ICML 2026 Papers

International Conference on Machine Learning

Decision breakdown

6,341papers

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

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    5368.5%
  • Poster
    5,80591.5%

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SPA: A Simple but Tough-to-Beat Baseline for Knowledge Injection

Kexian Tang, Jiani Wang, Shaowen Wang, Kaifeng Lyu

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While large language models (LLMs) are pretrained on massive amounts of data, their knowledge coverage remains incomplete in specialized, data-scarce domains, motivating extensive efforts to study synthetic data generation for knowledge injection. We propose $\textbf{SPA}$ ($\textbf{S}$caling $\textbf{P}$rompt-engineered $\textbf{A}$ugmentation), a simple but tough-to-beat baseline that uses a small set of carefully designed prompts to generate large-scale synthetic data for knowledge injection. Through systematic comparisons, we find that $\textbf{SPA}$ outperforms several strong baselines. Furthermore, we identify two key limitations of prior approaches: (1) while RL-based methods may improve the token efficiency of LLM-based data augmentation at small scale, they suffer from diversity collapse as data scales, leading to diminishing returns; and (2) while multi-stage prompting may outperform simple augmentation methods, their advantages can disappear after careful prompt tuning. Our results suggest that, for knowledge injection, careful prompt design combined with straightforward large-scale augmentation can be surprisingly effective, and we hope SPA can serve as a strong baseline for future studies in this area. Our code is available at https://github.com/Tangkexian/SPA.

Poster
Q-Sched: Pushing the Boundaries of Few-Step Diffusion Models with Quantization-Aware Scheduling

Natalia Frumkin, Diana Marculescu

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Text-to-image diffusion models remain computationally intensive: generating a single image typically requires dozens of passes through large transformer backbones (e.g., SDXL uses ~50 evaluations of a 2.6B-parameter model). Few-step variants reduce the step count to 2–8 but still rely on large, full-precision backbones, making inference impractical on resource-constrained platforms. Existing post-training quantization (PTQ) methods are further hampered by their dependence on full-precision calibration. We introduce **Q-Sched**, a scheduler-level PTQ approach that adapts the diffusion sampler while keeping the quantized weights fixed. By adjusting the few-step sampling trajectory with quantization-aware preconditioning coefficients, Q-Sched matches or surpasses full-precision quality while delivering a **4× reduction** in model size and preserving a single reusable checkpoint across bit-widths. To learn these coefficients, we propose a reference-free **Joint Alignment–Quality (JAQ)** loss, which combines text–image compatibility with an image-quality objective for fine-grained control. JAQ requires only a handful of calibration prompts and avoids any full-precision inference during calibration. Empirically, Q-Sched yields substantial gains: a **15.5%** FID improvement over the FP16 4-step Latent Consistency Model and a **16.6%** improvement over the FP16 8-step Phased Consistency Model, demonstrating that quantization and few-step distillation are complementary for high-fidelity generation. A large-scale user study with **80,000+** annotations further validates these results on both FLUX.1[schnell] and SDXL-Turbo. Code: [https://github.com/enyac-group/q-sched](https://github.com/enyac-group/q-sched)

Poster
Contextual Slate GLM Bandits with Limited Adaptivity

Tanmay Goyal, Sukruta Prakash Midigeshi, Gaurav Sinha

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We investigate the contextual slate bandit problem with generalized linear rewards under limited adaptivity. At each round, the learner is presented with $N$ sets of items, where each item is represented by a $d$-dimensional feature vector. The learner then constructs a slate by selecting one item per set; the resulting slate yields a scalar reward sampled from a Generalized Linear Model (GLM). We propose algorithms under two limited-adaptivity settings: (a) Batched and (b) Rarely-Switching. For the batched setting, we introduce B-SlateGLinCB, which partitions the time horizon into $\mathcal{O}(\log\log T)$ batches such that each batch's policy relies only on data from previous batches. For the rarely-switching setting, we propose RS-SlateGLinCB, which adaptively performs only $\mathcal{O}(Nd\log T)$ parameter updates. Under a diversity assumption on the item sequences, we prove that B-SlateGLinCB and RS-SlateGLinCB achieve regret bounds of $\mathcal{O}(Nd^{3/2}\sqrt{T})$ and $\mathcal{O}(Nd\sqrt{T})$, respectively. Notably, both bounds are independent of the non-linearity parameter $\kappa$ that is typically found to scale the regret of GLM bandit algorithms. Our algorithms are computationally efficient, requiring only $\text{poly}(N)$ time per round despite $2^{\Omega(N)}$ possible slates. Simulations show our algorithms outperform existing baselines with limited adaptivity and remain competitive with Slate-GLM-OFU, a fully adaptive state-of-the-art algorithm. Notably, a slightly modified B-SlateGLinCB empirically matches this baseline. Finally, we demonstrate strong performance in a practical in-context example selection task for language models.

