NeurIPS 2026 Papers

Conference on Neural Information Processing Systems

Decision breakdown

6,437papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    991.5%
  • Spotlight
    2403.7%
  • Poster
    6,09894.7%

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Position: A Safe LLM and a Safe Harness Do Not Make a Safe Agent

Vincent Siu, Kyle Montgomery, Yujin Potter, Zhun Wang, Dawn Song, Chenguang Wang

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AI agents combine a learned neural component, such as a language model, with symbolic components, such as memory, tools, and environments. Existing safety alignment work improves both sides independently: neural alignment reduces unsafe model behavior, while symbolic alignment constrains memory, tool use, permissions, and action. This position paper argues that safe neural and symbolic components do not necessarily compose into a safe agent. Agent safety is often contextual: whether an answer, retrieval, or tool call is safe can depend on broader safety context, e.g., prior interactions, provenance, user boundaries, and authorization. For example, a biosafety AI research assistant might answer separate, benign-looking questions about viral delivery systems, protocol troubleshooting, and relevant literature, while the accumulated interaction begins to support the design of a dangerous pathogen. We propose contextual agent alignment as a research agenda for identifying safety-relevant context, designing safer agents that use this context, and evaluating contextual safety. Several documented agent safety failures, including cumulative dual-use risk in research assistants, peer-preservation in oversight settings, and contextual privacy violations, can be viewed as instances of contextual safety failure. This agenda is important for the broader AI safety community because frontier systems are increasingly deployed as agents in real-world settings.

Poster
Policy-Level Exploration for Coordinated Multi-Agent Reinforcement Learning

Yucong Zhang, Chao Yu

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In multi-agent reinforcement learning (MARL), agents must not only discover high-reward behaviours but also reliably reproduce coordinated behaviours over time. A fundamental challenge arises from a mismatch between action-level stochastic exploration and temporally extended coordination. To address this issue, we propose a policy-level exploration framework with Deterministic Action Execution (DAE) for MARL, which shifts locally random action exploration to temporally extended policy selection via an option-based exploration mechanism. Specifically, at each time step, each agent selects a policy from a shared policy set\textemdash comprising one exploitation policy and multiple exploration policies\textemdash using a learned option policy, and actions are executed deterministically conditioned on the selected policy. By maintaining deterministic execution under temporally extended policy selection, DAE facilitates temporally coordinated behaviours across multiple time steps. Comprehensive experiments on four multi-agent tasks\textemdash Predator Prey, StarCraft II micro management challenge (SMAC), SMACv2, Google Research Football, and Multi-Agent Coordination benchmark (MACO)\textemdash demonstrate that DAE outperforms mainstream baselines, achieving superior sample efficiency and final learning performance.

Poster
Policy Regret Minimization in Partially Observable Markov Games

Lan Sang, Raman Arora, Thanh Nguyen-Tang

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We study policy regret minimization in partially observable Markov games (POMGs) between a learner and a strategic adaptive adversary who adapts to the learner's past strategies. We develop a model-based optimistic framework that operates on the learner-observable process using *joint* MLE confidence set and introduce an Observable Operator Model-based causal decomposition that disentangles the coupling between the world and the adversary model. Under multi-step weakly revealing observations and a bounded-memory, stationary and posterior-lipschitz adversary and planner stability, we prove an $\mathcal{O}(\sqrt{T})$ policy regret bound. This work advances regret analysis from Markov games to POMGs and provides the first policy regret guarantee under imperfect information against an adaptive opponent.

Poster
Playing Markov Games Without Observing Payoffs

Daniel Ablin, Alon Peled-Cohen

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Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated symmetric two-player matrix games without observing payoffs, as long as the opponent’s actions are observed. Extending this capability to the Markovian setting remains an open problem. In this paper, we introduce and formalize a new class of zero-sum symmetric Markov games, which extends the notion of symmetry from matrix games to the Markovian setting. We prove that a learner observing only the opponent's action sequence, without access to payoff information can successfully compete against an adversary possessing complete knowledge of the game. We formalize three distinct notions of symmetry in this domain and reveal a surprising structural hierarchy: the most holistic definitions of symmetry impose restrictive constraints that actually simplify the learning landscape, whereas the ``simplest'' definition represents the most general and challenging setting. We provide polynomial-time algorithms for all three settings that achieve sublinear regret. Crucially, we demonstrate that despite the complex Markovian dynamics, a simple strategy of locally mimicking the opponent's actions suffices to guarantee robustness. This finding significantly broadens the class of games where robust learning is possible under severe informational disadvantage, proving that knowledge of the transition laws is not required to force a draw.

