One-Shot Routing

Large Language Model (LLM) agents based on the ReAct paradigm have demonstrated remarkable capabilities in tool use and task execution. However, ReAct suffers from a fundamental efficiency problem: every query triggers a complete reasoning loop from scratch, and similar queries repeat identical steps without leveraging historical experience. We propose TRIAGE,a three-level routing framework that reduces token consumption by reusing historical execution trajectories. Its core innovation is TaaS (Trajectory-as-a-Skill), which abstracts historical execution trajectories into reusable skills, realizing 'experience as a service'. TRIAGE classifies queries into three levels: (1) Direct Reuse-identical queries, 0 tokens; (2) Skill Substitution-similar queries, 0 tokens via deterministic parameter substitution; (3) Full ReAct-novel queries, automatically stored for future reuse. In large-scale experiments on 1,007 security monitoring queries, TRIAGE achieves 62.3% token savings, with 56.0% of queries at Level 2 and 5.5% at Level 1, both executing at zero cost. Cross-domain validation on ToolBench (15 domains, 345 queries) achieves 76.3% token reduction, confirming the generalizability of semantic routing. An online learning experiment demonstrates cold-start-to-mature evolution: the L2 hit rate rises from 0% to 57% within the first 100 queries, and the average token cost drops from 198 to 74.7. We also propose an automatic Skill extraction mechanism that distills high-frequency trajectory patterns into deterministic Skills, creating a positive feedback loop of 'the more you use it, the more efficient it becomes'.

Before an intelligent system can decide whether an action is allowed, it must first know which rules the action has approached. A single proposed action can implicate several policy regimes at once. Their requirements may stack, overlap, or qualify one another, yet many remain written in natural language while the action itself arrives as an incomplete description of intent. The first problem is not judgment. It is attention. Policy-centroid routing creates a layer before adjudication. It compresses expressions within each policy regime into one or more representative centroids, places the proposed action in the same semantic space, applies a declared measure, and routes every regime crossing a declared threshold to authoritative review. Several regimes may trigger at once. The output is a review agenda, not permission, prohibition, legality, breach, compliance, certification, or enforcement. The paper develops six falsifiable propositions and seven follow-on studies comparing the hypothesis with structured workflows, lexical and semantic retrieval, hierarchical and direct classification, and selective prediction under matched review burden. The studies are designed to identify where policy geometry recovers applicable regimes, where compression loses rare or overlapping obligations, and where the mechanism should abstain. The paper includes a synthetic worked example and reports no empirical efficacy result.

Multi-agent large language model (LLM) workflows have emerged as a powerful paradigm for solving complex, open-ended tasks through collaborative reasoning among specialized LLM agents, but they incur substantial operating costs due to repeated LLM invocations and long-horizon context accumulation. Existing cascade routing methods make one-shot, query-level decisions and cannot adapt to the dynamic, state-dependent nature of multi-step workflows, in which the right LLM at each step depends on evolving task progress, remaining task difficulty, and cost-efficiency requirements. We present ProgRouter, an online progress-guided routing framework that adaptively selects LLM agents across workflow steps to preserve task-solving quality while adhering to time and cost budgets. ProgRouter introduces a multi-view task progress scorer that combines coarse workflow outcome regimes with fine-grained signals on subtask completion, progress trends, and workflow state quality. Then, a dual-path task progress predictor and an adaptive meta-gating mechanism estimate the progress gain for each candidate routed LLM. ProgRouter makes online step-wise routing decisions that balance progress gain, task time budgets, and long-term operating cost efficiency. Experiments on HumanEval Plus, MBPP, MATH-500, and ASQA, spanning agentic code generation, mathematical reasoning, and retrieval-augmented long-form question answering, demonstrate that ProgRouter reduces the operating cost relative to key baselines while maintaining strong task-solving performance.

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science and arises in many engineering applications, such as smart vehicles and intelligent transportation systems. In the "Euclidean" case, each node is defined by its coordinates in the plane and distances are computed using the Euclidean metric. In the Constraint Programming (CP) literature, the Euclidean TSP is typically addressed by computing the full distance matrix and treating it as a general case; however this approach ignores the geometric information carried by the points' coordinates. In this work, we propose new filtering algorithms, implemented in Constraint Logic Programming (CLP), that exploit such geometric information to achieve stronger constraint propagation than existing approaches. Moreover, we show how this methodology can be extended to other Euclidean variants of the TSP, including the Euclidean Generalized Traveling Salesperson Problem (EGTSP), which is relevant in practical routing and logistics applications. Experimental results demonstrate the computational advantages of the proposed approach.