Poster
Adaptive Code Watermarking Through Reinforcement Learning

Zhimeng Guo, Huaisheng Zhu, Siyuan Xu, Hangfan Zhang, Teng Xiao, Minhao Cheng

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As LLMs increasingly generate production code, protecting intellectual property demands watermarking techniques that respect code's strict syntactic constraints. In this work, we introduce CodeTracer, an innovative adaptive code watermarking framework underpinned by a reinforcement learning training paradigm. At its core, CodeTracer features a policy-driven approach that utilizes a parameterized model to intelligently bias token choices during next-token prediction. This strategy ensures that embedded watermarks maintain code functionality while exhibiting subtle yet statistically detectable deviations from typical token distributions. To facilitate policy learning, we devise a comprehensive reward system that seamlessly integrates execution feedback with watermark embedding signals, balancing process-level and outcome-level rewards. To enable gradient-based optimization of these discrete watermarking decisions, we employ Gumbel Top-k reparameterization. Extensive comparative evaluations demonstrate that CodeTracer outperforms state-of-the-art baselines across multiple benchmarks in both watermark detectability and code functionality. Our code is available at https://github.com/TimeLovercc/CodeTracer.

Poster
KernelFoundry: Hardware-Aware Evolutionary GPU Kernel Optimization

Nina Wiedemann, Quentin Leboutet, Michael Paulitsch, Diana Wofk, Benjamin Ummenhofer

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GPU kernel optimization challenges LLMs beyond standard coding tasks, as it requires an understanding of hardware architecture, parallel computing optimization strategies, and profiling outputs. However, most existing approaches leveraging LLMs for kernel generation apply standard prompting and feedback loops, considering hardware only through profiling feedback. We introduce KernelFoundry, an evolutionary framework that efficiently explores the space of GPU kernels through (1) MAP-Elites quality-diversity search with kernel-specific behavioral dimensions to sustain exploration; (2) meta-prompt evolution that co-evolves prompts with kernels to uncover task-specific optimization strategies, and (3) a template-based parameter optimization approach to tune kernels to inputs and hardware. We evaluate this framework on KernelBench, robust-kbench and custom tasks, generating SYCL kernels as a cross-platform GPU programming paradigm, and CUDA kernels for comparison to prior work. Our approach consistently outperforms the baseline methods and achieves an average speedup of 2.3 on KernelBench for SYCL. Moreover, KernelFoundry is implemented as a distributed framework with remote access to diverse hardware, allowing quick benchmarking and featuring a flexible user input layer to support kernel generation for a wide range of real use cases beyond benchmarking.

Poster
TDM-R1: Reinforcing Few-Step Diffusion Models with Non-Differentiable Reward

Yihong Luo, Tianyang Hu, Weijian Luo, Jing Tang

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While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for one- and few-step text-to-image models, scaling from 0.6B to 6B parameters while achieving state-of-the-art performance on both in-domain and out-of-domain metrics.

Poster
Balancing Learning Rates Across Layers: Exact Two-Step Dynamics and Optimal Scaling in Linear Neural Networks

Tianyu Pang, Vignesh Kothapalli, Shenyang Deng, Haohui Wang, Dawei Zhou, Yaoqing Yang

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We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions. In particular, we derive the exact closed-form expressions for the gradients and test loss after one and two steps of gradient descent, enabling a precise characterization of early training dynamics. We characterize how learning rates should scale under the gradient approximation in the first two steps, and prove that performing updates with this approximation yields a tractable surrogate loss with a tight, small approximation error. This formulation enables the theoretical analysis of layer-wise learning rates and reveals a distinct early-training regime: test loss can be minimized by unequal learning rates at the initial step, while equal learning rates become optimal in subsequent steps. Our numerical experiments validate the theory and demonstrate the importance of balancing layer-wise learning rates early during training. The code is available at: [TDCSZ327/Layer-Balancing](https://github.com/TDCSZ327/Layer-Balancing).