Poster
PithTrain: A Compact and Agent-Native MoE Training System

Ruihang Lai, Hao Kang, Haozhan Tang, Akaash Raghunathan Parthasarathy, Zichun Yu, Junru Shao, Todd Mowry, Chenyan Xiong, Tianqi Chen

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Mixture-of-Experts (MoE) has become the dominant architecture for frontier language models. To meet this demand, production frameworks have built optimized MoE training stacks over years of engineering effort. Yet evolving these stacks for new architectures and system optimizations remains expensive. With the rise of AI coding agents, they could automate parts of training-framework development and accelerate this evolution. But applying them to these existing frameworks carries hidden costs, invisible to today's throughput-only evaluations. We name this missing dimension agent-task efficiency (ATE): the cost of using coding agents to understand, operate, and extend a framework. Grounded in four agent-native design principles, we build PithTrain, a compact, agent-native MoE training framework. We further introduce ATE-Bench, covering real-world training-framework tasks. Our evaluation shows PithTrain matches the throughput of production frameworks, and on ATE-Bench, PithTrain enables higher agent-task efficiency, with up to 62% fewer Agent Turns and 64% less Active GPU Time.

Poster
Physical AI Smart Spaces: A Large-Scale Benchmark for Multi-Camera 3D Perception in Smart Spaces

Yuxing Wang, Yizhou Wang, Anqi Li, Shuo Wang, Sameer Satish Pusegaonkar, Haoquan Liang, Jiajun Li, Shenxin Jiang, Jianhe Yuan, Shangru Li, Tongwei Dai, Zihao Chen, David Anastasiu, Zheng (Thomas) Tang, Sujit Biswas, Xunlei Wu

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Physical AI Smart Spaces is, to the best of our knowledge, the first benchmark to simultaneously provide large-scale, multi-class, and multi-camera 3D perception data for indoor smart spaces. It contains over 280 hours of synchronized 1080p footage captured by nearly 1,800 cameras in warehouses, hospitals, retail venues, and similar settings, together with automatic annotations for multi-camera identities, 2D bounding boxes, 3D bounding boxes, camera calibration, and depth where available. The benchmark spans Isaac Sim synthetic generation, Cosmos Transfer appearance augmentation, and real-world Sim2Real evaluation. For the real-world target, we include two warehouse deployments with time-synchronized streams, automatic VGGT-based calibration, and a 3D labeling interface that projects world-frame 3D boxes into each view for cross-camera verification. We describe the dataset scope, annotation and calibration schema, generation workflow, benchmark protocols, and official evaluation system, which standardizes submission format, and leaderboard reporting. A central contribution is a 3D instantiation of Higher Order Tracking Accuracy (HOTA), extending the usual 2D box-based tracking evaluation to 3D locations and 3D boxes. We further report empirical baselines from the AI City Challenge leaderboards, showing how methods evolve from person-only 3D location tracking to multi-class 3D box tracking under realistic smart-space constraints. The release is available at https://huggingface.co/datasets/nvidia/PhysicalAI-SmartSpaces.

Poster
PhyMo: Learning Physical Dynamics with Accurate and Continuous Motion from Multi-View Videos

Shangjia Liu, Jinxi Li, Siyuan Zhou, Bo Yang, Bing Wang

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Recovering dynamic 3D scene geometry, appearance, and the physical motion states that govern scene evolution from multi-view videos is important yet challenging. A key difficulty is that appearance can be deceptive. When trained primarily with rendering supervision, existing methods may fit the observed appearance well by exploiting appearance shortcuts, rather than recovering the true evolving geometry and motion. This issue is especially severe in scenes with fast or locally complex motion, where inaccurate trajectories can still produce plausible images over the observed frames, but lead to unreliable reconstruction and discontinuous future prediction. In this paper, we propose PhyMo, a framework for learning evolving dynamics from multi-view videos. We introduce a Motion-Aware Trajectory Representation that drives the model to recover accurate motion from deformation, rather than relying on appearance shortcuts to explain observed motion. On top of this, we propose a Continuous Motion Evolution module with bidirectional kinematic continuity constraint to promote temporally consistent evolution of displacement, velocity, and acceleration. Together, these designs yield geometrically faithful interpolation and continuous motion extrapolation. Experiments on four dynamic scene benchmarks demonstrate state-of-the-art performance.

