Daily Papers

A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the entity exists and its orientation to represent the instantiation parameters. Active capsules at one level make predictions, via transformation matrices, for the instantiation parameters of higher-level capsules. When multiple predictions agree, a higher level capsule becomes active. We show that a discrimininatively trained, multi-layer capsule system achieves state-of-the-art performance on MNIST and is considerably better than a convolutional net at recognizing highly overlapping digits. To achieve these results we use an iterative routing-by-agreement mechanism: A lower-level capsule prefers to send its output to higher level capsules whose activity vectors have a big scalar product with the prediction coming from the lower-level capsule.

We propose Chain-of-Experts (CoE), a new Mixture-of-Experts (MoE) architecture that introduces sequential expert communication within each layer. Unlike traditional MoE models, where experts operate independently in parallel, CoE processes tokens iteratively across a chain of experts inside a layer. To support dynamic expert selection across iterations, CoE employs a dedicated router at each iteration step within a layer. This design allows tokens to re-evaluate and select different experts during each iteration, rather than being statically assigned. As a result, CoE introduces a flexible routing mechanism that increases the diversity of expert combinations and enriches the model's representational capacity. CoE demonstrates improved performance under fixed compute: on math reasoning tasks, it reduces validation loss from 1.20 to 1.12 compared to a standard MoE. Beyond performance, CoE offers a new scaling axis: depth through expert iteration, which complements conventional width/depth scaling. For example, using 2x iterations matches the performance of 3x expert selections (in width), while reducing memory usage by 17.6-42% relative to other scaling strategies. Our analysis reveals that CoE's benefits stem from its iterative residual structure and enhanced expert specialization empowered by iterative routing, which together unlock more expressive representations. Code is available at https://github.com/ZihanWang314/coe.

Natural data is redundant yet predominant architectures tile computation uniformly across their input and output space. We propose the Recurrent Interface Networks (RINs), an attention-based architecture that decouples its core computation from the dimensionality of the data, enabling adaptive computation for more scalable generation of high-dimensional data. RINs focus the bulk of computation (i.e. global self-attention) on a set of latent tokens, using cross-attention to read and write (i.e. route) information between latent and data tokens. Stacking RIN blocks allows bottom-up (data to latent) and top-down (latent to data) feedback, leading to deeper and more expressive routing. While this routing introduces challenges, this is less problematic in recurrent computation settings where the task (and routing problem) changes gradually, such as iterative generation with diffusion models. We show how to leverage recurrence by conditioning the latent tokens at each forward pass of the reverse diffusion process with those from prior computation, i.e. latent self-conditioning. RINs yield state-of-the-art pixel diffusion models for image and video generation, scaling to 1024X1024 images without cascades or guidance, while being domain-agnostic and up to 10X more efficient than 2D and 3D U-Nets.

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-agent systems built from prompted large language models can improve multi-round reasoning, yet most existing pipelines rely on fixed, trajectory-wide communication patterns that are poorly matched to the stage-dependent needs of iterative problem solving. We introduce DyTopo, a manager-guided multi-agent framework that reconstructs a sparse directed communication graph at each round. Conditioned on the manager's round goal, each agent outputs lightweight natural-language query (need) and \key (offer) descriptors; DyTopo embeds these descriptors and performs semantic matching, routing private messages only along the induced edges. Across code generation and mathematical reasoning benchmarks and four LLM backbones, DyTopo consistently outperforms over the strongest baseline (avg. +6.2). Beyond accuracy, DyTopo yields an interpretable coordination trace via the evolving graphs, enabling qualitative inspection of how communication pathways reconfigure across rounds.

Deploying language models (LMs) necessitates outputs to be both high-quality and compliant with safety guidelines. Although Inference-Time Guardrails (ITG) offer solutions that shift model output distributions towards compliance, we find that current methods struggle in balancing safety with helpfulness. ITG Methods that safely address non-compliant queries exhibit lower helpfulness while those that prioritize helpfulness compromise on safety. We refer to this trade-off as the guardrail tax, analogous to the alignment tax. To address this, we propose PrimeGuard, a novel ITG method that utilizes structured control flow. PrimeGuard routes requests to different self-instantiations of the LM with varying instructions, leveraging its inherent instruction-following capabilities and in-context learning. Our tuning-free approach dynamically compiles system-designer guidelines for each query. We construct and release safe-eval, a diverse red-team safety benchmark. Extensive evaluations demonstrate that PrimeGuard, without fine-tuning, overcomes the guardrail tax by (1) significantly increasing resistance to iterative jailbreak attacks and (2) achieving state-of-the-art results in safety guardrailing while (3) matching helpfulness scores of alignment-tuned models. Extensive evaluations demonstrate that PrimeGuard, without fine-tuning, outperforms all competing baselines and overcomes the guardrail tax by improving the fraction of safe responses from 61% to 97% and increasing average helpfulness scores from 4.17 to 4.29 on the largest models, while reducing attack success rate from 100% to 8%. PrimeGuard implementation is available at https://github.com/dynamofl/PrimeGuard and safe-eval dataset is available at https://huggingface.co/datasets/dynamoai/safe_eval.

Traditional Mixture-of-Experts (MoE) networks benefit from utilizing multiple smaller expert models as opposed to a single large network. However, these experts typically operate independently, leaving a question open about whether interconnecting these models could enhance the performance of MoE networks. In response, we introduce GRAPHMOE, a novel method aimed at augmenting the cognitive depth of language models via a self-rethinking mechanism constructed on Pseudo GraphMoE networks. GRAPHMOE employs a recurrent routing strategy to simulate iterative thinking steps, thereby facilitating the flow of information among expert nodes. We implement the GRAPHMOE architecture using Low-Rank Adaptation techniques (LoRA) and conduct extensive experiments on various benchmark datasets. The experimental results reveal that GRAPHMOE outperforms other LoRA based models, achieving state-of-the-art (SOTA) performance. Additionally, this study explores a novel recurrent routing strategy that may inspire further advancements in enhancing the reasoning capabilities of language models.

Retrieval-augmented generation (RAG) systems face significant challenges in multi-hop question answering (MHQA), where complex queries require synthesizing information across multiple document chunks. Existing approaches typically rely on iterative LLM-based query rewriting and routing, resulting in high computational costs due to repeated LLM invocations and multi-stage processes. To address these limitations, we propose TreeHop, an embedding-level framework without the need for LLMs in query refinement. TreeHop dynamically updates query embeddings by fusing semantic information from prior queries and retrieved documents, enabling iterative retrieval through embedding-space operations alone. This method replaces the traditional "Retrieve-Rewrite-Vectorize-Retrieve" cycle with a streamlined "Retrieve-Embed-Retrieve" loop, significantly reducing computational overhead. Moreover, a rule-based stop criterion is introduced to further prune redundant retrievals, balancing efficiency and recall rate. Experimental results show that TreeHop rivals advanced RAG methods across three open-domain MHQA datasets, achieving comparable performance with only 5\%-0.4\% of the model parameter size and reducing the query latency by approximately 99\% compared to concurrent approaches. This makes TreeHop a faster and more cost-effective solution for deployment in a range of knowledge-intensive applications. For reproducibility purposes, codes and data are available here: https://github.com/allen-li1231/TreeHop.

Open-source Large Language Models (LLMs) increasingly specialize by domain (e.g., math, code, general reasoning), motivating systems that leverage complementary strengths across models. Prior multi-LLM approaches either (i) route a query to one or a few experts and generate independently, (ii) aggregate outputs from each model via costly multi-turn exchanges, or (iii) fuse weights into a single model-typically requiring architectural homogeneity. We introduce Mixture of Thoughts (MoT), a simple method for latent-level collaboration among heterogeneous experts under a global routing scheme. For each query, a lightweight router selects top-K experts and designates a primary expert; uniformly placed interaction layers project hidden states into a shared latent space where the primary expert performs cross-attention over its active (selected) peers. Pre-trained experts remain frozen; only the router and the lightweight interaction layers are trained with a novel joint training objective that improves both the expert selection and inter-expert collaboration. Across five in-distribution (ID) and three out-of-distribution (OOD) benchmarks, MoT surpasses the current routing and aggregation-based state-of-the-art, Avengers, by +0.38% and +2.92%, respectively. Further, MoT significantly outperforms the best-performing single model. It achieves this with single-pass inference, runtime comparable to routing baselines, and none of the overheads of iterative aggregation. MoT offers a simple latent-space mechanism for combining heterogeneous LLMs, a practical step toward broader multi-LLM collaboration. Our code is publicly available at https://github.com/jacobfa/mot.