Web agents observe a browser through text, pixels, or both, and the choice is usually fixed once for all tasks. We measure six observation modes across eight site-model combinations (cells) on VisualWebArena and WebArena and ask what choosing per task would buy. The modes are complementary: each solves tasks the others miss, they fail in structurally different ways, and the best choice reverses between task sets. The obvious prize, an oracle that picks a winning mode for every task, looks large but is inflated by run-to-run noise: rerunning the same mode on the same tasks changes 12-14% of outcomes, so a second run of a mode already in hand gains about as much as adding a new one. What survives is a cost bound: sending only the tasks no mode solves to the cheapest mode cuts cost by 9.5-30.6% in 8 of 8 cells at unchanged success. We then test five routing policies (picking the mode, deciding when to spend on the strong mode, a zero-cost rule read off the task text, a confidence cascade, and pooled cost tiers), and none robustly beats simply fixing one well-chosen mode; the one exception is a fragile result in our sparsest cell. The central obstruction is that routing supervision is produced at the agent's success rate: the weaker the agent, the fewer labels a router gets, exactly where routing would be most valuable. This limit belongs to today's agents rather than to routing itself. Label supply and routing opportunity rise together (correlation 0.95 across cells), so a stronger agent can overturn the result, and we report the rerun noise bands and the full measurement protocol.

Agentic systems have emerged as a promising paradigm for solving complex tasks by coordinating specialized LLM-based agents. However, most existing systems primarily optimize task success while giving limited consideration to execution efficiency under practical constraints such as executor capability and computational cost. Existing router-based methods have limited ability to reason over rich, evolving task contexts, multi-step dependencies, and intermediate execution feedback, and often generalize poorly to unseen executors. We propose EASy, a trainable agentic framework that jointly optimizes task performance and computational efficiency through reinforcement learning. EASy equips an LLM-based orchestrator with explicit knowledge of the capability and cost profiles of heterogeneous executors, enabling context-sensitive coordination beyond performance-only routing. It further introduces a milestone-plan-act workflow that decomposes complex tasks into manageable milestones, constructs dependency-aware execution graphs, assigns suitable executors, and parallelizes independent steps while adapting subsequent decisions to intermediate outcomes. To train the orchestrator, we develop a tree-structured rollout procedure that explores alternative milestone decompositions and execution plans, together with multi-component rewards that capture task correctness, execution efficiency, and trajectory completeness. Extensive experiments on mathematical reasoning, embodied decision-making, and deep research benchmarks show that EASy consistently achieves stronger performance-efficiency trade-offs than strong agentic baselines.

Multi-page document visual question answering requires locating sparse evidence at both the page and region levels. Existing approaches typically emphasize one level over the other: page-centric methods focus on page acquisition, with region operations serving mainly as navigation aids, whereas region-centric methods assume that the relevant pages have already been supplied. Consequently, page and region selection remain disconnected rather than forming successive evidence decisions. We propose HierDoc, a hierarchical evidence-routing framework that formulates long-document evidence acquisition as two-stage set prediction from pages to regions. A page policy selects evidence pages from the full document; these pages are then parsed for semantic elements, after which a region policy selects the elements passed to a downstream answer model. Both answer-agnostic policies are optimized with stage-wise GRPO using granularity-specific structured-set rewards. The answer model receives selected full pages together with selected region crops and OCR or table text, preserving global context while emphasizing fine-grained evidence. Across the evaluated benchmarks, HierDoc achieves state-of-the-art or competitive performance among open-weight systems, improving LongDocURL by 16.87% relative to the strongest reported open-weight baseline. Controlled ablations further show that selected regional evidence improves the page-only system in accuracy and F1 by 5.51% and 4.82%, respectively. These results demonstrate the benefit of organizing coarse page routing and fine-grained region routing as successive, separately optimized stages of a unified evidence-acquisition process.

