ICLR 2026 Papers

International Conference on Learning Representations

Decision breakdown

5,358papers

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

  • Oral
    2244.2%
  • Poster
    5,13495.8%

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Measuring Physical-World Privacy Awareness of Large Language Models: An Evaluation Benchmark

Xinjie Shen, Mufei Li, Pan Li

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The deployment of Large Language Models (LLMs) in embodied agents creates an urgent need to measure their privacy awareness in the physical world. Existing evaluation methods, however, are confined to natural language based scenarios. To bridge this gap, we introduce EAPrivacy, a comprehensive evaluation benchmark designed to quantify the physical-world privacy awareness of LLM-powered agents. EAPrivacy utilizes procedurally generated scenarios across four tiers to test an agent's ability to handle sensitive objects, adapt to changing environments, balance task execution with privacy constraints, and resolve conflicts with social norms. Our measurements reveal a critical deficit in current models. The top-performing model, Gemini 2.5 Pro, achieved only 59\% accuracy in scenarios involving changing physical environments. Furthermore, when a task was accompanied by a privacy request, models prioritized completion over the constraint in up to 86\% of cases. In high-stakes situations pitting privacy against critical social norms, leading models like GPT-4o and Claude-3.5-haiku disregarded the social norm over 15\% of the time. These findings, demonstrated by our benchmark, underscore a fundamental misalignment in LLMs regarding physically grounded privacy and establish the need for more robust, physically-aware alignment. Datasets are available at https://github.com/Graph-COM/EAPrivacy

Poster
Causal Imitation Learning under Expert-Observable and Expert-Unobservable Confounding

Daqian Shao, Thomas Kleine Buening, Marta Kwiatkowska

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We propose a general framework for causal Imitation Learning (IL) with hidden confounders, which subsumes several existing settings. Our framework accounts for two types of hidden confounders: (a) variables observed by the expert but not by the imitator, and (b) confounding noise hidden from both. By leveraging trajectory histories as instruments, we reformulate causal IL in our framework into a Conditional Moment Restriction (CMR) problem. We propose DML-IL, an algorithm that solves this CMR problem via instrumental variable regression, and upper bound its imitation gap. Empirical evaluation on continuous state-action environments, including Mujoco tasks, demonstrates that DML-IL outperforms existing causal IL baselines.

Poster
Improved Object-Centric Diffusion Learning with Registers and Contrastive Alignment

Bac Nguyen, Yuhta Takida, Naoki Murata, Chieh-Hsin Lai, Toshimitsu Uesaka, Stefano Ermon, Yuki Mitsufuji

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Slot Attention (SA) with pretrained diffusion models has recently shown promise for object-centric learning (OCL), but suffers from slot entanglement and weak alignment between object slots and image content. We propose Contrastive Object-centric Diffusion Alignment (CODA), a simple extension that (i) employs register slots to absorb residual attention and reduce interference between object slots, and (ii) applies a contrastive alignment loss to explicitly encourage slot–image correspondence. The resulting training objective serves as a tractable surrogate for maximizing mutual information (MI) between slots and inputs, strengthening slot representation quality. On both synthetic (MOVi-C/E) and real-world datasets (VOC, COCO), CODA improves object discovery (e.g., +6.1% FG-ARI on COCO), property prediction, and compositional image generation over strong baselines. Register slots add negligible overhead, keeping CODA efficient and scalable. These results indicate potential applications of CODA as an effective framework for robust OCL in complex, real-world scenes. Code and pretrained models are available at https://github.com/sony/coda.

