ICML 2026 论文列表

International Conference on Machine Learning

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6,341篇论文

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LiMuon: Light and Fast Muon Optimizer for Large Models

Feihu Huang, Yuning Luo, Songcan Chen

展开摘要

Large models recently are widely applied in machine learning, so efficient training of large models has received widespread attention. More recently, the useful Muon optimizer is specifically designed for matrix-structured parameters of large models. Although some works have begun to study the Muon optimizer, the existing Muon and its variants still suffer from high sample complexity or high memory for large models. To fill this gap, we propose a light and fast Muon (LiMuon) optimizer for training large models, which builds on the momentum-based variance reduced technique and randomized Singular Value Decomposition (SVD). In particular, our LiMuon simultaneously has a lower memory and lower sample complexity than the Muon and its variants. Moreover, we prove that our LiMuon with lower memory has a lower sample complexity of $O(\epsilon^{-3})$ for finding an $\epsilon$-stationary solution of non-convex stochastic optimization under the generalized smoothness condition. To further narrow practice and theory gap, we also prove that our LiMuon with Newton-Schulz steps has a lower sample complexity than the Muon with Newton-Schulz steps. Numerical experimental results on training Mamba-130M, Qwen2.5-0.5B and ViT models demonstrate effectiveness of our LiMuon.

Poster
Unbiased Reward Modeling from Implicit Feedback for LLM Alignment

Hao Wang, Haocheng Yang, Licheng Pan, Zhichao Chen, Xiaoxi Li, Yinuo Wang, Lei Shen, Yuan Lu, Haoxuan Li, Zhouchen Lin

展开摘要

Despite the success of reinforcement learning from human feedback (RLHF), existing reward modeling methods largely rely on explicit feedback, which is costly to collect and difficult to scale. This work studies implicit reward modeling, learning reward models from implicit user feedback, such as clicks, copies and skips. While scalable and cost-effective, implicit feedback poses two key challenges: (1) It lacks definitive negative samples, which makes standard positive-negative classification methods inapplicable; (2) It suffers from selection bias, where responses have heterogeneous propensities to elicit feedback, which further obscures definitive negative samples. To address these challenges, we propose ImplicitRM, which learns unbiased reward models from implicit feedback. It stratifies training samples into four latent groups using a stratification model and derives a likelihood-maximization objective that is theoretically unbiased, thereby addressing both challenges. Experiments across diverse LLM backbones and benchmark datasets validate that ImplicitRM learns accurate reward models from implicit feedback and improves performance on downstream RLHF tasks.

Poster
SGMD: Score Gradient Matching Distillation for Few-Step Video Diffusion Distillation

Zhuguanyu Wu, Ruihao Gong, Yang Yong, Yushi Huang, Xiangyu Fan, Lei Yang, Dahua Lin, Xianglong Liu

展开摘要

Distribution Matching Distillation (DMD) is a widely used paradigm for accelerating inference in few-step video diffusion models. However, DMD-style training faces a structural bottleneck: the student-side auxiliary score network (the fake score) must closely track a continuously evolving generator. Updating the fake score too frequently increases training cost and can over-emphasize inner-loop tracking, while infrequent updates lead to tracking lag that destabilizes training and degrades generation consistency. To address this issue, we propose \textbf{Score Gradient Matching Distillation (SGMD)}. SGMD adopts a fake-score perspective by directly optimizing the fake score toward the teacher, while using teacher stop-gradient Fisher as a stable distribution-matching objective. We provide a gradient analysis that motivates this objective choice under ideal tracking. Building on this, SGMD introduces a pair of dual potentials: negative-residual (NR) for outer-loop correction and residual-contraction (RC) for inner-loop tracking. Empirically, compared to DMD, SGMD achieves an approximately $\sim 3\times$ training speedup and substantially improves motion dynamics for 4-step distilled models while preserving temporal consistency.