Agentic systems must repeatedly decide whether to answer directly, decompose a task, invoke a tool, execute code, delegate to a specialist, verify an intermediate result, or recover from failure. These meta-decisions affect not only task success but also operating cost and latency, yet they are often embedded inside an orchestration framework and evaluated only through aggregate task accuracy. We present MetaRoute-Bench, an open, inspectable framework for comparing meta-decision policies under a shared execution model. The initial benchmark contains 180 synthetic task profiles spanning data analysis, research, and document processing, eight routing policies, and 30 paired random seeds. Across 43,200 traces, a task-aware compositional policy achieves 79.4% success compared with 76.7% for a strong workload-specific static policy, 67.4% for one-shot task routing, and 52.9% for direct answering. Relative to the static policy, this is a 2.7 percentage-point improvement with paired 95% CI of plus or minus 2.0 points, at 4.7% higher mean cost and 6.4% higher latency. Ablations show the largest losses when route composition is restricted to one operation and when verification is removed. These results are generated by a seeded offline execution model rather than a live deployment; accordingly, the primary contribution is a reproducible evaluation method and an analysis of routing-policy tradeoffs, not evidence of production effectiveness. We release task generation, policies, traces, tests, and analysis artifacts to support live-system validation.

Agentic systems must decide not only what answer to produce, but which reasoning and execution operations should precede it. A controller may answer directly, decompose a request, retrieve evidence, execute code, delegate to a specialist, or verify an intermediate result. Existing routing work largely selects model endpoints, retrieval depth, or tools in isolation. We introduce an executable benchmark and a budget-aware meta-router that composes heterogeneous operations from raw task text. The benchmark contains 216 training, 72 development, 108 held-out test, and 108 locked lexical-shift challenge tasks across data analysis, frozen-corpus research, and document processing. Outcomes are machine checked after operations execute. Independent regularized logistic heads predict operation probabilities from word and character features, are temperature-scaled on development data, and are greedily composed under route-cost and action-count budgets. On the held-out test, the learned policy achieves 100% success versus 93.5% for strong static and fixed workflows, with 43% lower cost than the static policy; a matched learned one-shot router reaches 56.5%. On the untouched challenge split, learned success falls to 75.9% and trails static routing at 93.5%, while remaining 49% cheaper and exceeding one-shot routing by 34.3 points. The gap identifies lexical generalization, rather than route execution, as the principal limitation. These results establish a reproducible testbed and a bounded proof of concept, not evidence of live-LLM performance.

Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.

Vision-language-action (VLA) models have advanced generalist robotic manipulation, yet real-world deployment reveals a fundamental challenge: robots are equipped with diverse and heterogeneous sensor configurations, auxiliary sensors can fail unexpectedly during operation, and different robot embodiments often lack certain sensors by design. A unified policy that can exploit auxiliary perceptual inputs when available while remaining reliable under sensor absence, whether incidental or by design, is therefore essential for practical deployment. However, existing VLA policies couple action generation to a fixed sensor set through shared dense computation, making them brittle when sensors are missing and limiting their ability to specialize across diverse tasks and long-horizon behaviors. We propose CoRE-VLA, a scalable and robust VLA framework that formulates action generation as context-conditioned sparse computation. Sensor availability gates modality-specialized experts, enabling graceful degradation under missing sensors without retraining. Task intent further routes action-side representations to task-relevant experts, improving specialization across diverse tasks and long-horizon subgoals. While the framework is designed to accommodate different auxiliary sensors, we focus on depth as a representative and practically important auxiliary modality in our experiments. Experiments on LIBERO, RoboCasa GR1 Tabletop, and real-world dual-arm manipulation show that CoRE-VLA achieves strong results on long-horizon and multi-task benchmarks, and outperforms both a dense-action-generator ablation and a strong pretrained VLA baseline, including in zero-shot generalization to unseen scenarios. Modality analysis shows that CoRE-VLA can exploit auxiliary depth when available while remaining robust when depth is unavailable during deployment.

