Daily Papers

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.

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

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.

Independently trained domain specialists can be fused post-hoc into a single model that outperforms any individual specialist, and the gain is predictable: gain = 0.82 x divergence - 2.72 (R^2 = 0.856, n=6, 3-26% divergence). This enables practitioners to estimate cooperative value before committing compute. Below ~3.3% divergence, gains approach zero.In the KALAVAI protocol, contributors fine-tune copies of a shared checkpoint independently, then submit for lightweight MoE routing (500 steps). Gains are consistent: +7.72% at 410M (+/-0.02%, 3 seeds), +7.49% at 1B (+/-0.01%, 3 seeds), +6.53% at 6.9B, each over the best specialist. The router matches domain-oracle routing within <10^{-5} nats. Cross-lingual fusion (Tamil/Yoruba/Welsh/Code) achieves +21.76%, with Yoruba perplexity falling 41.9 to 7.7. A 20-contributor federation achieves +16.71% (+/-0.07pp, 3 seeds).Three requirements bound the protocol. Shared initialisation is necessary: checkpoint mismatch degrades routing. Frozen layers are optional below ~10,000 steps and beneficial beyond. Learned routing is essential: uniform averaging degrades by -1.2% vs. best specialist, while any trained router achieves oracle-optimal assignment.

Standard representation probing for visual models relies on mathematically permutation-invariant operations like Global Average Pooling (GAP) or CLS tokens, treating patch representations as an unstructured bag-of-words. We challenge this paradigm by demonstrating that token order is a critical, exploitable dimension in frozen visual representations (e.g., MAE, BEiT, DINOv2, and ViT as CLS-ablation extreme). We propose SSMProbe, a probing framework driven by a State Space Model (SSM). Operating as discrete Linear Time-Invariant (LTI) dynamical systems, SSMs act as permutation-sensitive probes where sequence order strictly dictates the final state due to inherent memory decay. Formulating token ordering as an information scheduling problem, we compare fixed scan heuristics against a differentiable soft permutation (Sinkhorn-based) learned from downstream supervision. Evaluations on standard and fine-grained classification benchmarks reveal a striking order gap: while fixed scans fail dramatically on highly localized patch features, our learned soft permutation successfully extracts highly competitive performance from otherwise heavily localized patch sequences. We find that pre-training objectives fundamentally shape token structure: DINOv2 concentrates global semantics in optimized CLS tokens leaving patches hyperspecialized, pure MAE preserves distributed representations with heterogeneous patch informativeness, and ViT represents a supervised CLS-dominated extreme. BEiT occupies middle ground. This heterogeneity is order-dependent -- meaning the SSM probe's performance depends critically on which tokens are placed at which temporal positions -- and is not merely a topological property of the spatial grid. SSMProbe's learned routing effectively discovers and exploits this heterogeneity, offering a powerful new diagnostic lens for visual representation analysis.

Multi-agent systems built on large language models (LLMs) require many coordination choices that are difficult to fix a priori: which skill protocol to invoke, which agent role should perform a subtask, which model to bind to each role, how roles should interact, when to use retrieval or verification, and when to omit a step entirely. These choices interact with task regime and operational constraints, so static pipelines and one-off model comparisons provide only a limited view of the design space. This paper introduces AgensFlow, an open-source framework that treats multi-agent coordination as an online policy-learning problem under partial observability. The framework makes coordination decisions observable and learnable from repeated trajectories, rather than treating skill, role, model, topology, and evaluation choices as fixed pipeline design. AgensFlow is evaluated on two corpora: distributed-systems incident tasks and security-advisory tasks. The evaluation shows three main results: learned routing reaches a higher-quality operating point than a fixed pipeline baseline on coordination-heavy classes; skip:X isolates topology compression as a meaningful part of the substrate; and warm-started policy graphs can reduce exploration cost while preserving plateau quality. Overall, the results support that learned, auditable routing can improve coordination-heavy multi-agent workflows over static wiring.

Recent works suggest that transformer models are capable of multi-tasking on diverse NLP tasks and adapting to new tasks efficiently. However, the potential of these multi-task models may be limited as they use the same set of parameters for all tasks. In contrast, humans tackle tasks in a more flexible way, by making proper presumptions on what skills and knowledge are relevant and executing only the necessary computations. Inspired by this, we propose to use task-level mixture-of-expert models, which has a collection of transformer layers (i.e., experts) and a router component that chooses from these experts dynamically and flexibly. We find that these models help improve the average performance gain (ARG) metric by 2.6% when adapting to unseen tasks in the few-shot setting and by 5.6% in the zero-shot generalization setting. Further, we show that the learned routing decisions partly rediscover human categorization of NLP tasks -- certain experts are strongly associated with extractive tasks, some with classification tasks, and some with tasks requiring world knowledge.

We introduce MoMa, a novel modality-aware mixture-of-experts (MoE) architecture designed for pre-training mixed-modal, early-fusion language models. MoMa processes images and text in arbitrary sequences by dividing expert modules into modality-specific groups. These groups exclusively process designated tokens while employing learned routing within each group to maintain semantically informed adaptivity. Our empirical results reveal substantial pre-training efficiency gains through this modality-specific parameter allocation. Under a 1-trillion-token training budget, the MoMa 1.4B model, featuring 4 text experts and 4 image experts, achieves impressive FLOPs savings: 3.7x overall, with 2.6x for text and 5.2x for image processing compared to a compute-equivalent dense baseline, measured by pre-training loss. This outperforms the standard expert-choice MoE with 8 mixed-modal experts, which achieves 3x overall FLOPs savings (3x for text, 2.8x for image). Combining MoMa with mixture-of-depths (MoD) further improves pre-training FLOPs savings to 4.2x overall (text: 3.4x, image: 5.3x), although this combination hurts performance in causal inference due to increased sensitivity to router accuracy. These results demonstrate MoMa's potential to significantly advance the efficiency of mixed-modal, early-fusion language model pre-training, paving the way for more resource-efficient and capable multimodal AI systems.