Poster
BEAR: Dissecting Embodied Abilities in Multimodal Language Models through Skill-level Evaluation and Diagnosis

Yu Qi, Haibo Zhao, Ziyu Guo, Siyuan Ma, Ziyan Chen, Yaokun Han, Renrui Zhang, Zitiantao Lin, Yizhe Zhu, Shiji Xin, Yijian Huang, Boce Hu, Kai Cheng, Jiayi Zhang, Peiheng Wang, jiazheng liu, Wenqing Wang, Yiran Qin, Haojie Huang, Lawson L.S. Wong

展开摘要

Understanding the capability bottlenecks of embodied multimodal large language models (MLLMs) is crucial for improvement. However, existing embodied benchmarks fail to provide actionable insights because they focus on task-level evaluation rather than discovering capability bottlenecks. To address this, we introduce BEAR, where we divide embodied tasks into 14 atomic skills for skill-level evaluation. BEAR comprises 4,469 interleaved image–video–text entries across 14 skills in 6 categories, ranging from low-level perception to high-level planning. We evaluate 20 MLLMs on BEAR under a hierarchical skill-level diagnosis framework and discover that (1) perceptual capabilities are major bottlenecks behind reasoning failures, and (2) models fail due to unstable spatiotemporal modeling which remain unexposed in previous benchmarks. Furthermore, building on these insights, we propose BEAR-Agent, a multimodal conversable agent that augments MLLMs with visual and spatial tools. It substantially enhances MLLMs’ performance across skills, yielding a relative improvement of 17.5% on GPT-5 on BEAR and outperform baselines by a large margin in both simulation and real-robot experiments across models. We provide our project website at https://bear-official66.github.io/.

Poster
Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State

Nicholas Gao, Till Grutschus, Frank Noe, Stephan Günnemann

展开摘要

Neural-network wave functions in Variational Monte Carlo (VMC) have achieved great success in accurately representing both ground and excited states. However, achieving sufficient numerical accuracy in state overlaps requires increasing the number of Monte Carlo samples, and consequently the computational cost, with the number of states. We present a nearly constant sample-size approach, Multi-State Importance Sampling (MSIS), that leverages samples from all states to estimate pairwise overlap. To efficiently evaluate all states for all samples, we introduce Excited Pfaffians. Inspired by Hartree-Fock, this architecture represents many states within a single neural network. Excited Pfaffians also serve as generalized wave functions, allowing a single model to represent multi-state potential energy surfaces. On the carbon dimer, we match the $\mathcal{O}(N_s^4)$-scaling natural excited states while training $>200\times$ faster and modeling 50\% more states. Our favorable scaling enables us to be the first to use neural networks to find all distinct energy levels of the beryllium atom. Finally, we demonstrate that a single wave function can represent excited states across various molecules.

Spotlight
CADFit: Precise Mesh-to-CAD Program Generation with Hybrid Optimization

Ghadi Nehme, Eamon Whalen, Faez Ahmed

展开摘要

Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets. We introduce CADFit, a hybrid optimization-based CAD reconstruction framework that recovers complex, editable CAD construction sequences from meshes by incrementally fitting and validating parametric operations using geometric feedback. Our approach is distinguished by formulating reconstruction as an IoU-driven optimization over structured CAD programs and supporting a rich set of operations, including extrusions, revolutions, fillets, and chamfers. Experiments on multiple CAD benchmarks show that CADFit outperforms state-of-the-art mesh-to-CAD methods in volumetric Intersection-over-Union and Chamfer Distance, while substantially reducing the Invalid Ratio of reconstructed CAD programs, particularly for complex designs. We further present a multimodal pipeline that enables end-to-end reconstruction of CAD construction sequences from images by combining image-based geometry reconstruction with CADFit. By enabling accurate reconstruction of higher-complexity CAD models, CADFit provides a practical foundation for generating richer datasets and advancing future learning-based approaches to CAD reverse engineering. The code is available at: https://github.com/ghadinehme/CADFit.

