts increases. The routing stage in MoE relies on the efficiency of the All2All communication collective, which suffers from network congestion and has poor scalability. To mitigate these issues, we introduce SMILE, which exploits heterogeneous network bandwidth and splits a single-step routing into bi-level routing. Our experimental results show that the proposed method obtains a 2.5x speedup over Switch Transformer in terms of pretraining throughput on the Colossal Clean Crawled Corpus without losing any convergence speed.

Retrieval-Augmented Generation (RAG) significantly improves the performance of Large Language Models (LLMs) on knowledge-intensive tasks. However, varying response quality across LLMs under RAG necessitates intelligent routing mechanisms, which select the most suitable model for each query from multiple retrieval-augmented LLMs via a dedicated router model. We observe that external documents dynamically affect LLMs' ability to answer queries, while existing routing methods, which rely on static parametric knowledge representations, exhibit suboptimal performance in RAG scenarios. To address this, we formally define the new retrieval-augmented LLM routing problem, incorporating the influence of retrieved documents into the routing framework. We propose RAGRouter, a RAG-aware routing design, which leverages document embeddings and RAG capability embeddings with contrastive learning to capture knowledge representation shifts and enable informed routing decisions. Extensive experiments on diverse knowledge-intensive tasks and retrieval settings show that RAGRouter outperforms the best individual LLM by 3.61% on average and existing routing methods by 3.29%-9.33%. With an extended score-threshold-based mechanism, it also achieves strong performance-efficiency trade-offs under low-latency constraints.

Mainstream parameter-efficient fine-tuning (PEFT) methods, such as LoRA or Adapter, project a model's hidden states to a lower dimension, allowing pre-trained models to adapt to new data through this low-rank bottleneck. However, PEFT tasks involving multiple modalities, like vision-language (VL) tasks, require not only adaptation to new data but also learning the relationship between different modalities. Targeting at VL PEFT tasks, we propose a family of operations, called routing functions, to enhance VL alignment in the low-rank bottlenecks. The routing functions adopt linear operations and do not introduce new trainable parameters. In-depth analyses are conducted to study their behavior. In various VL PEFT settings, the routing functions significantly improve performance of the original PEFT methods, achieving over 20% improvement on VQAv2 (RoBERTa_{large}+ViT-L/16) and 30% on COCO Captioning (GPT2-medium+ViT-L/16). Also when fine-tuning a pre-trained multimodal model such as CLIP-BART, we observe smaller but consistent improvements across a range of VL PEFT tasks.

Sparse Mixture-of-Experts (SMoE) models enable scaling language models efficiently, but training them remains challenging, as routing can collapse onto few experts and auxiliary load-balancing losses can reduce specialization. Motivated by these hurdles, we study how routing decisions in SMoEs are formed mechanistically. First, we reveal a geometric coupling between routers and their corresponding experts. For a given token, the router weights for the selected expert and the expert weights processing it receive gradients along the same input direction, differing only in scalar coefficients. Thus, matched router--expert directions accumulate the same routed token history. This theoretical coupling also appears empirically in routing dynamics. In a 1B SMoE trained from scratch, higher router scores predict stronger expert neuron activations, showing that routing decisions are mirrored inside the selected expert. Next, we analyze the effects of auxiliary load balancing on the router--expert geometric coupling, showing that such losses break this structure by spreading input-directed gradients across router weights, making distinct router directions nearly three times more similar to each other. Last, we demonstrate the centrality of geometric coupling for effective routing with a parameter-free online K-Means router, in which each expert maintains a running average of the hidden states routed to it and tokens are assigned based on cosine similarity. Compared with auxiliary-loss and loss-free balancing, this router achieves the lowest load imbalance with only a modest perplexity increase, indicating that geometric coupling captures a substantial part of what the router learns. Overall, our results explain how routers form assignment geometry that supports an effective division of labor.

We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are related to competitive bidding by persons for objects and the attendant market equilibrium, which underlie auction processes. However, the starting point of our algorithms is different, namely weighted and unweighted path construction in directed graphs, rather than assignment of persons to objects. The new algorithms have several potential advantages over existing methods: they are empirically faster in some important contexts, such as max-flow, they are well-suited for on-line replanning, and they can be adapted to distributed asynchronous operation. Moreover, they allow arbitrary initial prices, without complementary slackness restrictions, and thus are better-suited to take advantage of reinforcement learning methods that use off-line training with data, as well as on-line training during real-time operation. The new algorithms may also find use in reinforcement learning contexts involving approximation, such as multistep lookahead and tree search schemes, and/or rollout algorithms.

Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can improve storage, compute, memory bandwidth, and energy usage. In this paper we propose a novel accurate pruning technique that allows precise control over the output network size. Our method uses an efficient optimal transportation scheme which we make end-to-end differentiable and which automatically tunes the exploration-exploitation behavior of the algorithm to find accurate sparse sub-networks. We show that our method achieves state-of-the-art performance compared to previous pruning methods on 3 different datasets, using 5 different models, across a wide range of pruning ratios, and with two types of sparsity budgets and pruning granularities.