Poster
Prompt and Parameter Co-Optimization for Large Language Models

Xiaohe Bo, Rui Li, Zexu Sun, Quanyu Dai, Zeyu Zhang, Zihang Tian, Xu Chen, Zhenhua Dong

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Prompt optimization and fine-tuning are two major approaches to improve the performance of Large Language Models (LLMs). They enhance the capabilities of LLMs from complementary perspectives: the former through explicit natural language, and the latter through implicit parameter updates. However, prior work has typically studied them in isolation, leaving their synergistic potential largely underexplored. To bridge this gap, in this paper, we introduce MetaTuner, a novel framework that jointly integrates prompt optimization and fine-tuning for LLM training. Specifically, we introduce two neural networks to generate prompts and parameters, respectively, while allowing them to share a common bottom encoding layer to enable knowledge sharing. By the guidance of the final supervised signals, our framework is optimized to discover the optimal combinations between the prompts and parameters. Given that prompt learning involves discrete optimization while fine-tuning operates in a continuous parameter space, we design a supervised regularization loss to train our framework effectively. Extensive experiments across diverse benchmarks show that our method consistently outperforms the baselines. To benefit the research community, we have released our project at https://anonymous.4open.science/r/metatuner.

Poster
DP-Fusion: Token-Level Differentially Private Inference for Large Language Models

Rushil Thareja, Preslav Nakov, Praneeth Vepakomma, Nils Lukas

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Large language models (LLMs) do not preserve privacy at inference-time. The LLM's outputs can inadvertently reveal information about the model's context, which presents a privacy challenge when the LLM is augmented via tools or databases containing sensitive information. Existing privacy-preserving methods at inference-time have significant limitations since they (i) lack provable guarantees or (ii) have a poor utility/privacy trade-off. We propose DP-Fusion, a Differentially Private Inference (DPI) mechanism for LLMs that provably bounds the influence a set of tokens in the context can have on the LLM's output. DP-Fusion works as follows: (1) label a subset of sensitive tokens, (2) infer the LLM without any sensitive tokens to obtain a baseline, (3) infer the LLM with the sensitive tokens, and (4) blend distributions so that the final output remains within a bounded distance of the baseline distribution. While this per-token influence bound also mitigates jailbreak-style prompt injection, we focus on document privatization, where the goal is to paraphrase a document containing sensitive tokens, e.g., personally identifiable information, so that no attacker can reliably infer them from the paraphrased document while preserving high text quality. The privacy/utility trade-off is controlled by $\epsilon$, where $\epsilon=0$ hides sensitive tokens entirely, while higher values trade off privacy for improved text quality. We show that our method creates token-level provably privatized documents with substantially improved theoretical and empirical privacy, achieving $6\times$ lower perplexity than related DPI methods.

Poster
ACPBench Hard: Unrestrained Reasoning about Action, Change, and Planning

Harsha Kokel, Michael Katz, Kavitha Srinivas, Shirin Sohrabi

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We introduce ACPBench Hard, a dataset of generative, open-ended questions which LLM models needs to answer in order to plan. Models that perform well on these tasks could in principle be integrated into a planner or be used directly as a policy. We discuss the complexity of these tasks as well as the complexity of validating the correctness of their answers and present validation algorithms for each task. Equipped with these validators, we test the performance of a variety of models on our tasks and find that for most of these tasks, the performance of even the largest models is still subpar. The models do not possess even the most basic capability of identifying which actions can be performed in a given state. No model outperforms any other on our proposed tasks and, with a few exceptions, all tested language models score below 65\%, indicating that even the current frontier language models as well as so-called reasoning models have a long way to go before they can reliably reason about planning.

Poster
Evaluating Text Creativity across Diverse Domains: a Dataset and Large Language Model Evaluator

Qian Cao, Xiting Wang, Yuzhuo Yuan, Yahui Liu, Fang Luo, Ruihua Song

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Creativity evaluation remains a challenging frontier for large language models (LLMs). Current evaluations heavily rely on inefficient and costly human judgments, hindering progress in enhancing machine creativity. While automated methods exist, ranging from psychological testing to heuristic- or prompting-based approaches, they often lack generalizability or alignment with human judgment. To address these issues, in this paper, we propose a novel pairwise-comparison framework for assessing textual creativity, leveraging shared contextual instructions to improve evaluation consistency. We introduce CreataSet, a large-scale dataset with 100K+ human-level and 1M+ synthetic creative instruction-response pairs spanning diverse open-domain tasks. Through training on CreataSet, we develop an LLM-based evaluator named CrEval. CrEval demonstrates remarkable superiority over existing methods in alignment with human judgments. Experimental results underscore the indispensable significance of integrating both human-generated and synthetic data in training highly robust evaluators, and showcase the practical utility of CrEval in boosting the creativity of LLMs. We will release all data, code, and models publicly to support further research.