Poster
Efficient Learning of Deep State Space Models via Importance Smoothing

John-Joseph Brady, Nikolas Nüsken, Yunpeng Li

展开摘要

Latent state space systems are ubiquitous in statistical modelling, arising naturally when time series are observed through noisy measurements. However, training deep state space models (DSSMs) at scale remains difficult. Two largely distinct strategies have emerged for training DSSMs. The first, auto-encoding DSSMs, trains generative models by optimising a variational lower bound. The second backpropagates through the outputs of classical sequential Monte Carlo (SMC) algorithms. Such approaches can train DSSMs for both discriminative and generative tasks, but their inherently sequential forward passes scale poorly on modern hardware. We propose \emph{parallel variational Monte Carlo} (PVMC), a new training method that bridges these paradigms and robustly trains DSSMs for both discriminative and generative tasks. Across a set of benchmark experiments, PVMC matches or exceeds state-of-the-art performance while training $10\times$ faster than the fastest competing SMC-based approach.

Poster
PSG-Nav: Probabilistic Scene Graph Navigation via Multiverse Decision Making

Rufeng Chen, Yue Chang, Xiaqiang Tang, Hechang Chen, Sihong Xie

展开摘要

Open-vocabulary navigation requires embodied agents to manage significant perception uncertainty stemming from semantic ambiguity and model errors. However, most existing works settle for local optimal deterministic approaches, depriving complex navigation decision-making over multiple composite possibilities that are critical for globally better solutions. In this paper, we propose Probabilistic Scene Graph Navigation (PSG-Nav), which constructs a 3D Probabilistic Scene Graph that uses full semantic categorical distributions to account for perception uncertainty. To efficiently use the local distributions to compose and reason about the optimal navigation landmarks, we propose Multiverse Decision to sample multiple most likely world settings from the joint distribution, and evaluate navigation landmarks based on the compatibility between landmarks and multiverses. To mitigate false positives due to epistemic uncertainty in open-vocabulary navigation, we introduce the Evidential Experience Calibrator, which enables online lifelong adaptation by cross-validating detections against memories of past successes and failures. Extensive experiments on widely-used benchmarks MP3D, HM3D, and HSSD demonstrate that PSG-Nav establishes new state-of-the-art results, achieving Success Rates of 66.1%, 44.8%, and 67.9%, respectively. Code is available at: https://psg-nav.github.io

Poster
Trading Complexity for Expressivity Through Structured Generalized Linear Token Mixing

Erwan Fagnou, Paul Caillon, Blaise Delattre, Alexandre Allauzen

展开摘要

Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed and the memory requirements, along with the cache size. Considering causal generation, this paper explores new trade-offs thanks to a unified framework which separates two crucial features: (i) the direct influence of inputs on outputs in one generation step; (ii) the recurrent propagation of information through past outputs. This framework encompasses major architectures such as attention and state-space models, but also generalizes the recurrence equations by allowing each state to depend on multiple past states rather than only the immediate predecessor. By introducing structure, we design new recurrence patterns that provably achieve the desired complexity, while providing theoretical insights on their expressivity -- trading runtime for expressivity in a principled way. Empirical validation is performed on synthetic tasks, along with language modeling. Together, these results provide a unified toolkit for the understanding and design of efficient and expressive token mixers across model families.

Poster
MineDraft: A Framework for Batch Parallel Speculative Decoding

Zhenwei Tang, Arun Verma, Zijian Zhou, Zhaoxuan Wu, Alok Prakash, Daniela Rus, Bryan Kian Hsiang Low

展开摘要

Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to propose draft tokens that are subsequently verified by a larger target model. However, the performance of standard SD is often limited by the strictly sequential execution of these drafting and verification stages. To address this, this paper proposes MineDraft, a batch parallel speculative decoding (PSD) framework designed to effectively hide drafting latency by overlapping it with verification. Our theoretical analysis shows that PSD is substantially more efficient than standard SD. MineDraft realizes the PSD through a novel batch-parallel design that maintains two batches of requests, overlapping drafting for one batch with verification for the other. Our experimental results show significant improvements of MineDraft in both throughput (up to 75%) and end-to-end latency (up to 39%) over standard SD. Furthermore, we have implemented MineDraft as a plugin for vLLM, demonstrating its practicality for production-ready inference systems. The code is publicly available in the [MineDraft GitHub repository](https://github.com/electron-shaders/MineDraft).