Poster
Permutation Sensitivity in t-SVD-based Multi-view Clustering

Jintian Ji, Yanjun Zhang, He Zhang, Leo Yu Zhang, Cong Wang, Shirui Pan

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Tensor Singular Value Decomposition (t-SVD) has achieved strong empirical performance in multi-view clustering (MVC) and its incomplete setting (IMVC). However, the success of this framework heavily relies on the implicit dependency of its Fourier transform on the sample sequence, which raises serious concerns regarding sample-permutation sensitivity. To address this issue, we first formulate the permutation sensitivity in multi-view clustering by providing rigorous definitions of invariance at both the outcome level and the representation level. Secondly, by revealing the potential structural risks associated with the fixed Fourier basis, we propose two plug-and-play strategies: (1) an Order-Restoration strategy (K-OR), designed to reconstruct a locally smooth signal favored by the Fourier transform; and (2) an equivariant t-SVD framework (Cor-SVD), which fundamentally resolves the sensitivity of the Fourier transform by replacing fixed bases with data-dependent, equivariant transforms. Finally, we design a controlled permutation evaluation protocol to verify the robustness of tensorial clustering models. Extensive experiments demonstrate the significant performance variability of existing t-SVD-based methods under sample permutations, whereas our approaches substantially improve their permutation robustness while maintaining competitive clustering performance. These findings reveal critical vulnerabilities in current tensorial clustering benchmarks and underscore the necessity of the proposed method for achieving robust performance and reliable evaluation.

Poster
PREPING: Building Agent Memory without Tasks

Yumin Choi, Sangwoo Park, Minki Kang, Jinheon Baek, Sung Ju Hwang

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Agent memory is typically constructed either offline from curated demonstrations or online from post-deployment interactions. However, regardless of how it is built, an agent faces a cold-start gap when first introduced to a new environment without any task-specific experience available. In this paper, we study pre-task memory construction: whether an agent can build procedural memory before observing any target-environment tasks, using only self-generated synthetic practice. Yet, synthetic interaction alone is insufficient, as without controlling what to practice and what to store, synthetic tasks become redundant, infeasible, and ultimately uninformative, and memory further degrades quickly due to unfiltered trajectories. To overcome this, we present Preping, a proposer-guided memory construction framework. At its core is proposer memory, a structured control state that shapes future practice. A Proposer generates synthetic tasks conditioned on this state, a Solver executes them, and a Validator determines which trajectories are eligible for memory insertion while also providing feedback to guide future proposals. Experiments on AppWorld, BFCL v3, and MCP-Universe show that Preping substantially improves over a no-memory baseline and achieves performance competitive with strong playbook-based methods built from offline or online experience, with deployment cost $2.99\times$ lower on AppWorld and $2.23\times$ lower on BFCL v3 than online memory construction. Further analyses reveal that the main benefit does not come from synthetic volume alone, but from proposer-side control over feasibility, redundancy, and coverage, combined with selective memory updates.

Poster
PLATO: Pointer Learner for Agent and Task Openness

Alireza Saleh Abadi, Leen-Kiat Soh, Daniel A Redder, Adam Eck, Prashant Doshi

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Open agent systems (OASYS) are increasingly prevalent in real-world domains where the sets of agents and tasks change unpredictably over time. Such openness, including agent openness (AO) and task openness (TO), poses a fundamental challenge to multi-agent reinforcement learning (MARL), which typically assumes fixed state and action spaces. Existing methods address openness only partially: padding and masking approaches introduce artificial bounds, while recent graph-based or hypergraph methods handle one dimension of openness but still depend on restrictive assumptions. In this paper, we introduce Pointer Learner for Agent and Task Openness (PLATO), a pointer-network-based actor combined with a centralized graph neural network (GNN) critic, trained with multi-agent proximal policy optimization under a centralized training and decentralized execution paradigm. Our pointer-based actor outputs distributions directly over the current task set. This directly supports changing action spaces without masking or retraining. Our GNN critic encodes agent–task interactions as a graph that changes shape with task and agent composition. Together, these components consider AO and TO without the boundedness of existing approaches. We formalize PLATO in a Task-and-Agent-Open Markov Game (TaAgO-MG), extending prior task-open formulations, and prove it is well-defined over the resulting unbounded state and action spaces. We evaluate PLATO with the Methods for Open Agent Systems Evaluation Initiative (MOASEI) wildfire suppression domain, an environment designed for open multi-agent system evaluation, and we demonstrate strong performance and more consistent zero-shot generalization than state-of-the-art baselines in OASYS.