Long-context inference in modern LLMs is increasingly constrained by decoding efficiency, especially in reasoning-heavy settings where models generate long intermediate chains of thought. Existing sparse attention methods often face a practical efficiency-quality trade-off. Structured block sparse methods typically provide stronger acceleration but incur noticeable quality loss, while token sparse methods are usually more accurate yet deliver limited end-to-end speedup because top-k routing over the full cache remains expensive. In this work, we propose cross-layer sparse attention (CLSA), which is built on top of KV-sharing architectures such as YOCO. The core idea is to share not only the KV cache across cross-decoder layers, but also the routing index. A single indexer computes token-level top-k selection once and reuses the resulting index across layers, thereby preserving the fine-grained selectivity of token sparse attention while amortizing the routing overhead. The resulting architecture improves all major inference bottlenecks jointly, including pre-filling, KV-cache storage, and long-context decoding. Experiments across short-context and long-context benchmarks show that CLSA is both accurate and efficient, achieving up to 7.6x decoding speedup and 17.1x overall throughput improvement at 128K context. These results suggest a more complete architectural solution for long-context LLMs that jointly advances model quality and inference efficiency.

Modern retrieval-augmented generation(RAG) deployments increasingly rely on caching to reduce token cost and time-to-first-token(TTFT). Prefix-level KV reuse is now standard in serving stacks such as vLLM, and chunk-level and position-independent reuse have been pushed further by recent systems(RAGCache, TurboRAG, CacheBlend, EPIC, ContextPilot, PCR, LMCache). Output-level semantic answer caches, by contrast, remain fragile: similar prompts can map to different correct answers, retrieved evidence drifts as the corpus is updated, and adversarial collision attacks have been shown to hijack cached responses. We argue that the right framing for cached answer reuse is not how to reuse faster but when reuse is safe. We propose GroundedCache, an evidence-validated cache router that admits a cached answer only when 4 cheap gates simultaneously hold: query similarity, retrieved-evidence overlap, source-version validity, and lexical (or judge-based) support of the cached answer by the freshly retrieved evidence. We build a six-regime workload that stress-tests cache safety rather than only hit rate, and introduce an operator-facing metric, the unsafe-served rate (USR), fraction of all queries that received a wrong cached answer. Across 2 datasets and 12,000 real-LLM generations(Qwen2.5-7B-Instruct on vLLM with Automatic Prefix Caching), GroundedCache drives USR to 0.0% on every HotpotQA regime(vs. 15-35% under naive caching) and to 1.5% on mtRAG document drift(vs. 51.5%), a 34x reduction on the design-point adversarial regime and 3-10x reductions across the other mtRAG regimes, while end-to-end p50 latency stays within 1.04-1.07x of a no-cache RAG baseline. A per-gate ablation isolates the lexical support gate as the load-bearing safety mechanism on both datasets, with the remaining gates providing defense-in-depth at near-zero cost. We release the implementation, workload, and evaluation harness.

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.

Class-incremental learning (CIL) requires models to learn new classes sequentially while preserving prior knowledge. Recently, approaches that combine pre-trained models with mixture-of-experts (MoE) have received increasing attention in CIL: they typically expand experts during learning and employ a router to assign weights across experts. However, existing MoE methods often overlook routing drift induced by expert expansion. Once new experts are introduced, the router may reassign samples from earlier classes to newly added experts, thereby perturbing previously established expert compositions and causing interference even when old experts remain frozen. We argue that expandable MoE in CIL requires two complementary properties: stable old-class routing for knowledge preservation and sufficient capacity utilization for new-class adaptation. To this end, we propose Stable Routing for MoE (StaR-MoE), a routing-level framework for expandable MoE in CIL. By incorporating sensitivity-aware routing alignment, StaR-MoE aligns current old-class routing behavior with historical routing distributions through sensitivity-guided constraints. Complementarily, StaR-MoE introduces asymmetric capacity regularization to encourage effective utilization of the expanded expert pool without compromising class-specific routing specialization. Extensive experiments across four standard CIL benchmarks demonstrate that StaR-MoE consistently improves both average and last accuracy over state-of-the-art methods, highlighting the importance of stable routing.