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.

Large reasoning models (LRMs) achieve strong performance on complex reasoning tasks by generating long, multi-step reasoning trajectories, but inference-time scaling incurs substantial deployment cost. A key challenge is that generation difficulty varies within a single output, whereas existing efficiency-oriented approaches either ignore this intra-generation variation or rely on supervised token-level routing with high system complexity. We present RelayGen, a training-free, segment-level runtime model switching framework that exploits difficulty variation in long-form reasoning. Through offline analysis of generation uncertainty using token probability margins, we show that coarse-grained segment-level control is sufficient to capture difficulty transitions within a reasoning trajectory. RelayGen identifies model-specific switch cues that signal transitions to lower-difficulty segments and dynamically delegates their continuation to a smaller model, while preserving high-difficulty reasoning on the large model. Across multiple reasoning benchmarks, RelayGen substantially reduces inference latency while preserving most of the accuracy of large models. When combined with speculative decoding, RelayGen achieves up to 2.2times end-to-end speedup with less than 2\% accuracy degradation, without requiring additional training or learned routing components.

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.

Despite their remarkable achievement, gigantic transformers encounter significant drawbacks, including exorbitant computational and memory footprints during training, as well as severe collapse evidenced by a high degree of parameter redundancy. Sparsely-activated Mixture-of-Experts (SMoEs) have shown promise to mitigate the issue of training efficiency, yet they are prone to (1) redundant experts due to representational collapse; and (2) poor expert scalability for inference and downstream fine-tuning, primarily due to overfitting of the learned routing policy to the number of activated experts during training. As recent research efforts are predominantly focused on improving routing policies to encourage expert specializations, this work focuses on exploring the overlooked scalability bottleneck of SMoEs and leveraging it to effectively scale dense transformers. To this end, we propose a new plug-and-play training framework, SMoE-Dropout, to enable scaling transformers to better accuracy in their full capacity without collapse. Specifically, SMoE-Dropout consists of a randomly initialized and fixed router network to activate experts and gradually increases the activated expert number as training progresses over time. Transformers trained by SMoE-Dropout naturally exhibit a self-slimmable property subject to resource availability, offering smooth and consistent performance boosts with an increase in activated experts during inference or fine-tuning. Our extensive experiments demonstrate the superior performance and substantial computation savings of SMoE-Dropout, compared to dense training baselines with equivalent parameter counts. In particular, our trained BERT outperforms its densely trained counterpart with consistent improvements of {1.03%, 0.78%, 1.09%} on challenging reasoning tasks {ASDiv-A, MAWPS, SVAMP}, respectively.

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

Universal Multimodal Retrieval requires unified embedding models capable of interpreting diverse user intents, ranging from simple keywords to complex compositional instructions. While Multimodal Large Language Models (MLLMs) possess strong reasoning capabilities, prevailing adaptations confine them to static encoders, underutilizing their generative potential. This encoder-only paradigm struggles with complex intents that demand logical deduction rather than superficial pattern matching. To address this, we introduce TRACE (Task-adaptive Reasoning And Compressing Embeddings). TRACE unifies generative reasoning with discriminative representation learning. It first generates a structured Chain-of-Thought (CoT) to explicitly reason about the query, and subsequently compresses this reasoning trace into a compact embedding via a dedicated token. To train this framework, we construct M-BEIR-CoT, a large-scale dataset featuring a difficulty-aware routing strategy. Experiments on the M-BEIR benchmark establish TRACE as the new state-of-the-art. Crucially, TRACE demonstrates a learned implicit routing behavior. It autonomously activates reasoning for complex queries while bypassing it for simpler ones, achieving an optimal balance between retrieval accuracy and inference throughput. Furthermore, by internalizing the deductive process, TRACE exhibits remarkable zero-shot transferability to unseen domains and novel constraints.

This paper presents LOLA, a massively multilingual large language model trained on more than 160 languages using a sparse Mixture-of-Experts Transformer architecture. Our architectural and implementation choices address the challenge of harnessing linguistic diversity while maintaining efficiency and avoiding the common pitfalls of multilinguality. Our analysis of the evaluation results shows competitive performance in natural language generation and understanding tasks. Additionally, we demonstrate how the learned expert-routing mechanism exploits implicit phylogenetic linguistic patterns to potentially alleviate the curse of multilinguality. We provide an in-depth look at the training process, an analysis of the datasets, and a balanced exploration of the model's strengths and limitations. As an open-source model, LOLA promotes reproducibility and serves as a robust foundation for future research. Our findings enable the development of compute-efficient multilingual models with strong, scalable performance across languages.