Poster
Contrastive Weak-to-Strong Generalization

Houcheng Jiang, Junfeng Fang, Jiaxin Wu, Tianyu Zhang, Chen Gao, Xiang Wang, Xiangnan He, Yang Deng

展开摘要

Weak-to-strong generalization provides a promising paradigm for scaling large language models (LLMs) by training stronger models on samples from aligned weaker ones, without requiring human feedback or explicit reward modeling. However, its robustness and generalization are hindered by the noise and biases in weak-model outputs, which limit its applicability in practice. To address this challenge, we leverage implicit rewards, which approximate explicit rewards through log-likelihood ratios, and reveal their structural equivalence with Contrastive Decoding (CD), a decoding strategy shown to reduce noise in LLM generation. Building on this connection, we propose \textbf{Contrastive Weak-to-Strong Generalization (ConG)}, a framework that employs contrastive decoding between pre- and post-alignment weak models to generate higher-quality samples. This approach enables more reliable capability transfer, denoising, and improved robustness, substantially mitigating the limitations of traditional weak-to-strong methods. Empirical results across different model families confirm consistent improvements, demonstrating the generality and effectiveness of ConG. Taken together, our findings highlight the potential of ConG to advance weak-to-strong generalization and provide a promising pathway toward AGI. Our code is available at: \url{https://github.com/jianghoucheng/ConG}

Poster
ADEPT: RL-Aligned Agentic Decoding of Emotion via Evidence Probing Tools — From Consensus Learning to Ambiguity-Driven Emotion Reasoning

Esther Sun, Bo-Hao Su, Abinay Reddy Naini, Shinji Watanabe, Carlos Busso

展开摘要

Speech Large Language Models (SLLMs) enable high-level emotion reasoning, but often produce ungrounded, text-biased judgments without verifiable acoustic evidence. In contrast, SSL encoders such as WavLM yield strong acoustic representations yet remain opaque discriminative models that offer limited interpretability. To bridge this gap, we introduce the Agentic Decoding of Emotion via Probing Tools (ADEPT) framework, which reframes emotion recognition as a multi-turn inquiry process rather than a single-pass prediction. ADEPT transforms an SLLM into an agent that maintains an evolving candidate set and adaptively invokes dedicated semantic and acoustic probing tools within a structured pipeline of candidate generation, evidence collection, and adjudication. Crucially, ADEPT enables a paradigm shift from consensus learning to ambiguity-driven emotion reasoning. Since human affect exhibits complexity and co-occurrence of emotions, we leverage minority annotations as informative signals instead of discarding them as noise. Finally, we integrate Group Relative Policy Optimization (GRPO) with the Evidence Trust Gate to explicitly couple tool-usage behaviors with prediction quality and enforce evidence-based reasoning. Experiments demonstrate that ADEPT improves in most cases the primary emotion accuracy while substantially improving minor emotion characterization, producing explanations grounded in auditable evidence.

Spotlight
Once-for-All: Scalable Simultaneous Forecasting via Equilibrium State Estimation

Beinan Xu, Andy Song, Jiti Gao, Feng Liu

展开摘要

We introduce Equilibrium State Estimation (ESE), a novel paradigm for simultaneous prediction, where multiple interacting systems require separate yet coordinated forecasts. Such scenarios often arise in real-world such as economics and healthcare modeling. Unlike existing approaches that predict one system at a time, ESE forecasts all systems in a single pass. It first estimates the equilibrium state across systems, then generates holistic forecasts based on the difference between the current state and the estimated equilibrium. Extensive experiments on synthetic and real-world datasets, including currency exchange and COVID-19 spread modeling, demonstrate that ESE is at least as accurate as state-of-the-art (SOTA) methods while being significantly faster. In addition, ESE integrates seamlessly with conventional predictors, combining their accuracy with its exceptional efficiency and delivering a 10–70× speedup. With linear-time complexity, ESE scales far better than SOTA methods as the number of systems increases. Moreover, it remains accurate under diverse perturbations, establishing ESE as a fast, generalizable, robust, and scalable multi-prediction method.