Poster
PHOEBI: An Open-World Benchmark for Multi-Label Bacterial Identification in Phase-Contrast Microscopy

Aaditya Baranwal, Md Jahid Hasan, Shruti Vyas

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Optical microscopy lets us watch living bacteria in real time without stains or labels, and it remains the standard instrument for identifying species across clinical, environmental and industrial microbiology. Yet real samples rarely hold a single species. They arrive as mixtures and sometimes carry an organism no model has ever seen. What happens when a model trained on familiar mixtures meets one it has never encountered? No benchmark has asked this of phase-contrast images, so we built one. **PHOEBI** brings together 120,000 phase-contrast images of 40 mixtures of six bacterial species that we cultured and imaged ourselves, and it holds whole mixtures out of training so that every test is a combination the model has never seen. The answer is sobering. Classifiers that are nearly perfect on the mixtures they know collapse on new ones, and no choice of backbone or pretraining rescues them. The features turn out to be sound and the failure lies in how the evidence within each image is pooled. A culture looks the same everywhere, and decoders built on this simple fact hold steady where large networks fail even though one of them is never trained by gradient descent. The same features go further still. They notice when a species outside the catalogue appears, and the simplest way of giving it a class of its own proves the most effective while leaving the known species almost untouched. PHOEBI turns the mixed culture, the everyday case at the bench, into a measurable target for open-world recognition.

Poster
PAIR: Prefix-Aware Internal Reward Model for Multi-Turn Agent Optimization

Wonjoong Kim, Yeonjun In, Sangwu Park, Dongha Lee, Chanyoung Park

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A significant hurdle for current LLMs is the execution of complex, multi-stage tasks. Group Relative Policy Optimization (GRPO) has been emerging as a leading choice, but its reliance on sparse outcome rewards severely limits credit assignment across intermediate steps. Existing remedies—running full rollouts to assign step-level advantages, calling external LLM judges at each step, or computing intrinsic rewards that require ground-truth answers at every evaluation—introduce significant costs or practical constraints. We hypothesize that internal correctness probing over LLM hidden states can be repurposed as a step-level reward signal, potentially addressing all of these limitations at once. However, existing probing research assumes clean inputs, and we first show that this assumption breaks down in multi-step settings: hidden-state probes degrade severely under prefix contamination—tracking coherence with the (possibly corrupted) prefix rather than grounded correctness—while attention-based features remain robust to contamination but underperform on clean prefixes. Building on this complementary relationship, we propose the Prefix-Aware Internal Reward (PAIR)—a two-stage model with a frozen hidden-state probe estimating belief-consistency and a lightweight attention-based head correcting it toward grounded correctness. Experimental results show that PAIR achieves the highest AUROC on contaminated trajectories while operating at negligible inference cost, enabling dense step-level reward signals for GRPO training without external model calls, ground-truth dependencies, or full-trajectory rollouts.

Poster
PAI-Actor: Cinematic Multi-Actor Character Replacement in Dynamic Scenes

Heyuan Gao, Bangxun Tang, Yiren Song, Guian Fang, Zijian He, Jie Yang, Mike Zheng Shou

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We present PAI-Actor, a cinematic multi-character animation framework for character replacement in dynamic movie scenes. Unlike conventional animation systems that mainly drive a single static image or a single subject, our goal is to replace and animate multiple characters within real video clips while preserving the original scene dynamics, camera motion, and background content. This setting is particularly challenging because the generated characters must remain consistent with the source performance in motion and interaction, while also matching the surrounding background in lighting, shadow, composition, and overall cinematic appearance. To address this, we formulate multi-character animation as a structure-guided human recovery problem and build a movie-driven training pipeline from high-quality film data. Furthermore, to support practical cinematic production, we introduce a bidirectional-to-autoregressive distillation framework: we first train a bidirectional diffusion transformer for high-quality short-clip generation at 1080P resolution, and then distill it into an autoregressive video-to-video model for efficient inference and longer video generation. Experiments show that PAI-Actor enables high-fidelity multi-character animation with strong scene consistency, cinematic visual quality, and efficient long-form generation.