Poster
FedPDG: Prediction Discrepancy–Guided Data Generation for Heterogeneous Federated Learning

Yuqi Wang, Jianwei Niu, Xinghao Wu, Xuefeng Liu, Xin Hao

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One emerging approach to mitigating data heterogeneity in Federated Learning (FL) is to employ diffusion models to generate synthetic data for clients, thereby aligning local data distributions with the global distribution. Prior work has primarily focused on balance-oriented augmentation, which assumes a balanced global class distribution and thus generates samples of rare classes to rebalance each client's local dataset. However, in practice, global data distributions are often inherently imbalanced. Moreover, privacy constraints in FL hinder the server’s ability to accurately estimate the global distribution, rendering balance-oriented augmentation suboptimal. This raises a key, underexplored challenge: How can synthetic data be generated and selected to align local distributions with the true, yet unknown, global distribution? Our key insight is that a model’s performance implicitly reflects the data distribution it has been trained on. Based on this observation, we use the performance discrepancy between local and global models to identify the regions where each client’s local dataset is lacking, and generate corresponding samples for clients. Furthermore, we adapt the diffusion model via preference optimization, enabling it to generate data that better aligns with the true global distribution. Extensive experiments on multiple benchmarks demonstrate that FedPDG outperforms state-of-the-art methods, achieving up to 3.82\% improvement.

Poster
Resting Neurons, Active Insights: Robustifying Activation Sparsity in LLMs via Spontaneity

Haotian Xu, Jiannan Yang, Tian Gao, Tsui-Wei Weng, Tengfei Ma

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Activation sparsity offers a compelling route to accelerate large language model (LLM) inference by selectively suppressing hidden activations, yet existing approaches exhibit severe accuracy degradation at high sparsity. We show that this failure stems from representational instability: *activation sparsity disrupts input-dependent activation learned during pretraining, inducing distribution shifts in hidden states*. We address this issue by reframing activation sparsity as a representational alignment problem and introducing **Spontaneous Neurons (SPON)**, a lightweight mechanism inspired by spontaneous neural activity in biological systems. SPON injects a small set of learnable, input-independent activation vectors that act as persistent representational anchors for sparse computation. These vectors are trained via distribution matching to the dense model and can be absorbed into bias terms after training, incurring negligible inference overhead. Across multiple LLM backbones, SPON consistently restores performance, stabilizes latent representations, and preserves generalization. Our results establish SPON as an effective and principled solution for reliable activation-sparse inference, and offer new insights into knowledge retention in LLMs.

Poster
Homophily-Heterogeneity Gradient Surgery for Federated Graph Learning

Sujia Huang, Lele Fu, Shunxin Xiao, Xiaoya Zhang, Chunyan Xu, Tong Zhang, Bo Huang, Zhen Cui

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Federated Graph Learning (FGL) facilitates privacy-preserving collaborative training of graph neural networks, yet homophily heterogeneity across subgraphs can induce optimization conflicts that degrade model generalization. Many existing solutions rely on multi-channel architectures to mitigate such conflicts, which increase the burden on edge devices and lack theoretical convergence analysis. To overcome these limitations, we propose FedGCM, a novel FGL framework with Group-oriented Conflict Mitigation, which aligns inconsistent optimization objectives via a tailored gradient surgery. Specifically, FedGCM first divides clients into distinct groups based on their homophily levels, thereby avoiding exhaustive client-to-client conflict assessments. To resolve inter-group interference, we develop RPGrad, a gradient surgery mechanism based on residual projection, which integrates synergistic knowledge while filtering inter-group conflicts. The refined updates are then transmitted in a group-wise fashion, effectively alleviating optimization conflicts induced by homophily heterogeneity without augmenting the client-side burden. Furthermore, we provide a formal theoretical analysis establishing the convergence. Extensive experiments on both homophilous and heterophilous graphs demonstrate that FedGCM consistently achieves superior performance.