Despite the syntactic fluency of Large Language Models (LLMs), ensuring their logical correctness in high-stakes domains remains a fundamental challenge. We present a neurosymbolic framework that combines LLMs with SMT solvers to produce verification-guided answers through iterative refinement. Our approach decomposes LLM outputs into atomic claims, autoformalizes them into first-order logic, and verifies their logical consistency using automated theorem proving. We introduce three key innovations: (1) multi-model consensus via formal semantic equivalence checking to ensure logic-level alignment between candidates, eliminating the syntactic bias of surface-form metrics, (2) semantic routing that directs different claim types to appropriate verification strategies: symbolic solvers for logical claims and LLM ensembles for commonsense reasoning, and (3) precise logical error localization via Minimal Correction Subsets (MCS), which pinpoint the exact subset of claims to revise, transforming binary failure signals into actionable feedback. Our framework classifies claims by their logical status and aggregates multiple verification signals into a unified score with variance-based penalty. The system iteratively refines answers using structured feedback until acceptance criteria are met or convergence is achieved. This hybrid approach delivers formal guarantees where possible and consensus verification elsewhere, advancing trustworthy AI. With the GPT-OSS-120B model, VERGE demonstrates an average performance uplift of 18.7% at convergence across a set of reasoning benchmarks compared to single-pass approaches.

This paper introduces KunLunBaizeRAG, a reinforcement learning-driven reasoning framework designed to enhance the reasoning capabilities of large language models (LLMs) in complex multi-hop question-answering tasks. The framework addresses key limitations of traditional RAG, such as retrieval drift, information redundancy, and strategy rigidity. Key innovations include the RAG-driven Reasoning Alignment (RDRA) mechanism, the Search-Think Iterative Enhancement (STIE) mechanism, the Network-Local Intelligent Routing (NLR) mechanism, and a progressive hybrid training strategy. Experimental results demonstrate significant improvements in exact match (EM) and LLM-judged score (LJ) across four benchmarks, highlighting the framework's robustness and effectiveness in complex reasoning scenarios.

How well do AI systems perform in algorithm engineering for hard optimization problems in domains such as package-delivery routing, crew scheduling, factory production planning, and power-grid balancing? We introduce ALE-Bench, a new benchmark for evaluating AI systems on score-based algorithmic programming contests. Drawing on real tasks from the AtCoder Heuristic Contests, ALE-Bench presents optimization problems that are computationally hard and admit no known exact solution. Unlike short-duration, pass/fail coding benchmarks, ALE-Bench encourages iterative solution refinement over long time horizons. Our software framework supports interactive agent architectures that leverage test-run feedback and visualizations. Our evaluation of frontier LLMs revealed that while they demonstrate high performance on specific problems, a notable gap remains compared to humans in terms of consistency across problems and long-horizon problem-solving capabilities. This highlights the need for this benchmark to foster future AI advancements.

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.

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.

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}}.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of states and demonstration trajectories. In this paper, we introduce scaling techniques based on graph compression, spatial parallelization, and improved initialization conditions inspired by a connection to eigenvector algorithms. We revisit classic IRL methods in the routing context, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. This insight is leveraged in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in route quality at a global scale, and to the best of our knowledge, represents the largest published study of IRL algorithms in a real-world setting to date. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.

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.

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.

The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping (i.e., assigning each query to a single model in isolation), which limits their capability to tackle complex tasks that demand the complementary strengths of multiple LLMs. In this paper, we present Router-R1, a reinforcement learning (RL)-based framework that formulates multi-LLM routing and aggregation as a sequential decision process. Router-R1 instantiates the router itself as a capable LLM, leveraging its reasoning ability to interleave "think" actions (internal deliberation) with "route" actions (dynamic model invocation), and integrates each response into its evolving context. To guide learning, we employ a lightweight rule-based reward comprising format rewards, final outcome rewards, and a novel cost reward for performance and cost trade-off optimization, opening a pathway toward optimizing performance-cost tradeoffs via RL. Router-R1 also conditions only on simple model descriptors such as pricing, latency, and example performance, enabling strong generalization to unseen model selection. Experiments on seven general and multi-hop QA benchmarks show that Router-R1 outperforms over several strong baselines, achieving superior performance while maintaining robust generalization and cost management.Code is available at https://github.com/ulab-uiuc/Router-R1.

We formulate and solve the H-SARA Problem, a Vehicle Routing and Appointment Scheduling Problem motivated by home services management. We assume that travel times, service durations, and customer cancellations are stochastic. We use a two-stage process that first generates teams and routes using a VRP Solver with optional extensions and then uses an MC Scheduler that determines expected arrival times by teams at customers. We further introduce two different models of cancellation and their associated impacts on routing and scheduling. Finally, we introduce the Route Fracture Metaheuristic that iteratively improves an H-SARA solution by replacing the worst-performing teams. We present insights into the problem and a series of numerical experiments that illustrate properties of the optimal routing, scheduling, and the impact of the Route Fracture Metaheuristic for both models of cancellation.

Networks in the current 5G and beyond systems increasingly carry heterogeneous traffic with diverse quality-of-service constraints, making real-time routing decisions both complex and time-critical. A common approach, such as a heuristic with human intervention or training a single centralized RL policy or synchronizing updates across multiple learners, struggles with scalability and straggler effects. We address this by proposing an asynchronous multi-agent reinforcement learning (AMARL) framework in which independent PPO agents, one per service, plan routes in parallel and commit resource deltas to a shared global resource environment. This coordination by state preserves feasibility across services and enables specialization for service-specific objectives. We evaluate the method on an O-RAN like network simulation using nearly real-time traffic data from the city of Montreal. We compared against a single-agent PPO baseline. AMARL achieves a similar Grade of Service (acceptance rate) (GoS) and end-to-end latency, with reduced training wall-clock time and improved robustness to demand shifts. These results suggest that asynchronous, service-specialized agents provide a scalable and practical approach to distributed routing, with applicability extending beyond the O-RAN domain.

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.

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.

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.

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.

With the rise of the Agent Web and Model Context Protocol (MCP), the agent ecosystem is evolving into an open collaborative network, exponentially increasing accessible tools. However, current architectures face severe scalability and generality bottlenecks. To address this, we propose ToolACE-MCP, a pipeline for training history-aware routers to empower precise navigation in large-scale ecosystems. By leveraging a dependency-rich candidate Graph to synthesize multi-turn trajectories, we effectively train routers with dynamic context understanding to create the plug-and-play Light Routing Agent. Experiments on the real-world benchmarks MCP-Universe and MCP-Mark demonstrate superior performance. Notably, ToolACE-MCP exhibits critical properties for the future Agent Web: it not only generalizes to multi-agent collaboration with minimal adaptation but also maintains exceptional robustness against noise and scales effectively to massive candidate spaces. These findings provide a strong empirical foundation for universal orchestration in open-ended ecosystems.

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

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.

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.

Recent advancements in Large Language Models (LLMs) have demonstrated their potential in planning and reasoning tasks, offering a flexible alternative to classical pathfinding algorithms. However, most existing studies focus on LLMs' independent reasoning capabilities and overlook the potential synergy between LLMs and traditional algorithms. To fill this gap, we propose a comprehensive evaluation benchmark GridRoute to assess how LLMs can take advantage of traditional algorithms. We also propose a novel hybrid prompting technique called Algorithm of Thought (AoT), which introduces traditional algorithms' guidance into prompting. Our benchmark evaluates six LLMs ranging from 7B to 72B parameters across various map sizes, assessing their performance in correctness, optimality, and efficiency in grid environments with varying sizes. Our results show that AoT significantly boosts performance across all model sizes, particularly in larger or more complex environments, suggesting a promising approach to addressing path planning challenges. Our code is open-sourced at https://github.com/LinChance/GridRoute.