Poster
Video-o3: Native Interleaved Clue Seeking for Long Video Multi-Hop Reasoning

Xiangyu Zeng, Zhiqiu Zhang, Yuhan Zhu, Xinhao Li, Zikang Wang, Changlian Ma, Qingyu Zhang, Zizheng Huang, Kun Ouyang, Tianxiang Jiang, Ziang Yan, Yi Wang, Hongjie Zhang, Yali Wang, Limin Wang

展开摘要

Existing multimodal large language models for long-video understanding predominantly rely on uniform sampling and single-turn inference, limiting their ability to identify sparse yet critical evidence amid extensive redundancy. We introduce Video-o3, a novel framework that supports iterative discovery of salient visual clues, fine-grained inspection of key segments, and adaptive termination once sufficient evidence is acquired. Technically, we address two core challenges in interleaved tool invocation. First, to mitigate attention dispersion induced by the heterogeneity of reasoning and tool-calling, we propose Task-Decoupled Attention Masking, which isolates per-step concentration while preserving shared global context. Second, to control context length growth in multi-turn interactions, we introduce a Verifiable Trajectory-Guided Reward that balances exploration coverage with reasoning efficiency. To support training at scale, we further develop a data synthesis pipeline and construct Seeker-173K, comprising 173K high-quality tool-interaction trajectories for effective supervised and reinforcement learning. Extensive experiments show that Video-o3 substantially outperforms state-of-the-art methods, achieving 72.1% accuracy on MLVU and 46.5% on Video-Holmes. These results demonstrate Video-o3's strong multi-hop evidence-seeking and reasoning capabilities, and validate the effectiveness of native tool invocation in long-video scenarios.

Poster
Skewness-Robust Causal Discovery in Location-Scale Noise Models

Daniel Klippert, Alexander Marx

展开摘要

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. A flexible class of models that is general and identifiable in most cases are location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on its causes $\boldsymbol{X}$ as $Y = f(\boldsymbol{X}) + g(\boldsymbol{X})N$. To facilitate the estimation of these models, a prominent assumption is that the noise variable $N$ follows a symmetric distribution. We show that when $N$ is a skewed random variable, which is likely in real-world domains, such approaches drop in performance. To address this limitation, we propose SkewD, a likelihood-based method for causal discovery under LSNMs with skewed noise, employing a combination of heuristic search and expectation conditional maximization for parameter estimation. SkewD extends the usual normal distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. While our main focus is on bivariate cause-effect inference, we further showcase how SkewD can be extended to the multivariate setting.

Poster
Measuring Agents in Production

Melissa Pan, Negar Arabzadeh, Riccardo Cogo, Yuxuan Zhu, Alexander Xiong, Lakshya A Agrawal, Huanzhi Mao, Emma Shen, Sid Pallerla, Liana Patel, Shu Liu, Tianneng Shi, Xiaoyuan Liu, Jared Quincy Davis, Emmanuele Lacavalla, Alessandro Basile, Shuyi Yang, Paul Castro, Daniel Kang, Koushik Sen, Dawn Song, Joseph E. Gonzalez, Ion Stoica, Matei Zaharia, Marquita Ellis

展开摘要

LLM-based agents already operate in production across many industries, yet we lack an understanding of what technical methods make deployments successful. We present the first systematic study of **M**easuring **A**gents in **P**roduction, MAP, using first-hand data from agent developers. We conducted 20 case studies via in-depth interviews and surveyed 86 deployed systems practitioners across 26 domains. We investigate why organizations build agents, how they build them, how they evaluate them, and their top development challenges. Our study finds that production agents are built using simple, controllable approaches: 68% execute at most 10 steps before human intervention, 70% rely on prompting off-the-shelf models instead of weight tuning, and 74% depend primarily on human evaluation. Reliability (consistent correct behavior over time) remains the top development challenge, which practitioners currently address through systems-level design. MAP documents the current state of production agents, providing the research community with visibility into deployment realities and underexplored research avenues.