Poster
DIVE: Scaling Diversity in Agentic Task Synthesis for Generalizable Tool Use

Aili Chen, Chi Zhang, Junteng Liu, Jiangjie Chen, Chengyu Du, Yunji Li, Ming Zhong, Qin Wang, Zhengmao Zhu, Jiayuan Song, Ke Ji, Junxian He, Pengyu Zhao, Yanghua Xiao

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Recent work increasingly synthesizes agentic tasks for post-training tool-using LLMs, yet robust generalization under shifts in tasks and toolsets remains an open challenge. We trace this brittleness to insufficient diversity in synthesized training tasks. Scaling diversity is difficult because training requires tasks to remain executable and verifiable, while generalization demands diverse tool types, toolset combinations, and heterogeneous tool-use patterns. We propose DIVE, an evidence-driven recipe that inverts synthesis order, executing diverse real-world tools first and reverse-deriving tasks strictly entailed by the resulting traces, providing grounding by construction. DIVE scales structural diversity along two controllable axes, tool-pool coverage and per-task toolset variety, synthesizing 48k trajectories over 374 tools across five domains that cover 46,398 unique toolsets and 39,810 unique tool-call graphs. Training Qwen3-8B on DIVE data (48k SFT + 3.2k RL) improves by +22 average points across 9 OOD benchmarks and outperforms the strongest 8B baseline by +68%. Under a fixed budget, controlled scaling shows diversity scaling consistently outperforms quantity scaling, even with 4× less data.

Poster
Training-Free Hashing-Based Attention via Binary Principal Components

Daohai Yu, Zhanpeng Zeng, Keyu Chen, Wenhao Li, Zhifeng Shen, Luxi Lin, Ruizhi Qiao, Xing Sun, Rongrong Ji

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Long-context large language models (LLMs) are increasingly deployed in real-world applications, yet self-attention remains a major efficiency bottleneck -- especially during decoding -- due to the necessity of repeatedly processing ever-growing key-value (KV) caches. Existing sparse attention reduce computation by attending to fewer KV pairs, but often suffer from substantial accuracy degradation, require additional training, or rely on expensive hashing. In this work, we present \textbf{BinaryPC}, a training-free, data-aware hashing-based sparse attention for long-context LLMs. BinaryPC constructs compact binary hash codes and corresponding hash function by computing binary principal components of data. Unlike Locality-Sensitive Hashing (LSH) with data-independent random projections or learned non-linear hashing methods, BinaryPC constructs binary codes that explicitly preserve the structural information of data without requiring gradient-based training. Comprehensive experiments across multiple model families and long-context benchmarks show that BinaryPC preserves accuracy relative to full attention while achieving superior performance among sparse and hashing-based baselines. On modern GPUs, BinaryPC improves end-to-end decoding throughput by 3.56$\times$ over the FlashAttention kernel. Our code is available at https://github.com/yudaohai666/BPC.

Poster
RSA-CP: Efficient Conformal Prediction in Small-Sample Regimes via Random Score Alignment

Pankaj Bhagwat, Zhixian Yang, Yihao Wang, Bei Jiang, Linglong Kong

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Conformal Prediction (CP) provides rigorous finite-sample coverage guarantees, yet its statistical efficiency hinges critically on the size of the calibration set. In data-scarce regimes, CP often suffers from volatile quantile estimation, leading to overly conservative and wide prediction intervals. To address this, we propose Random Score Alignment-Conformal Prediction (RSA-CP), a simple framework designed to improve sample efficiency in small-sample CP. Instead of requiring the computationally intensive generation of full synthetic datasets, RSA-CP enhances calibration by directly aligning real scores with a high-resolution reference score distribution. By employing an optimal transport mapping, our framework refines "step-like" quantile increments through a globally optimal use of reference information. We provide theoretical guarantees establishing that RSA-CP maintains robust coverage without any distributional assumptions on the reference scores. Empirical evaluations demonstrate that RSA-CP consistently produces shorter and more precise prediction intervals while maintaining finite-sample coverage guarantees. Overall, RSA-CP offers a computationally efficient and theoretically grounded solution for robust uncertainty quantification under limited data.