Current alignment evaluation mostly measures whether models encode dangerous concepts and whether they refuse harmful requests. Both miss the layer where alignment often operates: routing from concept detection to behavioral policy. We study political censorship in Chinese-origin language models as a natural experiment, using probes, surgical ablations, and behavioral tests across nine open-weight models from five labs. Three findings follow. First, probe accuracy alone is non-diagnostic: political probes, null controls, and permutation baselines can all reach 100%, so held-out category generalization is the informative test. Second, surgical ablation reveals lab-specific routing. Removing the political-sensitivity direction eliminates censorship and restores accurate factual output in most models tested, while one model confabulates because its architecture entangles factual knowledge with the censorship mechanism. Cross-model transfer fails, indicating that routing geometry is model- and lab-specific. Third, refusal is no longer the dominant censorship mechanism. Within one model family, hard refusal falls to zero while narrative steering rises to the maximum, making censorship invisible to refusal-only benchmarks. These results support a three-stage descriptive framework: detect, route, generate. Models often retain the relevant knowledge; alignment changes how that knowledge is expressed. Evaluations that audit only detection or refusal therefore miss the routing mechanism that most directly determines behavior.

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.

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.

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.

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}}.

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

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.

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

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.

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.

We investigate the temporal concatenation of sub-policies in Markov Decision Processes (MDP) with time-varying reward functions. We introduce General Dijkstra Search (GDS), and prove that globally optimal goal-reaching policies can be recovered through temporal composition of intermediate optimal sub-policies. Motivated by the "search, select, update" principle underlying GDS, we propose Dynamic Latent Routing (DLR), a language-model post-training method that jointly learns discrete latent codes, routing policies, and model parameters through dynamic search in a single training stage. In low-data fine-tuning settings, DLR matches or outperforms supervised fine-tuning across four datasets and six models, achieving a mean gain of +6.6 percentage points, while prior discrete-latent baselines consistently underperform SFT. Mechanistic analyses and targeted code ablations show that DLR learns structured routing behaviors with distinct causal roles.

We study LLM routing, the problem of selecting the best model for each query while balancing user satisfaction, model expertise, and inference cost. We formulate routing as contextual dueling bandits, learning from pairwise preference feedback rather than absolute scores, thereby yielding label-efficient and dynamic adaptation. Building on this formulation, we introduce Category-Calibrated Fine-Tuning (CCFT), a representation-learning method that derives model embeddings from offline data using contrastive fine-tuning with categorical weighting. These embeddings enable the practical instantiation of Feel-Good Thompson Sampling for Contextual Dueling Bandits (FGTS.CDB), a theoretically grounded posterior-sampling algorithm. We propose four variants of the categorical weighting that explicitly integrate model quality and cost, and we empirically evaluate the proposed methods on the RouterBench and MixInstruct datasets. Across both benchmarks, our methods achieve lower cumulative regret and faster convergence, with better robustness and performance-cost balance than strong baselines built with a general-purpose OpenAI embedding model.

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.

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.

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.

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

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.

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

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.

Large language models (LLMs) demonstrate remarkable capabilities, but their broad deployment is limited by significant computational resource demands, particularly energy consumption during inference. Static, one-model-fits-all inference strategies are often inefficient, as they do not exploit the diverse range of available models or adapt to varying query requirements. This paper presents GreenServ, a dynamic, context-aware routing framework that optimizes the trade-off between inference accuracy and energy efficiency. GreenServ extracts lightweight contextual features from each query, including task type, semantic cluster, and text complexity, and routes queries to the most suitable model from a heterogeneous pool, based on observed accuracy and energy usage. We employ a multi-armed bandit approach to learn adaptive routing policies online. This approach operates under partial feedback, eliminates the need for extensive offline calibration, and streamlines the integration of new models into the inference pipeline. We evaluated GreenServ across five benchmark tasks and a pool of 16 contemporary open-access LLMs. Experimental results show that GreenServ consistently outperforms static (single-model) and random baselines. In particular, compared to random routing, GreenServ achieved a 22% increase in accuracy while reducing cumulative energy consumption by 31%. Finally, we evaluated GreenServ with RouterBench, achieving an average accuracy of 71.7% with a peak accuracy of 75.7%. All artifacts are open-source and available here: https://github.com/TZData1/llm-inference-router{GitHub}

Recently, there has been a widespread proliferation of "expert" language models that are specialized to a specific task or domain through parameter-efficient fine-tuning. How can we recycle large collections of expert language models to improve zero-shot generalization to unseen tasks? In this work, we propose Post-Hoc Adaptive Tokenwise Gating Over an Ocean of Specialized Experts (PHATGOOSE), which learns to route among specialized modules that were produced through parameter-efficient fine-tuning. Unlike past methods that learn to route among specialized models, PHATGOOSE explores the possibility that zero-shot generalization will be improved if different experts can be adaptively chosen for each token and at each layer in the model. Crucially, our method is post-hoc - it does not require simultaneous access to the datasets used to create the specialized models and only requires a modest amount of additional compute after each expert model is trained. In experiments covering a range of specialized model collections and zero-shot generalization benchmarks, we find that PHATGOOSE outperforms past methods for post-hoc routing and, in some cases, outperforms explicit multitask training (which requires simultaneous data access). To better understand the routing strategy learned by PHATGOOSE, we perform qualitative experiments to validate that PHATGOOSE's performance stems from its ability to make adaptive per-token and per-module expert choices. We release all of our code to support future work on improving zero-shot generalization by recycling specialized experts.

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.

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

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.

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/

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.

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.

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.

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

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.