Spotlight
Approximation Error Upper and Lower Bounds for Hölder Class with Transformers

Xin He, Yuling Jiao, Xiliang Lu, Jerry Zhijian Yang

展开摘要

We explore the expressive power of Transformers by establishing precise approximation error upper and lower bounds for Hölder class. Specifically, a new approximation upper bound is derived for the standard Transformer architecture equipped with Softmax operators, ReLU activation functions, and residual connections. We prove that a Transformer network composed of at most $\mathcal{O}(\varepsilon^{-{d_{0}}/{\alpha}})$ blocks can approximate any bounded Hölder function with $d_{0}$-dimensional input and smoothness $\alpha\in(0,1]$ under any accuracy $\varepsilon>0$. In the case of approximation lower bounds, leveraging the VC-dimension upper bound, we are the first to rigorously prove that Transformers demand for at least $\Omega(\varepsilon^{-{d_{0}}/({4\alpha})})$ blocks to achieve the $\varepsilon$ approximation accuracy. As a final step, we extend the derived results for standard Transformers to a general regression task and establish the corresponding excess risk rates demonstrating Transformers' empirical effectiveness in real-world settings.

Poster
Metric—Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds

Jiayi Kong, Xuhui Chen, Chen Zong, Fei Hou, Junhui Hou, Wenping Wang, Ying He

展开摘要

Neural Signed Distance Functions (SDFs) excel at reconstructing watertight manifolds but fail on thin structures and open boundaries due to strict inside—outside constraints. Conversely, Unsigned Distance Fields (UDFs) accommodate general geometries but suffer from gradient singularities at the zero-level set, hindering optimization and extraction. We introduce Metric—Phase Fields (MPFs), a decoupled implicit representation that separates metric proximity from topological phase. Given an unoriented point cloud, MPFs learn (i) an unsigned metric field $r$ and (ii) a smooth phase field $\theta$, for which we derive a bounded phase indicator $P=\tanh(\beta\theta)$ that provides soft inside—outside cues where they are meaningful. We couple the two fields via a gated-metric formulation with a residual phase injection to obtain a signed implicit function with stable near-surface gradients. The phase coefficient $\beta$ is learnable, allowing MPFs to adaptively control the sharpness of the phase transition and the degree of saturation of the soft sign indicator. Experiments on both synthetic and scanned thin-shell and thin-plate shapes demonstrate that MPFs preserve thin and layered structures more faithfully than recent SDF-based methods, while also enabling more robust training and more reliable surface extraction than UDF-based approaches. Check out [MPFs-GitHub](https://github.com/JIAYI-Scarlett/ICML2026-MPF) for source code and test models.

Poster
PINNfluence: Interpreting PINNs through Influence Functions

Aleksander Krasowski, Jonas Naujoks, Moritz Weckbecker, Galip Ümit Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René Pascal Klausen

展开摘要

Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability. To address this issue, we introduce PINNfluence, a training data attribution framework for interpreting PINNs based on influence functions. By extending influence functions to composite physics-informed training objectives, we enable fine-grained attribution between predictions, loss components, and training data points. Through benchmark experiments across various PDEs, we demonstrate that influence patterns provide granular diagnostics that distinguish structural characteristics across well-trained and poorly-trained PINNs. PINNfluence thus opens a new avenue for understanding and improving the reliability of PINNs through the lens of their data.

Poster
Optimizing Agentic Reasoning with Retrieval via Synthetic Semantic Information Gain Reward

Senkang Hu, Yong Dai, Yuzhi Zhao, Yihang Tao, Yu Guo, Zhengru Fang, Sam Kwong, Yuguang Fang

展开摘要

Agentic reasoning enables large reasoning models (LRMs) to dynamically acquire external knowledge, yet optimizing the retrieval process remains challenging due to the lack of dense, principled reward signals. In this paper, we introduce *InfoReasoner*, a unified framework that incentivizes effective information seeking via a *synthetic semantic information gain reward*. Theoretically, we redefine information gain as uncertainty reduction over the model's belief states, establishing key properties including non-negativity, telescoping additivity, and channel monotonicity. Practically, to enable scalable optimization without manual intermediate retrieval annotations, we instantiate this principle as a semantic information gain reward computed from the model's output distributions using *semantic clustering via bidirectional textual entailment*. This training reward provides dense credit for retrieval steps while remaining anchored to final-answer correctness, enabling efficient training via Group Relative Policy Optimization (GRPO). Experiments on seven question-answering benchmarks, MATH500, and WebDetective show consistent gains over strong retrieval-augmented baselines, supporting our dense semantic information gain as a practical training signal for agentic retrieval.

Poster