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

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

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.

With the rapid growth in the number of Large Language Models (LLMs), there has been a recent interest in LLM routing, or directing queries to the cheapest LLM that can deliver a suitable response. Following this line of work, we introduce CARROT, a Cost AwaRe Rate Optimal rouTer that can select models based on any desired trade-off between performance and cost. Given a query, CARROT selects a model based on estimates of models' cost and performance. Its simplicity lends CARROT computational efficiency, while our theoretical analysis demonstrates minimax rate-optimality in its routing performance. Alongside CARROT, we also introduce the Smart Price-aware Routing (SPROUT) dataset to facilitate routing on a wide spectrum of queries with the latest state-of-the-art LLMs. Using SPROUT and prior benchmarks such as Routerbench and open-LLM-leaderboard-v2 we empirically validate CARROT's performance against several alternative routers.

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.

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.

Large Language Models (LLMs) deliver state-of-the-art performance across many tasks but impose high computational and memory costs, limiting their deployment in resource-constrained or real-time settings. To address this, we propose HierRouter, a hierarchical routing approach that dynamically assembles inference pipelines from a pool of specialized, lightweight language models. Formulated as a finite-horizon Markov Decision Process (MDP), our approach trains a Proximal Policy Optimization (PPO)-based reinforcement learning agent to iteratively select which models to invoke at each stage of multi-hop inference. The agent conditions on the evolving context and accumulated cost to make context-aware routing decisions. Experiments with three open-source candidate LLMs across six benchmarks, including QA, code generation, and mathematical reasoning, show that HierRouter improves response quality by up to 2.4x compared to using individual models independently, while incurring only a minimal additional inference cost on average. These results highlight the promise of hierarchical routing for cost-efficient, high-performance LLM inference. All codes can be found here https://github.com/ Nikunj-Gupta/hierouter.

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 Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity in practical VRP applications, it remains unexplored. In this paper, we propose RouteExplainer, a post-hoc explanation framework that explains the influence of each edge in a generated route. Our framework realizes this by rethinking a route as the sequence of actions and extending counterfactual explanations based on the action influence model to VRP. To enhance the explanation, we additionally propose an edge classifier that infers the intentions of each edge, a loss function to train the edge classifier, and explanation-text generation by Large Language Models (LLMs). We quantitatively evaluate our edge classifier on four different VRPs. The results demonstrate its rapid computation while maintaining reasonable accuracy, thereby highlighting its potential for deployment in practical applications. Moreover, on the subject of a tourist route, we qualitatively evaluate explanations generated by our framework. This evaluation not only validates our framework but also shows the synergy between explanation frameworks and LLMs. See https://ntt-dkiku.github.io/xai-vrp for our code, datasets, models, and demo.

We give a deterministic O(mlog^{2/3}n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the O(m+nlog n) time bound of Dijkstra's algorithm on sparse graphs, showing that Dijkstra's algorithm is not optimal for SSSP.

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.

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.

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.

Multimodal recommendation enhances ranking by integrating user-item interactions with item content, which is particularly effective under sparse feedback and long-tail distributions. However, multimodal signals are inherently heterogeneous and can conflict in specific contexts, making effective fusion both crucial and challenging. Existing approaches often rely on shared fusion pathways, leading to entangled representations and modality imbalance. To address these issues, we propose MAGNET, a Modality-Guided Mixture of Adaptive Graph Experts Network with Progressive Entropy-Triggered Routing for Multimodal Recommendation, designed to enhance controllability, stability, and interpretability in multimodal fusion. MAGNET couples interaction-conditioned expert routing with structure-aware graph augmentation, so that both what to fuse and how to fuse are explicitly controlled and interpretable. At the representation level, a dual-view graph learning module augments the interaction graph with content-induced edges, improving coverage for sparse and long-tail items while preserving collaborative structure via parallel encoding and lightweight fusion. At the fusion level, MAGNET employs structured experts with explicit modality roles-dominant, balanced, and complementary-enabling a more interpretable and adaptive combination of behavioral, visual, and textual cues. To further stabilize sparse routing and prevent expert collapse, we introduce a two-stage entropy-weighting mechanism that monitors routing entropy. This mechanism automatically transitions training from an early coverage-oriented regime to a later specialization-oriented regime, progressively balancing expert utilization and routing confidence. Extensive experiments on public benchmarks demonstrate consistent improvements over strong baselines.

Multi-agent Pathfinding (MAPF) problem generally asks to find a set of conflict-free paths for a set of agents confined to a graph and is typically solved in a centralized fashion. Conversely, in this work, we investigate the decentralized MAPF setting, when the central controller that posses all the information on the agents' locations and goals is absent and the agents have to sequientially decide the actions on their own without having access to a full state of the environment. We focus on the practically important lifelong variant of MAPF, which involves continuously assigning new goals to the agents upon arrival to the previous ones. To address this complex problem, we propose a method that integrates two complementary approaches: planning with heuristic search and reinforcement learning through policy optimization. Planning is utilized to construct and re-plan individual paths. We enhance our planning algorithm with a dedicated technique tailored to avoid congestion and increase the throughput of the system. We employ reinforcement learning to discover the collision avoidance policies that effectively guide the agents along the paths. The policy is implemented as a neural network and is effectively trained without any reward-shaping or external guidance. We evaluate our method on a wide range of setups comparing it to the state-of-the-art solvers. The results show that our method consistently outperforms the learnable competitors, showing higher throughput and better ability to generalize to the maps that were unseen at the training stage. Moreover our solver outperforms a rule-based one in terms of throughput and is an order of magnitude faster than a state-of-the-art search-based solver.

Connected Autonomous Vehicles (CAVs) promise to reduce congestion in future urban networks, potentially by optimizing their routing decisions. Unlike for human drivers, these decisions can be made with collective, data-driven policies, developed by machine learning algorithms. Reinforcement learning (RL) can facilitate the development of such collective routing strategies, yet standardized and realistic benchmarks are missing. To that end, we present : Urban Routing Benchmark for RL-equipped Connected Autonomous Vehicles. is a comprehensive benchmarking environment that unifies evaluation across 29 real-world traffic networks paired with realistic demand patterns. comes with a catalog of predefined tasks, four state-of-the-art multi-agent RL (MARL) algorithm implementations, three baseline methods, domain-specific performance metrics, and a modular configuration scheme. Our results suggest that, despite the lengthy and costly training, state-of-the-art MARL algorithms rarely outperformed humans. Experimental results reported in this paper initiate the first leaderboard for MARL in large-scale urban routing optimization and reveal that current approaches struggle to scale, emphasizing the urgent need for advancements in this domain.

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.

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the power of the interaction order. This bottleneck limits its use in large-scale or real-time applications, forcing traditional tools to rely on heuristics to reduce the number of path candidates at the cost of potentially reduced accuracy. To overcome this limitation, we propose a comprehensive machine-learning-assisted framework that replaces exhaustive path searching with intelligent sampling via Generative Flow Networks. Applying such generative models to this domain presents significant challenges, particularly sparse rewards due to the rarity of valid paths, which can lead to convergence failures and trivial solutions when evaluating high-order interactions in complex environments. To ensure robust learning and efficient exploration, our framework incorporates three key architectural components. First, we implement an experience replay buffer to capture and retain rare valid paths. Second, we adopt a uniform exploratory policy to improve generalization and prevent the model from overfitting to simple geometries. Third, we apply a physics-based action masking strategy that filters out physically impossible paths before the model even considers them. As demonstrated in our experimental validation, the proposed model achieves substantial speedups over exhaustive search -- up to 10times faster on GPU and 1000times faster on CPU -- while maintaining high coverage accuracy and successfully uncovering complex propagation paths. The complete source code, tests, and tutorial are available at https://github.com/jeertmans/sampling-paths.