Machine unlearning (MU) for large language models has become critical for AI safety, yet existing methods fail to generalize to Mixture-of-Experts (MoE) architectures. We identify that traditional unlearning methods exploit MoE's architectural vulnerability: they manipulate routers to redirect queries away from knowledgeable experts rather than erasing knowledge, causing a loss of model utility and superficial forgetting. We propose Geometric Routing Invariance Preservation (GRIP), an algorithm-agnostic framework for unlearning for MoE. Our core contribution is a geometric constraint, implemented by projecting router gradient updates into an expert-specific null-space. Crucially, this decouples routing stability from parameter rigidity: while discrete expert selections remain stable for retained knowledge, the continuous router parameters remain plastic within the null space, allowing the model to undergo necessary internal reconfiguration to satisfy unlearning objectives. This forces the unlearning optimization to erase knowledge directly from expert parameters rather than exploiting the superficial router manipulation shortcut. GRIP functions as an adapter, constraining router parameter updates without modifying the underlying unlearning algorithm. Extensive experiments on large-scale MoE models demonstrate that our adapter eliminates expert selection shift (achieving over 95% routing stability) across all tested unlearning methods while preserving their utility. By preventing existing algorithms from exploiting MoE model's router vulnerability, GRIP adapts existing unlearning research from dense architectures to MoEs.

Edge deployment of large language models (LLMs) increasingly relies on libraries of lightweight LoRA adapters, yet GPU/DRAM can keep only a small resident subset at a time. Serving a request through a non-resident adapter requires paging its weights from storage, incurring measurable latency. This creates a two-timescale online control problem: on a slow timescale, the system selects which adapters remain resident in fast memory, while on a fast timescale it routes each request to an adapter whose context-dependent utility is unknown a priori. The two decisions are tightly coupled: the cache determines the cost of exploration, and the router determines which adapters receive informative feedback. We formulate this joint caching-and-routing problem as a two-timescale contextual bandit and propose POLAR (Paging and Online Learning for Adapter Routing). POLAR pairs a cache-aware LinUCB router with an epoch-based cache controller. We study two variants. A fixed-epoch version provides a robust baseline with worst-case regret guarantees under arbitrary contexts. An epoch-doubling version, POLAR+, adds forced exploration and improved cache optimization to achieve mathcal{O}(dNT+KT) sublinear regret under stochastic regularity and cacheability conditions, where N is the adapter count, K the cache size, d the context dimension, and T the horizon. The routing term matches the standard contextual-bandit rate up to logarithmic factors, showing that the memory hierarchy does not fundamentally slow routing learning. Experiments using 15 real LoRA adapters for Qwen2.5-7B together with measured GPU paging latencies show that adaptive cache control substantially outperforms non-adaptive baselines and exhibits scaling trends consistent with the theory.

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.

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

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

Many applications must provide low-latency LLM service to users or risk unacceptable user experience. However, over-provisioning resources to serve fluctuating request patterns is often prohibitively expensive. In this work, we present a best-effort serving system that employs deep reinforcement learning to adjust service quality based on the task distribution and system load. Our best-effort system can maintain availability with over 10x higher client request rates, serves above 96% of peak performance 4.1x more often, and serves above 98% of peak performance 2.3x more often than static serving on unpredictable workloads. Our learned router is robust to shifts in both the arrival and task distribution. Compared to static serving, learned best-effort serving allows for cost-efficient serving through increased hardware utility. Additionally, we argue that learned best-effort LLM serving is applicable in wide variety of settings and provides application developers great flexibility to meet their specific needs.

Continual learning, especially class-incremental learning (CIL), on the basis of a pre-trained model (PTM) has garnered substantial research interest in recent years. However, how to effectively learn both discriminative and comprehensive feature representations while maintaining stability and plasticity over very long task sequences remains an open problem. We propose CaRE, a scalable {C}ontinual Le{a}rner with efficient Bi-Level {R}outing Mixture-of-{E}xperts (BR-MoE). The core idea of BR-MoE is a bi-level routing mechanism: a router selection stage that dynamically activates relevant task-specific routers, followed by an expert routing phase that dynamically activates and aggregates experts, aiming to inject discriminative and comprehensive representations into every intermediate network layer. On the other hand, we introduce a challenging dataset, OmniBenchmark-1K, for CIL performance evaluation on very long task sequences with hundreds of tasks. Extensive experiments show that CaRE demonstrates leading performance across a variety of datasets and task settings, including commonly used CIL datasets with classical CIL settings (e.g., 5-20 tasks). To the best of our knowledge, CaRE is the first continual learner that scales to very long task sequences (ranging from 100 to over 300 non-overlapping tasks), while outperforming all baselines by a large margin on such task sequences. We hope that this work will inspire further research into continual learning over extremely long task sequences. Code and dataset are publicly released at https://github.com/LMMMEng/CaRE.

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

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

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.

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

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.