Poster
Sample-Efficient Diffusion-based Reinforcement Learning with Critic Guidance

Shutong Ding, Zejia Zhong, Zhongyi Wang, Ke Hu, Bikang Pan, Jingya Wang, Ye Shi

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Recent advances in reinforcement learning (RL) have achieved great successes by leveraging the multimodality and exploration capability of diffusion policies. Among these approaches, one representative branch focuses on the sampling-based policy optimization. This design enables better exploration capability of the diffusion model, particularly at the beginning of training, but suffer from low exploitation in Q-value information, resulting in a slow policy convergence. Another branch pays attention to gradient-based policy optimization, which sufficiently exploits the gradient of the Q function yet tends to collapse into a unimodal policy with low diversity. To address this issue, we propose CGPO, \textbf{C}ritic-\textbf{G}uided diffusion \textbf{P}olicy \textbf{O}ptimization, which effectively balances exploration and exploitation with the training-free guidance technique integrated into the denoising process of diffusion policy. Concretely, CGPO steers action generation toward high-value regions defined by the critic network and uses the guided actions as regression objectives. In this manner, CGPO reduces the time required to obtain high-quality actions and improves final performance with better balance between the exploration-exploitation tradeoff. We validate the effectiveness of CGPO on 5 MuJoCo locomotion tasks, and CGPO achieves state-of-the-art performance compared with existing diffusion-based RL methods. Notably, CGPO is the first success to incorporate diffusion policy into real-world RL, with its superior performance on Franka robot arm grasping tasks. Our official page is released at \url{https://dingsht.tech/cgpo-webpage}.

Poster
Deep Coupling Learning for Solving PDEs

Lingshi MENG, Haosen Shi, Sinno Jialin Pan

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Physics-Informed Neural Networks (PINNs) represent a significant advancement in computational methods for solving partial differential equations (PDEs). However, the adoption of deeper neural network architectures presents significant challenges, as they struggle to address differential-related complications that arise during the computation of derivatives over the input of PINNs. These complications extend beyond traditional vanishing and exploding gradients to include vanishing and exploding differentials, with both phenomena becoming more severe as networks grow deeper. By examining the computation graph of derivatives in deep neural networks, we identify key bottlenecks causing numerical instabilities in deep architectures. In response, we introduce a novel approach that utilizes Coupling Layers with carefully regulated spectral norms of Jacobian matrices to stabilize and facilitate deep PINN training, effectively addressing differential-related challenges and improving model stability. Our proposed architecture successfully mitigates the fundamental constraints of deeper PINNs while maximizing their capabilities through consistent differential propagation. Comprehensive evaluations show that our approach surpasses conventional shallow PINN methods and alternative deep PINN designs across a range of challenging problems.

Poster
ExCyTIn-Bench: Evaluating LLM agents on Cyber Threat Investigation

Yiran Wu, Mauricio Velazco, Andrew Zhao, Manuel Raúl Meléndez Luján, Srisuma Movva, Yogesh K Roy, Quang Nguyen, Roberto Rodriguez, Qingyun Wu, Michael Albada, Julia Kiseleva, Anand Mudgerikar

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We present ExCyTIn-Bench, the first benchmark to Evaluate an LLM agent X on the task of Cyber Threat Investigation through security questions derived from investigation graphs. Real‑world security analysts must sift through a large number of heterogeneous security logs, follow multi‑hop chains of evidence to investigate threats. With the developments of LLMs, building LLM-based agents for automatic threat investigation is a promising direction. We construct a benchmark from a controlled Azure tenant including a SQL environment covering 57 log tables from Microsoft Sentinel and related services, and 7542 generated questions. We leverage security logs extracted with expert-crafted detection logic to build threat investigation graphs, and then generate questions with LLMs using paired nodes on the graph, taking the start node as background context and the end node as answer. Anchoring each question to these explicit nodes and edges not only provides automatic, explainable ground truth answers but also makes the pipeline reusable and readily extensible to new logs. Our comprehensive experiments on the test set with different models confirm the difficulty of the task: the best model so far can achieve a reward of 0.606, leaving much headroom for future research.