Vehicle Routing Problems (VRPs) are a class of NP-hard problems ubiquitous in several real-world logistics scenarios that pose significant challenges for optimization. Neural Combinatorial Optimization (NCO) has emerged as a promising alternative to classical approaches, as it can learn fast heuristics to solve VRPs. However, most research works in NCO for VRPs focus on simplified settings, which do not account for asymmetric distances and travel durations that cannot be derived by simple Euclidean distances and unrealistic data distributions, hindering real-world deployment. This work introduces RRNCO (Real Routing NCO) to bridge the gap of NCO between synthetic and real-world VRPs in the critical aspects of both data and modeling. First, we introduce a new, openly available dataset with real-world data containing a diverse dataset of locations, distances, and duration matrices from 100 cities, considering realistic settings with actual routing distances and durations obtained from Open Source Routing Machine (OSRM). Second, we propose a novel approach that efficiently processes both node and edge features through contextual gating, enabling the construction of more informed node embedding, and we finally incorporate an Adaptation Attention Free Module (AAFM) with neural adaptive bias mechanisms that effectively integrates not only distance matrices but also angular relationships between nodes, allowing our model to capture rich structural information. RRNCO achieves state-of-the-art results in real-world VRPs among NCO methods. We make our dataset and code publicly available at https://github.com/ai4co/real-routing-nco.

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.

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

This paper discusses the system architecture design and deployment of non-stationary multi-armed bandit approaches to determine a near-optimal payment routing policy based on the recent history of transactions. We propose a Routing Service architecture using a novel Ray-based implementation for optimally scaling bandit-based payment routing to over 10,000 transactions per second, adhering to the system design requirements and ecosystem constraints with Payment Card Industry Data Security Standard (PCI DSS). We first evaluate the effectiveness of multiple bandit-based payment routing algorithms on a custom simulator to benchmark multiple non-stationary bandit approaches and identify the best hyperparameters. We then conducted live experiments on the payment transaction system on a fantasy sports platform Dream11. In the live experiments, we demonstrated that our non-stationary bandit-based algorithm consistently improves the success rate of transactions by 0.92% compared to the traditional rule-based methods over one month.

Recently, large language models (LLMs) have demonstrated superior performance across various tasks by adhering to scaling laws, which significantly increase model size. However, the huge computation overhead during inference hinders the deployment in industrial applications. Many works leverage traditional compression approaches to boost model inference, but these always introduce additional training costs to restore the performance and the pruning results typically show noticeable performance drops compared to the original model when aiming for a specific level of acceleration. To address these issues, we propose a fine-grained token-wise pruning approach for the LLMs, which presents a learnable router to adaptively identify the less important tokens and skip them across model blocks to reduce computational cost during inference. To construct the router efficiently, we present a search-based sparsity scheduler for pruning sparsity allocation, a trainable router combined with our proposed four low-dimensional factors as input and three proposed losses. We conduct extensive experiments across different benchmarks on different LLMs to demonstrate the superiority of our method. Our approach achieves state-of-the-art (SOTA) pruning results, surpassing other existing pruning methods. For instance, our method outperforms BlockPruner and ShortGPT by approximately 10 points on both LLaMA2-7B and Qwen1.5-7B in accuracy retention at comparable token sparsity levels.

Robust routing under uncertainty is central to real-world logistics, yet most benchmarks assume static, idealized settings. We present SVRPBench, the first open benchmark to capture high-fidelity stochastic dynamics in vehicle routing at urban scale. Spanning more than 500 instances with up to 1000 customers, it simulates realistic delivery conditions: time-dependent congestion, log-normal delays, probabilistic accidents, and empirically grounded time windows for residential and commercial clients. Our pipeline generates diverse, constraint-rich scenarios, including multi-depot and multi-vehicle setups. Benchmarking reveals that state-of-the-art RL solvers like POMO and AM degrade by over 20% under distributional shift, while classical and metaheuristic methods remain robust. To enable reproducible research, we release the dataset and evaluation suite. SVRPBench challenges the community to design solvers that generalize beyond synthetic assumptions and adapt to real-world uncertainty.

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous applications, from growing markets like last-mile delivery to emerging use-cases like interactive logistics planning. Such applications involve solving similar problem instances repeatedly, yet current state-of-the-art solvers treat each instance on its own without leveraging previous examples. We introduce a novel optimization framework that uses a reinforcement learning agent - trained on prior instances - to quickly generate initial solutions, which are then further optimized by genetic algorithms. Our framework, Evolutionary Algorithm with Reinforcement Learning Initialization (EARLI), consistently outperforms current state-of-the-art solvers across various time scales. For example, EARLI handles vehicle routing with 500 locations within 1s, 10x faster than current solvers for the same solution quality, enabling applications like real-time and interactive routing. EARLI can generalize to new data, as demonstrated on real e-commerce delivery data of a previously unseen city. Our hybrid framework presents a new way to combine reinforcement learning and genetic algorithms, paving the road for closer interdisciplinary collaboration between AI and optimization communities towards real-time optimization in diverse domains.

In pruning, the Lottery Ticket Hypothesis posits that large networks contain sparse subnetworks, or winning tickets, that can be trained in isolation to match the performance of their dense counterparts. However, most existing approaches assume a single universal winning ticket shared across all inputs, ignoring the inherent heterogeneity of real-world data. In this work, we propose Routing the Lottery (RTL), an adaptive pruning framework that discovers multiple specialized subnetworks, called adaptive tickets, each tailored to a class, semantic cluster, or environmental condition. Across diverse datasets and tasks, RTL consistently outperforms single- and multi-model baselines in balanced accuracy and recall, while using up to 10 times fewer parameters than independent models and exhibiting semantically aligned. Furthermore, we identify subnetwork collapse, a performance drop under aggressive pruning, and introduce a subnetwork similarity score that enables label-free diagnosis of oversparsification. Overall, our results recast pruning as a mechanism for aligning model structure with data heterogeneity, paving the way toward more modular and context-aware deep learning.

Large language models (LLMs) exhibit strong generative capabilities and have shown great potential in code generation. Existing chain-of-thought (CoT) prompting methods enhance model reasoning by eliciting intermediate steps, but suffer from two major limitations: First, their uniform application tends to induce overthinking on simple tasks. Second, they lack intention abstraction in code generation, such as explicitly modeling core algorithmic design and efficiency, leading models to focus on surface-level structures while neglecting the global problem objective. Inspired by the cognitive economy principle of engaging structured reasoning only when necessary to conserve cognitive resources, we propose RoutingGen, a novel difficulty-aware routing framework that dynamically adapts prompting strategies for code generation. For simple tasks, it adopts few-shot prompting; for more complex ones, it invokes a structured reasoning strategy, termed Intention Chain-of-Thought (ICoT), which we introduce to guide the model in capturing task intention, such as the core algorithmic logic and its time complexity. Experiments across three models and six standard code generation benchmarks show that RoutingGen achieves state-of-the-art performance in most settings, while reducing total token usage by 46.37% on average across settings. Furthermore, ICoT outperforms six existing prompting baselines on challenging benchmarks.

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Although many works appear on this topic, all current algorithms struggle as the number of agents grows. The principal reason is that existing approaches typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. We evaluate the idea in two large-scale settings: one-shot MAPF, where each agent has a single destination, and lifelong MAPF, where agents are continuously assigned new destinations. Empirically, we report large improvements in solution quality for one-short MAPF and in overall throughput for lifelong MAPF.

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/

We study multi-agent reinforcement learning in the setting of episodic Markov decision processes, where multiple agents cooperate via communication through a central server. We propose a provably efficient algorithm based on value iteration that enable asynchronous communication while ensuring the advantage of cooperation with low communication overhead. With linear function approximation, we prove that our algorithm enjoys an mathcal{O}(d^{3/2}H^2K) regret with mathcal{O}(dHM^2) communication complexity, where d is the feature dimension, H is the horizon length, M is the total number of agents, and K is the total number of episodes. We also provide a lower bound showing that a minimal Omega(dM) communication complexity is required to improve the performance through collaboration.