Temporal credit assignment in reinforcement learning is often approached by introducing value estimates at multiple discount factors. A natural next step is to let the actor dynamically route among these temporal heads, using either differentiable attention or heuristic uncertainty weights. This paper argues that such routing can create a numerical shortcut rather than a reliable temporal abstraction. We study this issue in a controlled PPO setting on LunarLander-v2, using the environment as a visual sandbox for diagnosing failure modes. First, we formalize Surrogate Objective Hacking: a differentiable softmax router exposed to the PPO surrogate receives a direct gradient toward advantage heads that are numerically favorable for the current update, even when this routing change does not correspond to improved physical control. Because unnormalized advantages at different discount factors have different effective scales, this creates a scale-discrepancy vulnerability. Second, we identify the Paradox of Temporal Uncertainty in gradient-free error-based routing: short-horizon heads can receive the largest routing share because their prediction targets are easier, even when they are less aligned with delayed task success. As a structural response, we study Target Decoupling: the critic may retain multi-timescale auxiliary heads, but the actor is updated only with the long-horizon advantage. Target Decoupling is not presented as a broad performance booster; in this run set it removes the exploitable actor-side routing pathway and improves the observed worst-seed return. Code is available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

LLM routing has achieved promising results in integrating the strengths of diverse models while balancing efficiency and performance. However, to support more realistic and challenging applications, routing must extend into agentic LLM settings, where task planning, multi-round cooperation among heterogeneous agents, and memory utilization are indispensable. To address this gap, we propose GraphPlanner, a heterogeneous graph memory-augmented agentic router for multi-agent LLMs that generates routing workflows for each query and supports both inductive and transductive inference. GraphPlanner formulates workflow generation as a Markov Decision Process (MDP), where at each step it selects both the LLM backbone and the agent role, including Planner, Executor, and Summarizer. By leveraging a heterogeneous graph, denoted as GARNet, to capture interaction memories among queries, agents, and responses, GraphPlanner integrates historical memory and workflow memory into richer state representations. The entire pipeline is optimized with reinforcement learning, jointly improving task-specific performance and computational efficiency. We evaluate GraphPlanner across 14 diverse LLM tasks and demonstrate that: (1) GraphPlanner outperforms strong single-round and multi-round routers, improving accuracy by up to 9.3% while reducing GPU cost from 186.26 GiB to 1.04 GiB; (2) GraphPlanner generalizes robustly to unseen tasks and LLMs, exhibiting strong zero-shot capabilities; and (3) GraphPlanner effectively leverages historical memories, supporting both inductive and transductive inference for more adaptive routing. Our code for GraphPlanner is released at https://github.com/ulab-uiuc/GraphPlanner.

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.

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

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

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.

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.

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.

In large multimodal models (LMMs), the perception of non-language modalities (e.g., visual representations) is usually not on par with the large language models (LLMs)' powerful reasoning capabilities, deterring LMMs' performance on challenging downstream tasks. This weakness has been recently mitigated by replacing the vision encoder with a mixture-of-experts (MoE), which provides rich, multi-granularity, and diverse representations required by diverse downstream tasks. The performance of multimodal MoE largely depends on its router, which reweights and mixes the representations of different experts for each input. However, we find that the end-to-end trained router does not always produce the optimal routing weights for every test sample. To bridge the gap, we propose a novel and efficient method "Re-Routing in Test-Time(R2-T2) that locally optimizes the vector of routing weights in test-time by moving it toward those vectors of the correctly predicted samples in a neighborhood of the test sample. We propose three R2-T2 strategies with different optimization objectives and neighbor-search spaces. R2-T2 consistently and greatly improves state-of-the-art LMMs' performance on challenging benchmarks of diverse tasks, without training any base-model parameters.

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

Sparse Mixture-of-Experts (MoE) 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.

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.

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.

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

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.

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

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

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.

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

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.

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.

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

Mixture of Experts 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.

The digital transformation is pushing the existing network technologies towards new horizons, enabling new applications (e.g., vehicular networks). As a result, the networking community has seen a noticeable increase in the requirements of emerging network applications. One main open challenge is the need to accommodate control systems to highly dynamic network scenarios. Nowadays, existing network optimization technologies do not meet the needed requirements to effectively operate in real time. Some of them are based on hand-crafted heuristics with limited performance and adaptability, while some technologies use optimizers which are often too time-consuming. Recent advances in Deep Reinforcement Learning (DRL) have shown a dramatic improvement in decision-making and automated control problems. Consequently, DRL represents a promising technique to efficiently solve a variety of relevant network optimization problems, such as online routing. In this paper, we explore the use of state-of-the-art DRL technologies for real-time routing optimization and outline some relevant open challenges to achieve production-ready DRL-based solutions.

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.

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

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.

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

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

Mixture-of-Experts (MoE) architectures have become the key to scaling modern LLMs, yet little is understood about how their sparse routing dynamics respond to multilingual data. In this work, we analyze expert routing patterns using parallel multilingual datasets and present highly interpretable layer-wise phenomena. We find that MoE models route tokens in language-specific ways in the early and late decoder layers but exhibit significant cross-lingual routing alignment in middle layers, mirroring parameter-sharing trends observed in dense LLMs. In particular, we reveal a clear, strong correlation between a model's performance in a given language and how similarly its tokens are routed to English in these layers. Extending beyond correlation, we explore inference-time interventions that induce higher cross-lingual routing alignment. We introduce a method that steers the router by promoting middle-layer task experts frequently activated in English, and it successfully increases multilingual performance. These 1-2% gains are remarkably consistent across two evaluation tasks, three models, and 15+ languages, especially given that these simple interventions override routers of extensively trained, state-of-the-art LLMs. In comparison, interventions outside of the middle layers or targeting multilingual-specialized experts only yield performance degradation. Altogether, we present numerous findings that explain how MoEs process non-English text and demonstrate that generalization is limited by the model's ability to leverage language-universal experts in all languages.

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.