Poster
ResCP: Reservoir Conformal Prediction for Time Series Forecasting

Roberto Neglia, Andrea Cini, Michael M. Bronstein, Filippo Maria Bianchi

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Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

Poster
Local Linear Attention: An Optimal Interpolation of Linear and Softmax Attention For Test-Time Regression

Yifei Zuo, Yutong Yin, Zhichen Zeng, Ang Li, Banghua Zhu, Zhaoran Wang

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Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight—even at greater computational cost—has been relatively underexplored. In this work, we bridge this gap by proposing Local Linear Attention (LLA), a novel attention mechanism derived from nonparametric statistics through the lens of test-time regression. First, we show that LLA offers theoretical advantages over Linear and Softmax Attention for associative memory via a bias-variance trade-off analysis. Next, we address its computational challenges and propose two memory-efficient primitives to tackle the $\Theta(n^2d)$ and $\Theta(nd^2)$ complexity. We then introduce {FlashLLA}, a hardware-efficient, blockwise algorithm that enables scalable and parallel computation on modern accelerators. In addition, we implement and profile a customized inference kernel that significantly reduces memory overheads. Finally, we empirically validate the advantages and limitations of LLA on test-time regression, in-context regression, associative recall and state tracking tasks. Experiment results demonstrate that LLA effectively adapts to non-stationarity, outperforming strong baselines in test-time training and in-context learning, and exhibiting promising evidence for its scalability and applicability in large-scale models.

Poster
Unleashing Perception-Time Scaling to Multimodal Reasoning Models

Yifan Li, Zhenghao Chen, Ziheng Wu, Kun Zhou, Ruipu Luo, Can Zhang, Zhentao he, Yufei Zhan, Xin Zhao, Minghui Qiu

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Recent advances in inference-time scaling, particularly those leveraging reinforcement learning with verifiable rewards, have substantially enhanced the reasoning capabilities of Large Vision-Language Models (LVLMs). Inspired by this success, similar strategies have been applied to multimodal reasoning, yet their impact on visual perception remains unclear. To investigate this gap, we introduce DisTANCE, a perception-centric benchmark for visual estimation tasks. Evaluation results show that LVLMs exhibit limited estimation precision, and inference-time scaling offers only marginal gains. We attribute this to the fast perception paradigm of current LVLMs, where visual understanding is treated as a one-shot output without modeling the underlying perceptual process. To address this, we propose Perception-Time Scaling (PTS), a novel paradigm that encourages token-rich perception and decomposes complex perception problems into intermediate tractable sub-problems, thereby enabling perception to align with and benefit from inference-time scaling. Combined with reinforcement learning techniques, PTS significantly improves perception accuracy, raising high-precision performance on DisTANCE from 8.0% to 64.7%, and generalizes well to out-of-domain tasks. Surprisingly, even though PTS data are purely synthetic, combining them with math reasoning data yields consistent gains in both reasoning and real-world perception benchmarks. Further analysis reveals that PTS introduces more perception-related tokens and increases the model’s attention to image tokens. Our code and data will be publicly released.

Poster
Adversarial Déjà Vu: Jailbreak Dictionary Learning for Stronger Generalization to Unseen Attacks

Mahavir Dabas, Tran Huynh, Nikhil Reddy Billa, Jiachen T. Wang, Peng Gao, Charith Peris, Yao Ma, Rahul Gupta, Ming Jin, Prateek Mittal, Ruoxi Jia