Tool-using LLM agents face a reliability-cost tradeoff: routing every decision through the LLM improves correctness but incurs high latency and inference cost, while pre-coded workflow graphs reduce cost but become brittle under unanticipated compound tool failures. We present Self-Healing Router, a fault-tolerant orchestration architecture that treats most agent control-flow decisions as routing rather than reasoning. The system combines (i) parallel health monitors that assign priority scores to runtime conditions such as tool outages and risk signals, and (ii) a cost-weighted tool graph where Dijkstra's algorithm performs deterministic shortest-path routing. When a tool fails mid-execution, its edges are reweighted to infinity and the path is recomputed -- yielding automatic recovery without invoking the LLM. The LLM is reserved exclusively for cases where no feasible path exists, enabling goal demotion or escalation. Prior graph-based tool-use systems (ControlLLM, ToolNet, NaviAgent) focus on tool selection and planning; our contribution is runtime fault tolerance with deterministic recovery and binary observability -- every failure is either a logged reroute or an explicit escalation, never a silent skip. Across 19 scenarios spanning three graph topologies (linear pipeline, dependency DAG, parallel fan-out), Self-Healing Router matches ReAct's correctness while reducing control-plane LLM calls by 93% (9 vs 123 aggregate) and eliminating the silent-failure cases observed in a well-engineered static workflow baseline under compound failures.

Model routing allocates queries to the suitable model, improving system performance while reducing costs. However, existing routing methods face practical limitations that hinder scalability in large-scale applications and struggle to keep up with the rapid growth of the large language model (LLM) ecosystem. To tackle these challenges, we propose TagRouter, a training-free model routing method designed to optimize the synergy among multiple LLMs for open-domain text generation tasks. Experimental results demonstrate that TagRouter outperforms 13 baseline methods, increasing the accept rate of system by 6.15% and reducing costs by 17.20%, achieving optimal cost-efficiency. Our findings provides the LLM community with an efficient and scalable solution for model ensembling, offering users an evolvable "super model."

Vision-Language Models (VLMs) suffer from catastrophic forgetting when sequentially fine-tuned on new tasks, degrading performance on previously learned foundational and task-specific capabilities. While multi-task learning can mitigate forgetting, it requires simultaneous access to all datasets and imposes computational overhead that scales linearly with the number of tasks. In this work, we introduce a routing-based approach that enables the integration of new tasks while preserving the foundational knowledge acquired during pretraining. We evaluate our method using InternVL-2 models (2B and 8B parameters) and demonstrate that routing preserves the model's foundational capabilities by maintaining performance on general-purpose benchmarks such as ChartQA, MMBench, and DocVQA, while simultaneously improving accuracy on specialized tasks. Importantly, our approach achieves this without requiring concurrent access to data from all tasks, avoiding the significant computational and data overhead associated with traditional multi-task learning. We further conduct extensive ablation studies to evaluate the scalability and robustness of routing-based learning, showing that the approach is resilient to a growing number of tasks and performs particularly well when new tasks are semantically related. Finally, we show that the routing mechanism enables superior cross-modal transfer between language and vision capabilities, allowing knowledge learned in one modality to enhance performance in another capability not achieved by existing continual learning methods.

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.

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.

Large Language Models (LLMs) have revolutionized natural language processing, but their varying capabilities and costs pose challenges in practical applications. LLM routing addresses this by dynamically selecting the most suitable LLM for each query/task. Previous approaches treat this as a supervised learning problem, assuming complete knowledge of optimal query-LLM pairings. However, real-world scenarios lack such comprehensive mappings and face evolving user queries. We thus propose to study LLM routing as a contextual bandit problem, enabling adaptive decision-making using bandit feedback without requiring exhaustive inference across all LLMs for all queries (in contrast to supervised routing). To address this problem, we develop a shared embedding space for queries and LLMs, where query and LLM embeddings are aligned to reflect their affinity. This space is initially learned from offline human preference data and refined through online bandit feedback. We instantiate this idea through Preference-prior Informed Linucb fOr adaptive rouTing (PILOT), a novel extension of LinUCB. To handle diverse user budgets for model routing, we introduce an online cost policy modeled as a multi-choice knapsack problem, ensuring resource-efficient routing.

As a telecom provider, our company has a critical mission to maintain telecom services even during power outages. To accomplish the mission, it is essential to maintain the power of the telecom base stations. Here we consider a solution where electric vehicles (EVs) directly supply power to base stations by traveling to their locations. The goal is to find EV routes that minimize both the total travel distance of all EVs and the number of downed base stations. In this paper, we formulate this routing problem as a new variant of the Electric Vehicle Routing Problem (EVRP) and propose a solver that combines a rule-based vehicle selector and a reinforcement learning (RL)-based node selector. The rule of the vehicle selector ensures the exact environmental states when the selected EV starts to move. In addition, the node selection by the RL model enables fast route generation, which is critical in emergencies. We evaluate our solver on both synthetic datasets and real datasets. The results show that our solver outperforms baselines in terms of the objective value and computation time. Moreover, we analyze the generalization and scalability of our solver, demonstrating the capability toward unseen settings and large-scale problems. Check also our project page: https://ntt-dkiku.github.io/rl-evrpeps.

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.

Mixture of Experts models are widely assumed to achieve domain specialization through sparse routing. In this work, we question this assumption by introducing COMMITTEEAUDIT, a post hoc framework that analyzes routing behavior at the level of expert groups rather than individual experts. Across three representative models and the MMLU benchmark, we uncover a domain-invariant Standing Committee. This is a compact coalition of routed experts that consistently captures the majority of routing mass across domains, layers, and routing budgets, even when architectures already include shared experts. Qualitative analysis further shows that Standing Committees anchor reasoning structure and syntax, while peripheral experts handle domain-specific knowledge. These findings reveal a strong structural bias toward centralized computation, suggesting that specialization in Mixture of Experts models is far less pervasive than commonly believed. This inherent bias also indicates that current training objectives, such as load-balancing losses that enforce uniform expert utilization, may be working against the model's natural optimization path, thereby limiting training efficiency and performance.

Large language models (LLMs) and agent-based frameworks have advanced rapidly, enabling diverse applications. Yet, with the proliferation of models and agentic strategies, practitioners face substantial uncertainty in selecting the best configuration for a downstream task. Prior studies show that different agents and backbones exhibit complementary strengths, and that larger models are not always superior, underscoring the need for adaptive routing mechanisms. Existing approaches to agent routing, however, often emphasize cost efficiency while overlooking the fine-grained contextual and relational structure inherent in QA tasks. In this paper, we propose tAgentRouter, a framework that formulates multi-agent QA as a knowledge-graph-guided routing problem supervised by empirical performance signals. Specifically, we convert QA instance into a knowledge graph that jointly encodes queries, contextual entities, and agents, and then train a heterogeneous graph neural network (GNN) to propagate information across node types and produce task-aware routing distributions over agents. By leveraging soft supervision and weighted aggregation of agent outputs, AgentRouter learns principled collaboration schemes that capture the complementary strengths of diverse agents. Extensive experiments demonstrate that our framework consistently outperforms single-agent and ensemble baselines, while generalizing across benchmarks and LLM backbones. These results highlight the effectiveness and robustness of graph-supervised multi-agent routing for question answering.

We study cost-aware routing for large language models across diverse and dynamic pools of models. Existing approaches often overlook prompt-specific context, rely on expensive model profiling, assume a fixed set of experts, or use inefficient trial-and-error strategies. We introduce Cost-Spectrum Contrastive Routing (CSCR), a lightweight framework that maps both prompts and models into a shared embedding space to enable fast, cost-sensitive selection. CSCR uses compact, fast-to-compute logit footprints for open-source models and perplexity fingerprints for black-box APIs. A contrastive encoder is trained to favor the cheapest accurate expert within adaptive cost bands. At inference time, routing reduces to a single k-NN lookup via a FAISS index, requiring no retraining when the expert pool changes and enabling microsecond latency. Across multiple benchmarks, CSCR consistently outperforms baselines, improving the accuracy-cost tradeoff by up to 25%, while generalizing robustly to unseen LLMs and out-of-distribution prompts.

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.

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.