In-context reinforcement learning (ICRL) has emerged as a promising paradigm for adapting RL agents to downstream tasks through prompt conditioning. However, two notable challenges remain in fully harnessing in-context learning within RL domains: the intrinsic multi-modality of the state-action-reward data and the diverse, heterogeneous nature of decision tasks. To tackle these challenges, we propose T2MIR (Token- and Task-wise MoE for In-context RL), an innovative framework that introduces architectural advances of mixture-of-experts (MoE) into transformer-based decision models. T2MIR substitutes the feedforward layer with two parallel layers: a token-wise MoE that captures distinct semantics of input tokens across multiple modalities, and a task-wise MoE that routes diverse tasks to specialized experts for managing a broad task distribution with alleviated gradient conflicts. To enhance task-wise routing, we introduce a contrastive learning method that maximizes the mutual information between the task and its router representation, enabling more precise capture of task-relevant information. The outputs of two MoE components are concatenated and fed into the next layer. Comprehensive experiments show that T2MIR significantly facilitates in-context learning capacity and outperforms various types of baselines. We bring the potential and promise of MoE to ICRL, offering a simple and scalable architectural enhancement to advance ICRL one step closer toward achievements in language and vision communities. Our code is available at https://github.com/NJU-RL/T2MIR.

The advent of large language models has revolutionized natural language processing, but their increasing complexity has led to substantial training costs, resource demands, and environmental impacts. In response, sparse Mixture-of-Experts (MoE) models have emerged as a promising alternative to dense models. Since training MoE models from scratch can be prohibitively expensive, recent studies have explored leveraging knowledge from pre-trained non-MoE models. However, existing approaches have limitations, such as requiring significant hardware resources and data. We propose a novel algorithm, LaDiMo, which efficiently converts a Transformer-based non-MoE model into a MoE model with minimal additional training cost. LaDiMo consists of two stages: layer-wise expert construction and routing policy decision. By harnessing the concept of Knowledge Distillation, we compress the model and rapidly recover its performance. Furthermore, we develop an adaptive router that optimizes inference efficiency by profiling the distribution of routing weights and determining a layer-wise policy that balances accuracy and latency. We demonstrate the effectiveness of our method by converting the LLaMA2-7B model to a MoE model using only 100K tokens, reducing activated parameters by over 20% while keeping accuracy. Our approach offers a flexible and efficient solution for building and deploying MoE models.

Instruction-based fine-tuning of large language models (LLMs) has achieved remarkable success in various natural language processing (NLP) tasks. Parameter-efficient fine-tuning (PEFT) methods, such as Mixture of LoRA Experts (MoLE), combine the efficiency of Low-Rank Adaptation (LoRA) with the versatility of Mixture of Experts (MoE) models, demonstrating significant potential for handling multiple downstream tasks. However, the existing routing mechanisms for MoLE often involve a trade-off between computational efficiency and predictive accuracy, and they fail to fully address the diverse expert selection demands across different transformer layers. In this work, we propose DynMoLE, a hybrid routing strategy that dynamically adjusts expert selection based on the Tsallis entropy of the router's probability distribution. This approach mitigates router uncertainty, enhances stability, and promotes more equitable expert participation, leading to faster convergence and improved model performance. Additionally, we introduce an auxiliary loss based on Tsallis entropy to further guide the model toward convergence with reduced uncertainty, thereby improving training stability and performance. Our extensive experiments on commonsense reasoning benchmarks demonstrate that DynMoLE achieves substantial performance improvements, outperforming LoRA by 9.6% and surpassing the state-of-the-art MoLE method, MoLA, by 2.3%. We also conduct a comprehensive ablation study to evaluate the contributions of DynMoLE's key components.

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.

Routing has emerged as a promising strategy for balancing performance and cost in large language model (LLM) systems that combine lightweight models with powerful but expensive large models. Recent studies show that probe routing, which predicts the correctness of a small model using its hidden states, provides an effective solution in text-only LLMs. However, we observe that these probes degrade substantially when applied to multimodal LLMs (MLLMs). Through empirical analysis, we find that the presence of visual inputs weakens the separability of correctness signals in hidden states, making them harder to extract using standard probe designs. To address this challenge, we introduce two complementary approaches for improving probe routing in MLLMs. First, we propose the Attention Probe, which aggregates hidden states from the preceding layer based on attention scores to recover distributed correctness signals. Second, we present the KL-Regularized LoRA Probe (ReLope), which inserts a lightweight LoRA adapter and applies a KL regularizer to learn routing-aware representations. Comprehensive experiments show that our methods consistently outperform baselines, suggesting that improving the quality of hidden states is key to effective routing in MLLMs. Our code is available at https://github.com/Spinozaaa/ReLope.

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.

Recent advances in Large Reasoning Models (LRMs) have significantly improved long-chain reasoning capabilities over Large Language Models (LLMs). However, LRMs often produce unnecessarily lengthy outputs even for simple queries, leading to inefficiencies or even accuracy degradation compared to LLMs. To overcome this, we propose CP-Router, a training-free and model-agnostic routing framework that dynamically selects between an LLM and an LRM, demonstrated with multiple-choice question answering (MCQA) prompts. The routing decision is guided by the prediction uncertainty estimates derived via Conformal Prediction (CP), which provides rigorous coverage guarantees. To further refine the uncertainty differentiation across inputs, we introduce Full and Binary Entropy (FBE), a novel entropy-based criterion that adaptively selects the appropriate CP threshold. Experiments across diverse MCQA benchmarks, including mathematics, logical reasoning, and Chinese chemistry, demonstrate that CP-Router efficiently reduces token usage while maintaining or even improving accuracy compared to using LRM alone. We also extend CP-Router to diverse model pairings and open-ended QA, where it continues to demonstrate strong performance, validating its generality and robustness.