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Large language models remain vulnerable to jailbreak attacks that bypass safety guardrails to elicit harmful outputs. Defending against novel jailbreaks represents a critical challenge in AI safety. Adversarial training---designed to make models robust against worst-case perturbations---has been the dominant paradigm for adversarial robustness. However, due to optimization challenges and difficulties in defining realistic threat models, adversarial training methods often fail on newly developed jailbreaks in practice. This paper proposes a new paradigm for improving robustness against unseen jailbreaks, centered on the Adversarial Déjà Vu hypothesis: novel jailbreaks are not fundamentally new, but largely recombinations of adversarial skills from previous attacks. We study this hypothesis through a large-scale analysis of 32 attack papers published over two years. Using an automated pipeline, we extract and compress adversarial skills into a sparse dictionary of primitives, with LLMs generating human-readable descriptions. Our analysis reveals that unseen attacks can be effectively explained as sparse compositions of earlier skills, with explanatory power increasing monotonically as skill coverage grows. Guided by this insight, we introduce Adversarial Skill Compositional Training (ASCoT), which trains on diverse compositions of skill primitives rather than isolated attack instances. ASCoT substantially improves robustness to unseen attacks, including multi-turn jailbreaks, while maintaining low over-refusal rates. We also demonstrate that expanding adversarial skill coverage, not just data scale, is key to defending against novel attacks.

Poster
SpikeGen: Decoupled “Rods and Cones” Visual Representation Processing with Latent Generative Framework

Gaole Dai, Menghang Dong, Rongyu Zhang, Ruichuan An, Tiejun Huang, Shanghang Zhang

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The process through which humans perceive and learn visual representations in dynamic environments is highly complex. From a structural perspective, the human eye decouples the functions of cone and rod cells: cones are primarily responsible for color perception, while rods are specialized in detecting motion, particularly variations in light intensity. These two distinct modalities of visual information are integrated and processed within the visual cortex, thereby enhancing the robustness of the human visual system. Inspired by this biological mechanism, modern hardware systems have evolved to include not only color-sensitive RGB cameras but also motion-sensitive Dynamic Visual Systems, such as spike cameras. Building upon these advancements, this study seeks to emulate the human visual system by integrating decomposed multi-modal visual inputs with modern latent-space generative frameworks. We named it ***SpikeGen***. We evaluate its performance across various spike-RGB tasks, including conditional image and video deblurring, dense frame reconstruction from spike streams, and high-speed scene novel-view synthesis. Supported by extensive experiments, we demonstrate that leveraging the latent space manipulation capabilities of generative models enables an effective synergistic enhancement of different visual modalities, addressing spatial sparsity in spike inputs and temporal sparsity in RGB inputs.

Poster
CircuitSense: A Hierarchical Circuit System Benchmark Bridging Visual Comprehension and Symbolic Reasoning in Engineering Design Process

Arman Akbari, Jian Gao, Yifei Zou, Mei Yang, Jinru Duan, Dmitrii Torbunov, Yanzhi Wang, Yihui Ren, Xuan Zhang

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Engineering design operates through hierarchical abstraction from system specifications to component implementations, requiring visual understanding coupled with mathematical reasoning at each level. While Multi-modal Large Language Models (MLLMs) excel at natural image tasks, their ability to extract mathematical models from technical diagrams remains unexplored. We present \textbf{CircuitSense}, a comprehensive benchmark evaluating circuit understanding across this hierarchy through 8,006+ problems spanning component-level schematics to system-level block diagrams. Our benchmark uniquely examines the complete engineering workflow: Perception, Analysis, and Design, with a particular emphasis on the critical but underexplored capability of deriving symbolic equations from visual inputs. We introduce a hierarchical synthetic generation pipeline consisting of a grid-based schematic generator and a block diagram generator with auto-derived symbolic equation labels. Comprehensive evaluation of eight state-of-the-art MLLMs, including both closed-source and open-source models, reveals fundamental limitations in visual-to-mathematical reasoning. Closed-source models achieve over 85\% accuracy on perception tasks involving component recognition and topology identification, yet their performance on symbolic derivation and analytical reasoning falls below 19\%, exposing a critical gap between visual parsing and symbolic reasoning. Models with stronger symbolic reasoning capabilities consistently achieve higher design task accuracy, confirming the fundamental role of mathematical understanding in circuit synthesis and establishing symbolic reasoning as the key metric for engineering competence. Our synthetic pipeline code is available at \href{https://anonymous.4open.science/r/CircuitSense-8AC7/README.md}{URL}.