We introduce Olympus, a new approach that transforms Multimodal Large Language Models (MLLMs) into a unified framework capable of handling a wide array of computer vision tasks. Utilizing a controller MLLM, Olympus delegates over 20 specialized tasks across images, videos, and 3D objects to dedicated modules. This instruction-based routing enables complex workflows through chained actions without the need for training heavy generative models. Olympus easily integrates with existing MLLMs, expanding their capabilities with comparable performance. Experimental results demonstrate that Olympus achieves an average routing accuracy of 94.75% across 20 tasks and precision of 91.82% in chained action scenarios, showcasing its effectiveness as a universal task router that can solve a diverse range of computer vision tasks. Project page: http://yuanze-lin.me/Olympus_page/

Multimodal Large Language Models (MLLMs) achieve strong performance through instruction tuning, but real-world deployment requires them to continually expand their capabilities, making Multimodal Continual Instruction Tuning (MCIT) essential. Recent methods leverage sparse expert routing to promote task specialization, but we find that the expert routing process suffers from drift as the data distribution evolves. For example, a grounding query that previously activated localization experts may instead be routed to irrelevant experts after learning OCR tasks. Meanwhile, the grounding-related experts can be overwritten by new tasks and lose their original functionality. Such failure reflects two problems: router drift, where expert selection becomes inconsistent over time, and expert drift, where shared experts are overwritten across tasks. Therefore, we propose StAbilized Mixture-of-Experts (SAME) for MCIT. To address router drift, SAME stabilizes expert selection by decomposing routing dynamics into orthogonal subspaces and updating only task-relevant directions. To mitigate expert drift, we regulate expert updates via curvature-aware scaling using historical input covariance in a rehearsal-free manner. SAME also introduces adaptive expert activation to freeze selected experts during training, reducing redundant computation and cross-task interference. Extensive experiments demonstrate its SOTA performance.

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.

Reinforcement learning (RL) has emerged as a crucial approach for enhancing the capabilities of large language models. However, in Mixture-of-Experts (MoE) models, the routing mechanism often introduces instability, even leading to catastrophic RL training collapse. We analyze the training-inference consistency of MoE models and identify a notable discrepancy in routing behaviors between the two phases. Moreover, even under identical conditions, the routing framework can yield divergent expert selections across repeated forward passes. To address this foundational inconsistency, we propose Rollout Routing Replay (R3), a method that records routing distributions from the inference engine and replays them during training. R3 significantly reduces training-inference policy KL divergence and mitigates extreme discrepancies without compromising training speed. Extensive experiments on various settings confirm that R3 succeeds in stabilizing RL training, preventing collapse and outperforming methods such as GSPO and TIS. We believe this work can offer a new solution for stabilizing RL in MoE models.

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.

We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes the fixed points of a target graph system and decodes them to estimate the stationary properties of the system without the prior knowledge of existing solvers or intermediate solutions. The forward propagation of CGS proceeds in three steps: (1) constructing the input dependent linear contracting iterative maps, (2) computing the fixed-points of the linear maps, and (3) decoding the fixed-points to estimate the properties. The contractivity of the constructed linear maps guarantees the existence and uniqueness of the fixed points following the Banach fixed point theorem. To train CGS efficiently, we also derive a tractable analytical expression for its gradient by leveraging the implicit function theorem. We evaluate the performance of CGS by applying it to various network-analytic and graph benchmark problems. The results indicate that CGS has competitive capabilities for predicting the stationary properties of graph systems, irrespective of whether the target systems are linear or non-linear. CGS also shows high performance for graph classification problems where the existence or the meaning of a fixed point is hard to be clearly defined, which highlights the potential of CGS as a general graph neural network architecture.

Large Language Models (LLMs) have achieved remarkable advancements, but their monolithic nature presents challenges in terms of scalability, cost, and customization. This paper introduces the Composition of Experts (CoE), a modular compound AI system leveraging multiple expert LLMs. CoE leverages a router to dynamically select the most appropriate expert for a given input, enabling efficient utilization of resources and improved performance. We formulate the general problem of training a CoE and discuss inherent complexities associated with it. We propose a two-step routing approach to address these complexities that first uses a router to classify the input into distinct categories followed by a category-to-expert mapping to obtain desired experts. CoE offers a flexible and cost-effective solution to build compound AI systems. Our empirical evaluation demonstrates the effectiveness of CoE in achieving superior performance with reduced computational overhead. Given that CoE comprises of many expert LLMs it has unique system requirements for cost-effective serving. We present an efficient implementation of CoE leveraging SambaNova SN40L RDUs unique three-tiered memory architecture. CoEs obtained using open weight LLMs Qwen/Qwen2-7B-Instruct, google/gemma-2-9b-it, google/gemma-2-27b-it, meta-llama/Llama-3.1-70B-Instruct and Qwen/Qwen2-72B-Instruct achieve a score of 59.4 with merely 31 billion average active parameters on Arena-Hard and a score of 9.06 with 54 billion average active parameters on MT-Bench.

Mixture-of-Experts (MoE) models achieve efficient scaling through sparse expert activation, but often suffer from suboptimal routing decisions due to distribution shifts in deployment. While existing test-time adaptation methods could potentially address these issues, they primarily focus on dense models and require access to external data, limiting their practical applicability to MoE architectures. However, we find that, instead of relying on reference data, we can optimize MoE expert selection on-the-fly based only on input context. As such, we propose a data-free, online test-time framework that continuously adapts MoE routing decisions during text generation without external supervision or data. Our method cycles between two phases: During the prefill stage, and later in regular intervals, we optimize the routing decisions of the model using self-supervision based on the already generated sequence. Then, we generate text as normal, maintaining the modified router until the next adaption. We implement this through lightweight additive vectors that only update router logits in selected layers, maintaining computational efficiency while preventing over-adaptation. The experimental results show consistent performance gains on challenging reasoning tasks while maintaining robustness to context shifts. For example, our method achieves a 5.5\% improvement on HumanEval with OLMoE. Furthermore, owing to its plug-and-play property, our method naturally complements existing test-time scaling techniques, e.g., achieving 6\% average gains when incorporated with self-consistency on DeepSeek-V2-Lite.

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.

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.

Sparse Mixture-of-Experts (SMoE) has gained prominence as a scalable and computationally efficient architecture, enabling significant growth in model capacity without incurring additional inference costs. However, existing SMoE models often rely on auxiliary losses (e.g., z-loss, load balancing) and additional trainable parameters (e.g., noisy gating) to encourage expert diversity, leading to objective misalignment and increased model complexity. Moreover, existing Sinkhorn-based methods suffer from significant training overhead due to their heavy reliance on the computationally expensive Sinkhorn algorithm. In this work, we formulate token-to-expert assignment as an optimal transport problem, incorporating constraints to ensure balanced expert utilization. We demonstrate that introducing a minimal degree of optimal transport-based routing enhances SMoE performance without requiring auxiliary balancing losses. Unlike previous methods, our approach derives gating scores directly from the transport map, enabling more effective token-to-expert balancing, supported by both theoretical analysis and empirical results. Building on these insights, we propose Selective Sinkhorn Routing (SSR), a routing mechanism that replaces auxiliary loss with lightweight Sinkhorn-based routing. SSR promotes balanced token assignments while preserving flexibility in expert selection. Across both language modeling and image classification tasks, SSR achieves faster training, higher accuracy, and greater robustness to input corruption.

We propose JFR, a Bellman-Ford-based optimization framework leveraging frontier contraction and abstract multi-hop jump propagation to accelerate shortest-path computation while strictly preserving correctness. JFR achieves substantial reductions in relaxation operations, ranging from 25 to 99 percent, across sparse, dense, and negative-edge graphs, ensuring robust performance even under adversarial or highly connected topologies. On ultra-large graphs with up to N=20,000 nodes and 295 million edges, JFR maintains strong operational reductions and comparable or improved runtime relative to SPFA-SLF, demonstrating consistent robustness across graph size and density. Lower relaxation counts imply reduced memory-access overheads and computational effort; this normalized work reduction highlights JFR's suitability for scenarios requiring high throughput or energy-conscious operation. Future work focuses on integrating high-performance queue structures, adaptive frontier strategies, and cache-aware techniques to further reduce constant-factor overheads and fully realize JFR's practical runtime potential.