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.

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

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.

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

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.

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.

Modern Mixture-of-Experts (MoE) architectures allocate expert capacity through a rigid per-layer rule: each transformer layer owns a separate expert set. This convention couples depth scaling with linear expert-parameter growth and assumes that every layer needs isolated expert capacity. However, recent analyses and our routing probe challenge this allocation rule: replacing a deeper layer's learned top-k router with uniform random routing drops downstream accuracy by only 1.0-1.6 points across multiple production MoE models. Motivated by this redundancy, we propose UniPool, an MoE architecture that treats expert capacity as a global architectural budget by replacing per-layer expert ownership with a single shared pool accessed by independent per-layer routers. To enable stable and balanced training under sharing, we introduce a pool-level auxiliary loss that balances expert utilization across the entire pool, and adopt NormRouter to provide sparse and scale-stable routing into the shared expert pool. Across five LLaMA-architecture model scales (182M, 469M, 650M, 830M, and 978M parameters) trained on 30B tokens from the Pile, UniPool consistently improves validation loss and perplexity over the matched vanilla MoE baselines. Across these scales, UniPool reduces validation loss by up to 0.0386 relative to vanilla MoE. Beyond raw loss improvement, our results identify pool size as an explicit depth-scaling hyperparameter: reduced-pool UniPool variants using only 41.6%-66.7% of the vanilla expert-parameter budget match or outperform layer-wise MoE at the tested scales. This shows that, under a shared-pool design, expert parameters need not grow linearly with depth; they can grow sublinearly while remaining more efficient and effective than vanilla MoE. Further analysis shows that UniPool's benefits compose with finer-grained expert decomposition.

Large language models split into two families: reasoning-centric LLMs, which strengthen internal chain-of-thought reasoning but cannot invoke external tools, and agentic LLMs, which learn to interact with environments and leverage tools but often lag in deep reasoning. This divide arises from fundamentally different training objectives, leading to mismatched strengths and inefficiency on simple queries, where both families tend to overthink or over-call tools. In this work, we present Adaptive Agent Foundation Model (A^2FM), a unified framework that follows a route-then-align principle: the model first learns task-aware routing and then aligns mode-specific trajectories under a shared backbone. To address the inefficiency gap, we introduce a third mode-instant-that handles simple queries directly, preventing unnecessary reasoning or tool calls while complementing the agentic and reasoning modes. To jointly enhance accuracy and efficiency, we propose Adaptive Policy Optimization (APO), which enforces adaptive sampling across modes and applies a cost-regularized reward. On the 32B scale, A^2FM achieves 13.4% on BrowseComp, 70.4% on AIME25, and 16.7% on HLE, setting new SOTA among comparable models and performing competitively with frontier LLMs across agentic, reasoning, and general benchmarks. Notably, the adaptive execution achieves a cost of pass of only $0.00487 per correct answer-cutting cost by 45.2% relative to reasoning and 33.5% relative to agentic, thus delivering substantially higher cost efficiency while maintaining comparable accuracy.

There is a rapidly growing number of open-source Large Language Models (LLMs) and benchmark datasets to compare them. While some models dominate these benchmarks, no single model typically achieves the best accuracy in all tasks and use cases. In this work, we address the challenge of selecting the best LLM out of a collection of models for new tasks. We propose a new formulation for the problem, in which benchmark datasets are repurposed to learn a "router" model for this LLM selection, and we show that this problem can be reduced to a collection of binary classification tasks. We demonstrate the utility and limitations of learning model routers from various benchmark datasets, where we consistently improve performance upon using any single model for all tasks.

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

Conditional computing processes an input using only part of the neural network's computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: Reducing the computational burden is an obvious advantage. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to take a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources.

Deep Reinforcement Learning (DRL) has shown a dramatic improvement in decision-making and automated control problems. Consequently, DRL represents a promising technique to efficiently solve many relevant optimization problems (e.g., routing) in self-driving networks. However, existing DRL-based solutions applied to networking fail to generalize, which means that they are not able to operate properly when applied to network topologies not observed during training. This lack of generalization capability significantly hinders the deployment of DRL technologies in production networks. This is because state-of-the-art DRL-based networking solutions use standard neural networks (e.g., fully connected, convolutional), which are not suited to learn from information structured as graphs. In this paper, we integrate Graph Neural Networks (GNN) into DRL agents and we design a problem specific action space to enable generalization. GNNs are Deep Learning models inherently designed to generalize over graphs of different sizes and structures. This allows the proposed GNN-based DRL agent to learn and generalize over arbitrary network topologies. We test our DRL+GNN agent in a routing optimization use case in optical networks and evaluate it on 180 and 232 unseen synthetic and real-world network topologies respectively. The results show that the DRL+GNN agent is able to outperform state-of-the-art solutions in topologies never seen during training.

We propose UTSP, an unsupervised learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics. Our approach is parameter efficient as well as data efficient: the model takes sim 10\% of the number of parameters and sim 0.2\% of training samples compared with reinforcement learning or supervised learning methods.