Graph-based Multi-Agent Systems (MAS) enable complex cyclic workflows but suffer from inefficient static model allocation, where deploying strong models uniformly wastes computation on trivial sub-tasks. We propose CASTER (Context-Aware Strategy for Task Efficient Routing), a lightweight router for dynamic model selection in graph-based MAS. CASTER employs a Dual-Signal Router that combines semantic embeddings with structural meta-features to estimate task difficulty. During training, the router self-optimizes through a Cold Start to Iterative Evolution paradigm, learning from its own routing failures via on-policy negative feedback. Experiments using LLM-as-a-Judge evaluation across Software Engineering, Data Analysis, Scientific Discovery, and Cybersecurity demonstrate that CASTER reduces inference cost by up to 72.4% compared to strong-model baselines while matching their success rates, and consistently outperforms both heuristic routing and FrugalGPT across all domains.

Yuan 2.0-M32, with a similar base architecture as Yuan-2.0 2B, uses a mixture-of-experts architecture with 32 experts of which 2 experts are active. A new router network, Attention Router, is proposed and adopted for a more efficient selection of experts, which boosts the accuracy of 3.8% compared to the model with classical router network. Yuan 2.0-M32 is trained with 2000B tokens from scratch, and the training computation consumption is only 9.25% of a dense model at the same parameter scale. Yuan 2.0-M32 demonstrates competitive capability on coding, math, and various domains of expertise, with only 3.7B active parameters of 40B in total, and 7.4 GFlops forward computation per token, both of which are only 1/19 of Llama3-70B. Yuan 2.0-M32 surpass Llama3-70B on MATH and ARC-Challenge benchmark, with accuracy of 55.89 and 95.8 respectively. The models and source codes of Yuan 2.0-M32 are released at Github.

The availability of a wide range of large language models (LLMs) embedded in various agentic systems has significantly increased the potential of model selection strategies to improve the cost-performance tradeoff. Existing strategies involve either routing, where a single model is chosen per query, or cascading, which sequentially runs increasingly larger models until a satisfactory answer is found. However, current approaches face three key limitations: they (1) lack formal proofs of optimality, (2) fail to identify the conditions under which these strategies are most effective to improve the cost-performance tradeoff, and (3) are unable to combine both paradigms for further improvements. To address these issues, we first derive a novel optimal strategy for cascading and prove the optimality of an existing routing strategy. Further, we propose cascade routing, a unified framework that integrates routing and cascading into a theoretically optimal strategy. Through our analysis, we identify good quality estimators as the critical factor for the success of model selection paradigms. Finally, in our experiments, we show that cascade routing consistently outperforms the individual approaches by a large margin and we analyze quality estimators to determine when routing and/or cascading are useful paradigms for model selection.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

As large language models (LLMs) evolve into autonomous agents that execute long-horizon workflows, invoking a high-capability model at every step becomes economically unsustainable. While model routing is effective for single-turn queries, agentic routing is a sequential, path-dependent problem: early mistakes compound, feedback is often at the end of the episode, and deployments often demand strict per-task spending limits. We propose Budget-Aware Agentic Routing, which selects between a cheap and an expensive model at each step to optimize the cost--success frontier and to operate under strict per-task budgets. We propose Boundary-Guided Training, which leverages two boundary policies (always-small vs.\ always-large) to build a difficulty taxonomy and to anchor learning under sparse rewards. Our approach warms start with boundary-guided SFT data synthesis via stratified sampling of cost-efficient trajectories, then applies Boundary-Guided Policy Optimization (BoPO), combining boundary-relative rewards with a reference-guided advantage to avoid degenerate cheap-failure solutions. Experiment results show that our method improves the efficiency frontier, matching strong routing baselines at substantially lower cost while demonstrating generalization to strict inference-time budget constraints. Overall, our work establishes a foundational framework for agentic routing, shifting the paradigm from static model selection to dynamic, budget-aware sequential decision-making.

Large language model (LLM) routing has emerged as a crucial strategy for balancing computational costs with performance by dynamically assigning queries to the most appropriate model based on query complexity. Despite recent advances showing that preference-data-based routers can outperform traditional methods, current evaluation benchmarks remain limited. They largely focus on general model capabilities while overlooking task-specific behaviors and critical concerns such as privacy, safety, and potential backdoor vulnerabilities introduced through preference data. In response, we propose the DSC benchmark: Diverse, Simple, and Categorized, an evaluation framework that categorizes router performance across a broad spectrum of query types, including coding, translation, mathematics, human instructions, general knowledge, and LLM jailbreaking. Additionally, it integrates privacy and safety assessments to reveal hidden risks. Our experiments on three preference-based routers and two commercial counterparts demonstrate that while these systems improve efficiency, they often make suboptimal, category-driven decisions. For instance, a BERT-based router directs all coding and mathematics queries to the most powerful LLM even when simpler models would suffice, while routing jailbreaking attempts to weaker models, thereby elevating safety risks.