Multi-agent large language model (LLM) systems often rely on a controller to coordinate a pool of heterogeneous models, yet existing controllers are typically limited to one-shot routing: they select a model once and return its output directly. Such routing-only designs provide no mechanism to critique intermediate drafts or support iterative refinement. To address this limitation, we propose a critique-and-routing controller that casts multi-agent coordination as a sequential decision problem. At each turn, the controller evaluates the current draft, decides whether to stop or continue, and, if needed, selects the next agent for further refinement. We formulate this process as a finite-horizon Markov Decision Process (MDP) with explicit agent-utilization constraints, design a composite reward for controller decisions across turns, and optimize the controller via policy gradients under a Lagrangian-relaxed objective. Extensive experiments across multiple heterogeneous multi-agent systems and seven reasoning benchmarks show that our method consistently outperforms state-of-the-art baselines and substantially narrows the gap to the strongest agent, while using it for fewer than 25% of total calls.

Coarse-mask local image editing asks a model to modify a user-indicated region while preserving the surrounding scene. In practice, however, rough masks often become unintended shape priors: instead of serving as flexible edit support, the mask can pull the generated object toward its accidental boundary. We study this failure as mask-shape bias and frame the task through a Two-Zone Constraint, where the background should remain stable while the editable region should follow the instruction without being forced to inherit the mask contour. BRIDGE addresses this setting by keeping masks outside the DiT backbone for support construction and blending, avoiding DiT-internal mask injection and copied control branches. It uses BridgePath generation, where a Main Path preserves background context and a Subject Path generates editable content from independent noise. Motivated by a diagnostic Qwen-Image experiment showing that positional embeddings and attention connectivity regulate which image context visual tokens reuse, BRIDGE introduces a learnable Discrete Geometric Gate for token-level positional-embedding routing. This gate lets subject tokens borrow background-anchored coordinates near fusion regions or keep subject-centric coordinates for geometric freedom. We evaluate BRIDGE on BRIDGE-Bench, MagicBrush, and ICE-Bench. On BRIDGE-Bench, BRIDGE improves Local SigLIP2-T from 0.262 with FLUX.1-Fill and 0.390 with ACE++ to 0.503, with parallel gains in local DINO and DreamSim. Zero-shot results on MagicBrush and ICE-Bench further indicate competitive alignment and source preservation beyond the curated benchmark, while the added routing module remains compact at 13.31M parameters compared with ControlNet-style copied branches.

A key strategy for balancing performance and cost in modern machine learning systems is to dynamically route queries to either a low-cost model or a more expensive oracle (such as a large pretrained model or human expert), an approach known as model routing. In this work we present a new uncertainty-aware router that (1) avoids unnecessary oracle calls on inherently ambiguous queries, and (2) adapts dynamically to different loss functions and cost parameters through simple hyperparameter changes, without retraining. Our method, applicable to any classification setting where multiple independent annotations per input are available, is based on decomposing total uncertainty into irreducible and reducible components using higher-order predictors [Ahdritz et al., 2025]. This enables a unified approach to both routing and abstention: predict with the weak model when uncertainty is low, route to the oracle when reducible uncertainty is high, and abstain when irreducible uncertainty is high. Our router comes with strong theoretical guarantees bounding regret relative to optimal task-specific routers. We conduct experiments on both synthetic and real-world datasets that demonstrate the benefits of our approach in suitable regimes -- in particular, whenever reducible and irreducible uncertainty are not too correlated.

Prompt-based interventions can change model behavior, but trained success alone does not identify where the behaviorally relevant state is represented. We study this question in controlled routing tasks using interfaces chosen on support data, held-out query evaluation, and matched necessity, sufficiency, and wrong-interface controls. On GPT-2 triop, an early interface supports exact transfer under these tests. On GPT-2 add/sub, zero-retrain compiled transfer at the fixed interface recovers most of donor routing accuracy, while trainable prompt slots can relearn the same behavior at several other positions only after additional support examples and optimization. These results distinguish fixed-interface reuse from prompt relocation in a setting where the two can be tested directly. Qwen routing provides a cross-architecture consistency check for the same matched-interface pattern at the operator token, although donor-specific identity on the local V-path remains unresolved. Generation and reasoning branches are used to map scope: they show broader transport or weaker controller identifiability once control depends on longer trajectories or harder selection. In controlled routing, fixed-interface transfer is therefore stronger evidence of reuse than trained prompt success alone.