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.

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

The inherent capabilities of a language model (LM) and the reasoning strategies it employs jointly determine its performance in reasoning tasks. While test-time scaling is regarded as an effective approach to tackling complex reasoning tasks, it incurs substantial computational costs and often leads to "overthinking", where models become trapped in "thought pitfalls". To address this challenge, we propose Route-To-Reason (RTR), a novel unified routing framework that dynamically allocates both LMs and reasoning strategies according to task difficulty under budget constraints. RTR learns compressed representations of both expert models and reasoning strategies, enabling their joint and adaptive selection at inference time. This method is low-cost, highly flexible, and can be seamlessly extended to arbitrary black-box or white-box models and strategies, achieving true plug-and-play functionality. Extensive experiments across seven open source models and four reasoning strategies demonstrate that RTR achieves an optimal trade-off between accuracy and computational efficiency among all baselines, achieving higher accuracy than the best single model while reducing token usage by over 60%.

Large language models (LLMs) exhibit strengths across diverse domains. However, achieving strong performance across these domains with a single general-purpose model typically requires scaling to sizes that are prohibitively expensive to train and deploy. On the other hand, while smaller domain-specialized models are much more efficient, they struggle to generalize beyond their training distributions. To address this dilemma, we propose FusionRoute, a robust and effective token-level multi-LLM collaboration framework in which a lightweight router simultaneously (i) selects the most suitable expert at each decoding step and (ii) contributes a complementary logit that refines or corrects the selected expert's next-token distribution via logit addition. Unlike existing token-level collaboration methods that rely solely on fixed expert outputs, we provide a theoretical analysis showing that pure expert-only routing is fundamentally limited: unless strong global coverage assumptions hold, it cannot in general realize the optimal decoding policy. By augmenting expert selection with a trainable complementary generator, FusionRoute expands the effective policy class and enables recovery of optimal value functions under mild conditions. Empirically, across both Llama-3 and Gemma-2 families and diverse benchmarks spanning mathematical reasoning, code generation, and instruction following, FusionRoute outperforms both sequence- and token-level collaboration, model merging, and direct fine-tuning, while remaining competitive with domain experts on their respective tasks.

In deep learning, mixture-of-experts (MoE) activates one or few experts (sub-networks) on a per-sample or per-token basis, resulting in significant computation reduction. The recently proposed patch-level routing in MoE (pMoE) divides each input into n patches (or tokens) and sends l patches (lll n) to each expert through prioritized routing. pMoE has demonstrated great empirical success in reducing training and inference costs while maintaining test accuracy. However, the theoretical explanation of pMoE and the general MoE remains elusive. Focusing on a supervised classification task using a mixture of two-layer convolutional neural networks (CNNs), we show for the first time that pMoE provably reduces the required number of training samples to achieve desirable generalization (referred to as the sample complexity) by a factor in the polynomial order of n/l, and outperforms its single-expert counterpart of the same or even larger capacity. The advantage results from the discriminative routing property, which is justified in both theory and practice that pMoE routers can filter label-irrelevant patches and route similar class-discriminative patches to the same expert. Our experimental results on MNIST, CIFAR-10, and CelebA support our theoretical findings on pMoE's generalization and show that pMoE can avoid learning spurious correlations.

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.

When an LLM-based agent improves on a task, is the gain from the model itself or from the reasoning paradigm wrapped around it? We study this question by comparing six inference-time paradigms, namely Direct, CoT, ReAct, Plan-Execute, Reflection, and ReCode, across four frontier LLMs and ten benchmarks, yielding roughly 18,000 runs. We find that reasoning structure helps dramatically on some tasks but hurts on others: ReAct improves over Direct by 44pp on GAIA, while CoT degrades performance by 15pp on HumanEval. No single paradigm dominates, and oracle per-task selection beats the best fixed paradigm by 17.1pp on average. Motivated by this complementarity, we propose a select-then-solve approach: before answering each task, a lightweight embedding-based router selects the most suitable paradigm. Across four models, the router improves average accuracy from 47.6% to 53.1%, outperforming the best fixed paradigm at 50.3% by 2.8pp and recovering up to 37% of the oracle gap. In contrast, zero-shot self-routing only works for GPT-5 at 67.1% and fails for weaker models, all trailing the learned router. Our results argue that reasoning paradigm selection should be a per-task decision made by a learned router, not a fixed architectural choice.

ModeSwitch-LLM is a lightweight request-boundary controller for improving single-GPU large language model inference efficiency by routing each request to an appropriate fixed inference mode. Instead of relying on one static serving configuration, the system selects among FP16, quantized modes, speculative decoding, and hybrid modes such as GPTQ plus prefix caching and INT8 plus continuous batching using cheap workload-level features. We evaluate ModeSwitch-LLM on Meta-Llama-3.1-8B-Instruct served on a single NVIDIA A100 GPU. On deployment-style synthetic workloads, the online controller achieves a 2.10x mean latency speedup over FP16 and a 0.48x mean energy ratio, corresponding to 51.7% lower energy per token. On automatic benchmarks used as a quality gate, accuracy remains close to FP16 with a mean delta of +0.17 percentage points. We also evaluate lightweight learned routers, but find that they do not clearly outperform the rule-based controller because they add routing overhead and more often select modes that violate quality, energy, or memory constraints. These results show that simple request-aware routing can recover substantial efficiency from existing inference modes without retraining the model or changing its architecture.

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