Poster
Semi-Supervised Neural Super-Resolution for Mesh-Based Simulations

Jiyeon Kim, Youngjoon Hong, Won-Yong Shin

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Mesh-based simulations provide high-fidelity solutions to partial differential equations (PDEs), but achieving such accuracy typically requires fine meshes, leading to substantial computational overhead. Super-resolution techniques aim to mitigate this cost by reconstructing high-resolution (HR), high-fidelity solutions from low-cost, low-resolution (LR) counterparts. However, training neural networks for super-resolution often demands large amounts of expensive HR supervision data. To address this challenge, we propose SuperMeshNet, an HR data-efficient super-resolution framework for mesh-based simulations aided by message passing neural networks (MPNNs). At its core, SuperMeshNet introduces complementary learning, a semi-supervised approach that effectively leverages both 1) a small amount of paired LR-HR data and 2) abundant unpaired LR data via two jointly trained, complementary MPNN-based models. Additionally, our model is enriched by inductive biases, which are empirically shown to further improve super-resolution performance. Extensive experiments demonstrate that SuperMeshNet requires 90% less HR data to achieve even lower root mean square error (RMSE) than that of the fully supervised benchmark without the inductive biases. The source code and datasets are available at https://github.com/jykim-git/SuperMeshNet.git.

Poster
RiskZero: Plan More to Risk Less with a Learned Model

Yousef Yassin, Junfeng Wen

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*AlphaZero* and *MuZero* have demonstrated superhuman performance across a range of strategic tasks. Yet their reliance on maximizing expected returns limits their use in real-world settings, where even high-return policies may incur rare but catastrophic failures. We introduce *RiskZero* to address this limitation; the first *MuZero*-family method for risk-sensitive decision-making, and planning with *zero* prior knowledge of environment dynamics. *RiskZero* learns distributional quantities to estimate trajectory-level risk, guiding search toward policies that explicitly avoid rare but severe outcomes. We establish theoretical convergence to optimal, stationary risk-sensitive policies and validate our approach on environments designed to test risk-sensitive learning from pixels, as well as on larger-scale combinatorial tasks. Across all settings, *RiskZero* consistently outperforms state-of-the-art risk-sensitive baselines, and improves sample efficiency, providing a general framework for safer and reliable model-based reinforcement learning under uncertainty.

Poster
VT-Bench: A Unified Benchmark for Visual-Tabular Multi-Modal Learning

Ziyi Jia, Zi-Jian Cheng, Xinyue Zhang, Kun-Yang Yu, Zhi Zhou, Yu-Feng Li, Lan-Zhe Guo

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Multi-model learning has attracted great attention in visual-text tasks. However, visual-tabular data, which plays a pivotal role in high-stakes domains like healthcare and industry, remains underexplored. In this paper, we introduce \textit{VT-Bench}, the first unified benchmark for standardizing vision-tabular discriminative prediction and generative reasoning tasks. VT-Bench aggregates 14 datasets across 9 domains (medical-centric, while covering pets, media, and transportation) with over 756K samples. We evaluate 23 representative models, including unimodal experts, specialized visual-tabular models, general-purpose vision-language models (VLMs), and tool-augmented methods, highlighting substantial challenges of visual-tabular learning. We believe VT-Bench will stimulate the community to build more powerful multi-modal vision-tabular foundation models. Benchmark: \url{https://github.com/LAMDA-NeSy/VT-Bench}

Poster
Evaluating Relational Reasoning in LLMs with REL

Lukas Fesser, Yasha Ektefaie, Ada Fang, Sham M. Kakade, Marinka Zitnik

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Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. While this capability is essential for scientific reasoning, most existing evaluations of relational reasoning in large language models focus on structured inputs such as tables, graphs, or synthetic relational tasks, and do not isolate the sources of difficulty that arise from higher-arity relational binding. We study this problem through the lens of *Relational Complexity (RC)*, defined as the minimum number of independent entities or operands that must be simultaneously bound to apply a relation. RC provides a principled way to vary reasoning difficulty independently of confounders such as input size, vocabulary, and representational choices. Building on RC, we introduce REL, a generative benchmark framework spanning algebra, chemistry, and biology that varies RC within each domain. Evaluating frontier LLMs, we observe a consistent and monotonic degradation in performance as RC increases, even when the total number of entities is held fixed. This failure mode persists under increased test-time compute and with in-context learning, suggesting a limitation tied to the arity of the required relational binding rather than insufficient inference steps or exposure to examples. Our results identify a well-defined regime of higher-arity reasoning in which current models struggle and motivate revisiting reasoning benchmarks through the lens of relational complexity.

Poster