Poster
Explainable Token-level Noise Filtering for LLM Fine-tuning Datasets

Yuchen Yang, Wenze Lin, Enhao Huang, Zhixuan Chu, Hongbin Zhou, Lan Tao, Yiming Li, Zhan Qin, Kui Ren

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Large Language Models (LLMs) have seen remarkable advancements, achieving state-of-the-art results in diverse applications. Fine-tuning, an important step for adapting LLMs to specific downstream tasks, typically involves further training on corresponding datasets. However, a fundamental discrepancy exists between current fine-tuning datasets and the token-level optimization mechanism of LLMs: most datasets are designed at the sentence-level, which introduces token-level noise, causing negative influence to final performance. In this paper, we propose XTF, an explainable token-level noise filtering framework. XTF decomposes the complex and subtle contributions of token-level data to the fine-tuning process into three distinct and explicit attributes (reasoning importance, knowledge novelty, and task relevance), which can be assessed using scoring methods, and then masks the gradients of selected noisy tokens accordingly to optimize the performance of fine-tuned LLMs. We conduct extensive experiments on three representative downstream tasks (math, code and medicine) across 7 mainstream LLMs. The results demonstrate that XTF can significantly improve downstream performance by up to 13.7% compared to regular fine-tuning. Our work highlights the importance of token-level dataset optimization, and demonstrates the potential of strategies based on attribute decomposition for explaining complex training mechanisms.

Poster
Quantile Advantage Estimation for Entropy-Safe Reasoning

Junkang Wu, Kexin Huang, Jiancan Wu, An Zhang, Xiang Wang, Xiangnan He

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Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean-baseline used in value-free RL (\eg GRPO/DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise $K$-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries ($p \le 1{-}K$) it reinforces rare successes, while on easy queries ($p > 1{-}K$) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower/upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned $K$, roughly 80\% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME'24/'25 and AMC'23. These results identify {baseline design}—rather than token-level heuristics—as the primary mechanism for scaling RLVR.

Poster
ReCAPA: Hierarchical Predictive Correction to Mitigate Cascading Failures

Xiyin Zeng, Yuyu Sun, Haoyang Li, Shouqiang Liu, Hao Wang

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Vision–Language–Action (VLA) agents follow instructions to perform multi-step tasks in multimodal environments. To support planning and execution in such settings, many approaches typically adopt structured post-hoc or rely on fixed decomposition and rigid alignment to improve success rate. However, once an intermediate subgoal or action is mis-specified and without a flexible correction mechanism, local errors propagate through subsequent steps and eventually accumulate into cascading failures in long-horizon reasoning. To mitigate this compounding effect, we propose Reflective Contrastive Alignment and Planning Architecture (ReCAPA), a framework that uses predictive correction to anticipate deviations and adjust representations across three levels: actions, subgoals, and trajectories. Semantic alignment is enforced at all levels using a Sinkhorn-based module and a Score-field module. The corrective signals, derived from predictive correction and alignment mechanisms, jointly update the execution network during training, enabling it to flexibly adjust fine-grained steps to remain aligned with the overall intent. We further introduce two new metrics to quantify error propagation and recovery processes in tasks. Experiments show that ReCAPA achieves competitive results on embodied agent benchmarks such as VisualAgentBench, MineDojo, and MAP-THOR, outperforming strong proprietary and open-source Large Language Model (LLM) baselines.

Poster
Credit-Budgeted ICPC-Style Coding: When LLM Agents Must Pay for Every Decision

Lingfeng Zhou, Junhao Shi, Jin Gao, Dequan Wang

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Contemporary coding-agent benchmarks applaud “first correct answer,” silently assuming infinite tokens, container minutes, and developer patience. In production, every LLM call, test re-run, and rollback incurs hard cost; agents that cannot budget these resources are dead on arrival. We close the gap with USACOArena, an ICPC-inspired arena where agents pay deterministic credits for every prompt, compilation, test, or rollback. A task becomes a cost–benefit negotiation under uncertainty: is a second sample worth 15\% of the remaining budget, or should the agent pivot to a cheaper heuristic? Real-time deduction exposes decision profiles hidden from static leaderboards: the tax of over-specialized generators, the ROI of early-exit heuristics, and the compound interest of lightweight scaffolding. Even identically seeded agents diverge in self-play, revealing a rich policy space where the same model oscillates between spendthrift submission sprees and parsimonious exploration. Released as a reproducible benchmark and zero-shot curriculum, USACOArena provides the traces, credit engine, and six state-of-the-art decision logs to catalyze research on coding agents that know when to stop.