Poster
Overcoming Attention Distraction: Training-Free Latent Communication for Multi-Agent Systems

Zhengjie Zhou, Yahao Liu, Ziyue Feng, Tengfei Liu, Weiqiang Wang

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Scaling multi-agent systems driven by large language models is transitioning from lossy text-based communication to continuous latent interaction. However, existing latent interaction approaches relying on concatenation-based Softmax cross-attention suffer from an Attention Distraction Dilemma: due to the inherent anisotropy of latent spaces and the semantic misalignment induced by agent role heterogeneity, non-linear Softmax structurally amplifies irrelevant tokens, diluting the collaborative signal as interactions deepen. To address this issue, we propose a training-free additive mechanism that models upstream representations as a semantic manifold. By shifting from concatenation-based Softmax competition to linear subspace projection, this perspective inherently bypasses scalar noise accumulation. Specifically, we introduce two components: a Resonance Filter that extracts principal semantic directional alignments to overcome latent anisotropy, and an SNR-Adaptive Spectral Gain that dynamically regulates this projection to counteract role heterogeneity. We analyze this approach using the Asymptotic SNR Tipping Point Theorem, illustrating the scaling advantages of the mechanism beyond a critical noise threshold. Experiments indicate that the proposed approach outperforms baselines in 46 of 54 evaluated configurations, maintaining semantic reasoning in long-context collaborations.

Poster
Outlier-Robust Multi-Output Gaussian Processes

Joshua Rooijakkers, Leiv Rønneberg, Francois-Xavier Briol, Jeremias Knoblauch, Matias Altamirano

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Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes (GPs), MOGPs are sensitive to model misspecification and outliers, which can distort predictions within individual outputs. In the multi-output case, this situation can be further exacerbated as anomalous observations in one response can adversely influence predictions for other correlated outputs. To handle this situation, we propose R-MOGP—an MOGP that is provably robust to outliers in any individual response. Our approach preserves conjugacy, achieving robustness without sacrificing computational efficiency. Empirically, we show that R-MOGP achieves performance comparable to existing state-of-the-art robust MOGPs at a fraction of their computational costs.

Poster
Outbidding and Outbluffing Elite Humans: Mastering Liar’s Poker via Self-Play and Reinforcement Learning

Richard Dewey, Janos Botyanszki, Ciamac C. Moallemi, Andrew Zheng

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AI researchers have long focused on poker-like games as a testbed for environments characterized by multi-player dynamics, imperfect information, and reasoning under uncertainty. While recent breakthroughs have matched elite human play at no-limit Texas hold'em, the multi-player dynamics are subdued: most hands converge quickly with only two players engaged through multiple rounds of bidding. In this paper, we present Solly, the first AI agent to achieve elite human play in reduced-format Liar’s Poker, a game characterized by extensive multi-player engagement. We trained Solly using self-play with Regularized Nash Dynamics (R-NaD), a model-free, actor-critic, deep reinforcement learning algorithm, and we successfully extend R-NaD to the multi-player scenario for the first time. Solly played at an elite human level as measured by win rate (won over 50\% of hands) and equity (money won) in heads-up and multi-player Liar’s Poker. Solly also outperformed large language models (LLMs), including those with reasoning abilities, on the same metrics. Solly developed novel bidding strategies, randomized play effectively, and was not easily exploitable by world-class human players.