We introduce iterative retrieval, a novel framework that empowers retrievers to make iterative decisions through policy optimization. Finding an optimal portfolio of retrieved items is a combinatorial optimization problem, generally considered NP-hard. This approach provides a learned approximation to such a solution, meeting specific task requirements under a given family of large language models (LLMs). We propose a training procedure based on reinforcement learning, incorporating feedback from LLMs. We instantiate an iterative retriever for composing in-context learning (ICL) exemplars and apply it to various semantic parsing tasks that demand synthesized programs as outputs. By adding only 4M additional parameters for state encoding, we convert an off-the-shelf dense retriever into a stateful iterative retriever, outperforming previous methods in selecting ICL exemplars on semantic parsing datasets such as CalFlow, TreeDST, and MTOP. Additionally, the trained iterative retriever generalizes across different inference LLMs beyond the one used during training.

Large Language Model (LLM) workloads have distinct prefill and decode phases with different compute and memory requirements which should ideally be accounted for when scheduling input queries across different LLM instances in a cluster. However existing scheduling algorithms treat LLM workloads as monolithic jobs without considering the distinct characteristics of the two phases in each workload. This leads to sub-optimal scheduling and increased response latency. In this work, we propose a heuristic-guided reinforcement learning-based intelligent router for data-driven and workload-aware scheduling. Our router leverages a trainable response-length predictor, and a novel formulation for estimating the impact of mixing different workloads to schedule queries across LLM instances and achieve over 11\% lower end-to-end latency than existing approaches.

Mixture-of-Experts (MoE) models are typically pre-trained with explicit load-balancing constraints to ensure statistically balanced expert routing. Despite this, we observe that even well-trained MoE models exhibit significantly imbalanced routing. This behavior is arguably natural-and even desirable - as imbalanced routing allows models to concentrate domain-specific knowledge within a subset of experts. Expert parallelism (EP) is designed to scale MoE models by distributing experts across multiple devices, but with a less-discussed assumption of balanced routing. Under extreme imbalance, EP can funnel a disproportionate number of tokens to a small number of experts, leading to compute- and memory-bound failures on overloaded devices during post-training or inference, where explicit load balancing is often inapplicable. We propose Least-Loaded Expert Parallelism (LLEP), a novel EP algorithm that dynamically reroutes excess tokens and associated expert parameters from overloaded devices to underutilized ones. This ensures that all devices complete their workloads within the minimum collective latency while respecting memory constraints. Across different model scales, LLEP achieves up to 5x speedup and 4x reduction in peak memory usage compared to standard EP. This enables faster and higher-throughput post-training and inference, with ~1.9x faster for gpt-oss-120b. We support our method with extensive theoretical analysis and comprehensive empirical evaluations, including ablation studies. These results illuminate key trade-offs and enable a principled framework for hardware-specific hyper-parameter tuning to achieve optimal performance.

Route-planning agents powered by large language models (LLMs) have emerged as a promising paradigm for supporting everyday human mobility through natural language interaction and tool-mediated decision making. However, systematic evaluation in real-world mobility settings is hindered by diverse routing demands, non-deterministic mapping services, and limited reproducibility. In this study, we introduce MobilityBench, a scalable benchmark for evaluating LLM-based route-planning agents in real-world mobility scenarios. MobilityBench is constructed from large-scale, anonymized real user queries collected from Amap and covers a broad spectrum of route-planning intents across multiple cities worldwide. To enable reproducible, end-to-end evaluation, we design a deterministic API-replay sandbox that eliminates environmental variance from live services. We further propose a multi-dimensional evaluation protocol centered on outcome validity, complemented by assessments of instruction understanding, planning, tool use, and efficiency. Using MobilityBench, we evaluate multiple LLM-based route-planning agents across diverse real-world mobility scenarios and provide an in-depth analysis of their behaviors and performance. Our findings reveal that current models perform competently on Basic information retrieval and Route Planning tasks, yet struggle considerably with Preference-Constrained Route Planning, underscoring significant room for improvement in personalized mobility applications. We publicly release the benchmark data, evaluation toolkit, and documentation at https://github.com/AMAP-ML/MobilityBench .

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.

The quality of point clouds is often limited by noise introduced during their capture process. Consequently, a fundamental 3D vision task is the removal of noise, known as point cloud filtering or denoising. State-of-the-art learning based methods focus on training neural networks to infer filtered displacements and directly shift noisy points onto the underlying clean surfaces. In high noise conditions, they iterate the filtering process. However, this iterative filtering is only done at test time and is less effective at ensuring points converge quickly onto the clean surfaces. We propose IterativePFN (iterative point cloud filtering network), which consists of multiple IterationModules that model the true iterative filtering process internally, within a single network. We train our IterativePFN network using a novel loss function that utilizes an adaptive ground truth target at each iteration to capture the relationship between intermediate filtering results during training. This ensures that the filtered results converge faster to the clean surfaces. Our method is able to obtain better performance compared to state-of-the-art methods. The source code can be found at: https://github.com/ddsediri/IterativePFN.

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.

Sparse Mixture-of-Experts (MoE) have been widely adopted in recent large language models since it can efficiently scale up the model capability without increasing the inference cost. However, evaluations on broad downstream tasks reveal a consistent suboptimality of the routers in existing MoE LLMs, which results in a severe performance gap (e.g., 10-20% in accuracy) to the optimal routing. In this paper, we show that aligning the manifold of routing weights with that of task embedding can effectively reduce the gap and improve MoE LLMs' generalization performance. Our method, "Routing Manifold Alignment (RoMA)", introduces an additional manifold regularization term in the post-training objective and only requires lightweight finetuning of routers (with other parameters frozen). Specifically, the regularization encourages the routing weights of each sample to be close to those of its successful neighbors (whose routing weights lead to correct answers) in a task embedding space. Consequently, samples targeting similar tasks will share similar expert choices across layers. Building such bindings between tasks and experts over different samples is essential to achieve better generalization. Moreover, RoMA demonstrates the advantage of unifying the task understanding (by embedding models) with solution generation (by MoE LLMs). In experiments, we finetune routers in OLMoE, DeepSeekMoE, and Qwen3-MoE using RoMA. Evaluations on diverse benchmarks and extensive comparisons with baselines show the substantial improvement brought by RoMA.

Efficient use of large language models (LLMs) is critical for deployment at scale: without adaptive routing, systems either overpay for strong models or risk poor performance from weaker ones. Selecting the right LLM for each query is fundamentally an online decision problem: models differ in strengths, prices fluctuate, and users value accuracy and cost differently. Yet most routers are trained offline with labels for all candidate models, an assumption that breaks in deployment, where only the outcome of the chosen model is observed. We bridge this gap with BaRP, a Bandit-feedback Routing with Preferences approach that trains under the same partial-feedback restriction as deployment, while supporting preference-tunable inference: operators can dial the performance/cost trade-off at test time without retraining. Framed as a contextual bandit over prompt features and a user preference vector, our method simulates an online feedback setting during training and adapts its routing decisions to each new prompt, rather than depending on full-information offline supervision. Comprehensive experiments show that our method consistently outperforms strong offline routers by at least 12.46% and the largest LLM by at least 2.45%, and generalizes robustly for unseen tasks.