Poster
Learning to Summarize by Learning to Quiz: Adversarial Agentic Collaboration for Long Document Summarization

Weixuan Wang, Minghao Wu, Barry Haddow, Alexandra Birch

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Long document summarization remains a significant challenge for current large language models (LLMs), as existing approaches commonly struggle with information loss, factual inconsistencies, and coherence issues when processing excessively long documents. We propose SummQ, a novel adversarial multi-agent framework that addresses these limitations through collaborative intelligence between specialized agents operating in two complementary domains: summarization and quizzing. Our approach employs summary generators and reviewers that work collaboratively to create and evaluate comprehensive summaries, while quiz generators and reviewers create comprehension questions that serve as continuous quality checks for the summarization process. This adversarial dynamic, enhanced by an examinee agent that validates whether the generated summary contains the information needed to answer the quiz questions, enables iterative refinement through multifaceted feedback mechanisms. We evaluate SummQ on three widely used long document summarization benchmarks. Experimental results demonstrate that our framework significantly outperforms existing state-of-the-art methods across ROUGE and BERTScore metrics, as well as in LLM-as-a-Judge and human evaluations. Our comprehensive analyses reveal the effectiveness of the multi-agent collaboration dynamics, the influence of different agent configurations, and the impact of the quizzing mechanism. This work establishes a new approach for long document summarization that uses adversarial agentic collaboration to improve summarization quality.

Poster
Learning Admissible Heuristics for A*: Theory and Practice

Ehsan Futuhi, Nathan R. Sturtevant

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Heuristic functions are central to the performance of search algorithms such as A*, where \emph{admissibility}—the property of never overestimating the true shortest-path cost—guarantees solution optimality. Recent deep learning approaches often disregard full admissibility and provide limited guarantees on generalization beyond the training data. We address both of these limitations. First, we pose heuristic learning as a constrained optimization problem and introduce \emph{Cross-Entropy Admissibility (CEA)}, a loss function that enforces admissibility during training. When evaluated on the Rubik’s Cube domain, our method yields heuristics with near-perfect admissibility and significantly stronger guidance than compressed pattern database (PDB) heuristics. On the theoretical side, we derive a new upper bound on the expected suboptimality of A*. By leveraging PDB abstractions and the structural properties of graphs such as the Rubik’s Cube, we tighten the bound on the number of training samples needed for A* to generalize to unseen states. Replacing a general hypothesis class with a ReLU neural network gives bounds that depend primarily on the network’s width and depth, rather than on graph size. Using the same network, we also provide the first generalization guarantees for \emph{goal-dependent} heuristics.

Poster
High-dimensional Mean-Field Games by Particle-based Flow Matching

Jiajia Yu, Junghwan Lee, Yao Xie, Xiuyuan Cheng

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Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications, including optimal transport (OT) and generative models. Despite their broad applicability, solving high-dimensional MFGs remains a significant challenge due to fundamental computational and analytical obstacles. In this work, we propose a particle-based deep Flow-Matching (FM) method to tackle high-dimensional deterministic MFG computation. In each iteration of our proximal best response scheme, particles are updated using first-order information, and a flow neural network is trained to match the velocity of the sample trajectories in a simulation-free manner. Theoretically, in the optimal control setting, we prove that our scheme converges to a stationary point sublinearly, and upgrade to linear (exponential) convergence under additional convexity assumptions. Our proof uses FM to induce an Eulerian coordinate (density-based) from a Lagrangian one (particle-based), and this also leads to certain equivalence results between the two formulations for MFGs when the Eulerian solution is sufficiently regular. Our method demonstrates promising performance on non-potential MFGs and high-dimensional OT problems cast as MFGs through a relaxed terminal-cost formulation.

Poster