Poster
OrchestraRL: Learning to Orchestrate LLM Agent Swarms with Entropy-Aware Communication Control

Runze Fan, Shiyi Jiang, Junsheng Wang, Shuangjun Xie, Xiaodan Li, Yong Li

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Multi-agent LLM systems built on frontier backbones often fail to improve reliably as the swarm grows: under strong backbone models, performance frequently plateaus or declines beyond a small number of agents. In a budget-matched controlled intervention on SWE-bench Verified ($N{=}8$, Claude Opus 4.5 backbone, 64-call budget per instance), varying only the communication policy moves resolve rate from 80.4\% under random broadcast coordination (below the 80.9\% single-shot baseline) to 85.5\% under a learned orchestrator, a 5.1-point spread under matched compute. We introduce OrchestraRL, an orchestration layer trained over frozen LLMs. A centralized Macro-Orchestrator reads the swarm's context entropy $H(t)$, computed from the spread of agent output embeddings, and outputs communication mode (via learned entropy thresholds) and topology; per-agent Micro-Coordinators decide whom each agent addresses, when to speak, and at what granularity. Both are trained with REINFORCE and a learned value baseline. Across four benchmarks (SWE-bench Verified, GPQA Diamond, LiveCodeBench v6, SimpleQA), OrchestraRL is comparable to the strongest baseline at $N{=}2$ and achieves the best resolve rate at $N \in \{4, 8\}$ on every benchmark, with the gap widening as $N$ grows. The learned policy recovers interpretable task-dependent communication patterns, including clustered exploration, star-based synthesis, and pipeline reasoning, without these structures being hand-coded.

Poster
Optimizing Agent Tool-Use via Trajectory-based Insight Evolution

Hanchen Qiu, Haojia Zhu, Yifan Meng, Jiahui Jin

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Tool documentation is the critical interface bridging Large Language Model (LLM) agents and external environments. However, real-world documentation is often ambiguous or insufficient, leading to misaligned tool calls and task failures. While existing methods rely on parameter-efficient tuning or reinforcement learning to enhance tool-use capabilities, they incur substantial computational overhead and lack the agility to adapt to frequently updated toolkits. We propose OpTool , an evolutionary framework that treats tool documentation as an evolvable configuration. OpTool consists of three stages: (1) Contrastive Trajectory Generation, which explores diverse tool-use trajectories via contrastive beam search; (2) Trajectory-based Insight Extraction, which extracts tool-use insights through retrospective global credit assignment; and (3) Tool Documentation Evolution, which iteratively refines the documentation to mitigate information insufficiency. Experimental results across multiple domains demonstrate that OpTool significantly improves tool call accuracy and task success rates, providing a robust solution for tool-based LLM agents.

Poster
Optimize Once, Execute Fast: Latency-Aware Multi-Agent Workflow Learning for Recurrent Queries

Enpei Zhang, Feiyu Qu, Zheng Huang, Dawei Zhou, Elynn Chen, Yujun Yan

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Large Language Model-based Multi-Agent Systems (LLM-based MAS) have shown remarkable success in solving complex tasks by coordinating specialized agents through multi-step workflows. To overcome the high cost and specificity of manually designed workflows, recent research has shifted toward learning them automatically. However, a key limitation remains: while agent calls introduce significant latency due to model inference time and service congestion, most automated methods optimize solely for downstream performance, ignoring execution time (makespan). This issue is amplified when workflows are reused across recurring queries, making latency accumulate over time. This limits deployment in recurrent applications such as AI customer support and AI cloud troubleshooting, where users expect fast responses. To bridge this gap, we introduce a new problem, termed latency-aware workflow generation, where the objective is to minimize workflow makespan while aiming to retain downstream performance. We propose LAWA (Latency-Aware Workflow optimizAtion), a novel framework that reduces makespan via theoretically grounded graph edits targeting critical-path bottlenecks. By unifying a graph generator with this graph-editing procedure, LAWA supports both de novo workflow generation and refinement of existing ones. Empirical results across seven benchmarks demonstrate that LAWA significantly reduces makespan while achieving competitive task performance, supporting efficient reuse of multi-agent workflows for recurrent queries.

Poster
Optimal scaling laws in learning hierarchical multi-index models

Leonardo Defilippis, Florent Krzakala, Bruno Loureiro, Antoine Maillard

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In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited regime. We derive exact information-theoretic scaling laws for subspace recovery and prediction error, revealing how the hierarchical features of the target are sequentially learned through a cascade of phase transitions. We further show that these optimal rates are achieved by a simple, target-agnostic spectral estimator, which can be interpreted as the small learning-rate limit of gradient descent on the first-layer weights. Once an adapted representation is identified, the readout can be learned statistically optimally, using an efficient procedure. As a consequence, we provide a unified and rigorous explanation of scaling laws, plateau phenomena, and spectral structure in shallow neural networks trained on such hierarchical targets.

Poster