LLMs have shown impressive progress in robotics (e.g., manipulation and navigation) with natural language task descriptions. The success of LLMs in these tasks leads us to wonder: What is the ability of LLMs to solve vehicle routing problems (VRPs) with natural language task descriptions? In this work, we study this question in three steps. First, we construct a dataset with 21 types of single- or multi-vehicle routing problems. Second, we evaluate the performance of LLMs across four basic prompt paradigms of text-to-code generation, each involving different types of text input. We find that the basic prompt paradigm, which generates code directly from natural language task descriptions, performs the best for GPT-4, achieving 56% feasibility, 40% optimality, and 53% efficiency. Third, based on the observation that LLMs may not be able to provide correct solutions at the initial attempt, we propose a framework that enables LLMs to refine solutions through self-reflection, including self-debugging and self-verification. With GPT-4, our proposed framework achieves a 16% increase in feasibility, a 7% increase in optimality, and a 15% increase in efficiency. Moreover, we examine the sensitivity of GPT-4 to task descriptions, specifically focusing on how its performance changes when certain details are omitted from the task descriptions, yet the core meaning is preserved. Our findings reveal that such omissions lead to a notable decrease in performance: 4% in feasibility, 4% in optimality, and 5% in efficiency. Website: https://sites.google.com/view/words-to-routes/

The rapid advancement in large language models (LLMs) has brought forth a diverse range of models with varying capabilities that excel in different tasks and domains. However, selecting the optimal LLM for user queries often involves a challenging trade-off between accuracy and cost, a problem exacerbated by the diverse demands of individual queries. In this work, we present a novel framework that formulates the LLM selection process as a multi-armed bandit problem, enabling dynamic and intelligent routing of queries to the most appropriate model. Our approach incorporates a preference-conditioned dynamic routing mechanism, allowing users to specify their preferences at inference time, thereby offering a customizable balance between performance and cost. Additionally, our selection policy is designed to generalize to unseen LLMs, ensuring adaptability to new models as they emerge. Experimental results demonstrate that our method achieves significant improvements in both accuracy and cost-effectiveness across various LLM platforms, showcasing the potential of our framework to adaptively optimize LLM selection in real-world scenarios.

Acceleration of graph applications on GPUs has found large interest due to the ubiquitous use of graph processing in various domains. The inherent irregularity in graph applications leads to several challenges for parallelization. A key challenge, which we address in this paper, is that of load-imbalance. If the work-assignment to threads uses node-based graph partitioning, it can result in skewed task-distribution, leading to poor load-balance. In contrast, if the work-assignment uses edge-based graph partitioning, the load-balancing is better, but the memory requirement is relatively higher. This makes it unsuitable for large graphs. In this work, we propose three techniques for improved load-balancing of graph applications on GPUs. Each technique brings in unique advantages, and a user may have to employ a specific technique based on the requirement. Using Breadth First Search and Single Source Shortest Paths as our processing kernels, we illustrate the effectiveness of each of the proposed techniques in comparison to the existing node-based and edge-based mechanisms.

The rapid scaling of Large Language Models (LLMs) has achieved remarkable performance, but it also leads to prohibitive memory costs. Existing parameter-efficient approaches such as pruning and quantization mainly compress pretrained models without enhancing architectural capacity, thereby hitting the representational ceiling of the base model. In this work, we propose VersatileFFN, a novel feed-forward network (FFN) that enables flexible reuse of parameters in both width and depth dimensions within a fixed parameter budget. Inspired by the dual-process theory of cognition, VersatileFFN comprises two adaptive pathways: a width-versatile path that generates a mixture of sub-experts from a single shared FFN, mimicking sparse expert routing without increasing parameters, and a depth-versatile path that recursively applies the same FFN to emulate deeper processing for complex tokens. A difficulty-aware gating dynamically balances the two pathways, steering "easy" tokens through the efficient width-wise route and allocating deeper iterative refinement to "hard" tokens. Crucially, both pathways reuse the same parameters, so all additional capacity comes from computation rather than memory. Experiments across diverse benchmarks and model scales demonstrate the effectiveness of the method. The code will be available at https://github.com/huawei-noah/noah-research/tree/master/VersatileFFN.

Large Reasoning Models (LRMs) achieve remarkable performance by explicitly generating multi-step chains of thought, but this capability incurs substantial inference latency and computational cost. Collaborative inference offers a promising solution by selectively allocating work between lightweight and large models, yet a fundamental challenge remains: determining when a reasoning step requires the capacity of a large model or the efficiency of a small model. Existing routing strategies either rely on local token probabilities or post-hoc verification, introducing significant inference overhead. In this work, we propose a novel perspective on step-wise collaboration: the difficulty of a reasoning step can be inferred from its very first token. Inspired by the "Aha Moment" phenomenon in LRMs, we show that the entropy of the initial token serves as a strong predictor of step difficulty. Building on this insight, we introduce GlimpRouter, a training-free step-wise collaboration framework. GlimpRouter employs a lightweight model to generate only the first token of each reasoning step and routes the step to a larger model only when the initial token entropy exceeds a threshold. Experiments on multiple benchmarks demonstrate that our approach significantly reduces inference latency while preserving accuracy. For instance, GlimpRouter attains a substantial 10.7% improvement in accuracy while reducing inference latency by 25.9% compared to a standalone large model on AIME25. These results suggest a simple yet effective mechanism for reasoning: allocating computation based on a glimpse of thought rather than full-step evaluation.

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

The emergence of Large Language Models (LLMs) like ChatGPT has inspired the development of LLM-based agents capable of addressing complex, real-world tasks. However, these agents often struggle during task execution due to methodological constraints, such as error propagation and limited adaptability. To address this issue, we propose a multi-agent framework based on dynamic Task Decomposition and Agent Generation (TDAG). This framework dynamically decomposes complex tasks into smaller subtasks and assigns each to a specifically generated subagent, thereby enhancing adaptability in diverse and unpredictable real-world tasks. Simultaneously, existing benchmarks often lack the granularity needed to evaluate incremental progress in complex, multi-step tasks. In response, we introduce ItineraryBench in the context of travel planning, featuring interconnected, progressively complex tasks with a fine-grained evaluation system. ItineraryBench is designed to assess agents' abilities in memory, planning, and tool usage across tasks of varying complexity. Our experimental results reveal that TDAG significantly outperforms established baselines, showcasing its superior adaptability and context awareness in complex task scenarios.

Mixture-of-Experts (MoE) enables efficient scaling of large language models (LLMs) with sparsely activated experts during inference. To effectively deploy large MoE models on memory-constrained devices, many systems introduce *expert offloading* that caches a subset of experts in fast memory, leaving others on slow memory to run on CPU or load on demand. While some research has exploited the locality of expert activations, where consecutive tokens activate similar experts, the degree of this **local routing consistency** varies across models and remains understudied. In this paper, we propose two metrics to measure local routing consistency of MoE models: (1) **Segment Routing Best Performance (SRP)**, which evaluates how well a fixed group of experts can cover the needs of a segment of tokens, and (2) **Segment Cache Best Hit Rate (SCH)**, which measures the optimal segment-level cache hit rate under a given cache size limit. We analyzed 20 MoE LLMs with diverse sizes and architectures and found that models that apply MoE on every layer and do not use shared experts exhibit the highest local routing consistency. We further showed that domain-specialized experts contribute more to routing consistency than vocabulary-specialized ones, and that most models can balance between cache effectiveness and efficiency with cache sizes approximately 2x the active experts. These findings pave the way for memory-efficient MoE design and deployment without compromising inference speed. We publish the code for replicating experiments at https://github.com/ljcleo/moe-lrc .

The quadratic complexity of self-attention limits its applicability and scalability on large unstructured meshes. We introduce Fast Low-rank Attention Routing Engine (FLARE), a linear complexity self-attention mechanism that routes attention through fixed-length latent sequences. Each attention head performs global communication among N tokens by projecting the input sequence onto a fixed length latent sequence of M ll N tokens using learnable query tokens. By routing attention through a bottleneck sequence, FLARE learns a low-rank form of attention that can be applied at O(NM) cost. FLARE not only scales to unprecedented problem sizes, but also delivers superior accuracy compared to state-of-the-art neural PDE surrogates across diverse benchmarks. We also release a new additive manufacturing dataset to spur further research. Our code is available at https://github.com/vpuri3/FLARE.py.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural network and uses beam search for pathfinding. We demonstrate its efficiency by finding solutions for 4x4x4 and 5x5x5 Rubik's cubes with unprecedentedly short solution lengths, outperforming all available solvers and introducing the first machine learning solver beyond the 3x3x3 case. In particular, it surpasses every single case of the combined best results in the Kaggle Santa 2023 challenge, which involved over 1,000 teams. For the 3x3x3 Rubik's cube, our approach achieves an optimality rate exceeding 98%, matching the performance of task-specific solvers and significantly outperforming prior solutions such as DeepCubeA (60.3%) and EfficientCube (69.6%). Additionally, our solution is more than 26 times faster in solving 3x3x3 Rubik's cubes while requiring up to 18.5 times less model training time than the most efficient state-of-the-art competitor.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches on 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.