NeurIPS 2025 Papers

Conference on Neural Information Processing Systems

Decision breakdown

5,812papers

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

  • Oral
    931.6%
  • Spotlight
    73912.7%
  • Poster
    4,98085.7%

Browse all papers

Towards Understanding Transformers in Learning Random Walks

Wei Shi, Yuan Cao

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Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of transformers has not been well understood in theory. In this paper, we study the capability and interpretability of transformers in learning a family of classic statistical models, namely random walks on circles. We theoretically demonstrate that, after training with gradient descent, a one-layer transformer model can achieve optimal accuracy in predicting random walks. Importantly, our analysis reveals that the trained model is interpretable: the trained softmax attention serves as a token selector, focusing on the direct parent state; subsequently, the value matrix executes a one-step probability transition to predict the location of the next state based on this parent state. We also show that certain edge cases not covered by our theory are indeed failure cases, demonstrating that our theoretical conditions are tight. By investigating these success and failure cases, it is revealed that gradient descent with small initialization may fail or struggle to converge to a good solution in certain simple tasks even beyond random walks. Experiments are conducted to support our theoretical findings.

Poster
MiNT: Multi-Network Transfer Benchmark for Temporal Graph Learning

Kiarash Shamsi, Tran Gia Bao Ngo, Razieh Shirzadkhani, Shenyang Huang, Farimah Poursafaei, Poupak Azad, Reihaneh Rabbany, Baris Coskunuzer, Guillaume Rabusseau, Cuneyt Gurcan Akcora

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Temporal Graph Learning (TGL) aims to discover patterns in evolving networks or temporal graphs and leverage these patterns to predict future interactions. However, most existing research focuses on learning from a single network in isolation, leaving the challenges of within-domain and cross-domain generalization largely unaddressed. In this study, we introduce a new benchmark of 84 real-world temporal transaction networks and propose **Temporal Multi-network Transfer (MiNT)**, a pre-training framework designed to capture transferable temporal dynamics across diverse networks. We train MiNT models on up to 64 transaction networks and evaluate their generalization ability on 20 held-out, unseen networks. Our results show that MiNT consistently outperforms individually trained models, revealing a strong relation between the number of pre-training networks and transfer performance. These findings highlight scaling trends in temporal graph learning and underscore the importance of network diversity in improving generalization. This work establishes the first large-scale benchmark for studying transferability in TGL and lays the groundwork for developing Temporal Graph Foundation Models. Our code is available at \url{https://github.com/benjaminnNgo/ScalingTGNs}

Poster
Optimal Spectral Transitions in High-Dimensional Multi-Index Models

Leonardo Defilippis, Yatin Dandi, Pierre Mergny, Florent Krzakala, Bruno Loureiro

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We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of neural networks, results beyond the single-index setting remain elusive. In this work, we introduce spectral algorithms based on the linearization of a message passing scheme tailored to this problem. Our main contribution is to show that the proposed methods achieve the optimal reconstruction threshold. Leveraging a high-dimensional characterization of the algorithms, we show that above the critical threshold the leading eigenvector correlates with the relevant index subspace, a phenomenon reminiscent of the Baik–Ben Arous–Peche (BBP) transition in spiked models arising in random matrix theory. Supported by numerical experiments and a rigorous theoretical framework, our work bridges critical gaps in the computational limits of weak learnability in multi-index model.

Poster
Direct3D-S2: Gigascale 3D Generation Made Easy with Spatial Sparse Attention

Shuang Wu, Youtian Lin, Feihu Zhang, Yifei Zeng, Yikang Yang, Yajie Bao, Jiachen Qian, Siyu Zhu, Xun Cao, Philip Torr, Yao Yao

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Generating high-resolution 3D shapes using volumetric representations such as Signed Distance Functions (SDFs) presents substantial computational and memory challenges. We introduce Direct3D-S2, a scalable 3D generation framework based on sparse volumes that achieves superior output quality with dramatically reduced training costs. Our key innovation is the Spatial Sparse Attention (SSA) mechanism, which greatly enhances the efficiency of Diffusion Transformer (DiT) computations on sparse volumetric data. SSA allows the model to effectively process large token sets within sparse volumes, significantly reducing computational overhead and achieving a 3.9$\times$ speedup in the forward pass and a 9.6$\times$ speedup in the backward pass. Our framework also includes a variational autoencoder (VAE) that maintains a consistent sparse volumetric format across input, latent, and output stages. Compared to previous methods with heterogeneous representations in 3D VAE, this unified design significantly improves training efficiency and stability. Our model is trained on public datasets, and experiments demonstrate that Direct3D-S2 not only surpasses state-of-the-art methods in generation quality and efficiency, but also enables training at 1024³ resolution using only 8 GPUs—a task typically requiring at least 32 GPUs for volumetric representations at $256^3$ resolution, thus making gigascale 3D generation both practical and accessible. Project page: https://www.neural4d.com/research-page/direct3d-s2.

Poster
CoDA: Coordinated Diffusion Noise Optimization for Whole-Body Manipulation of Articulated Objects

Huaijin Pi, Zhi Cen, Zhiyang Dou, Taku Komura

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Synthesizing whole-body manipulation of articulated objects, including body motion, hand motion, and object motion, is a critical yet challenging task with broad applications in virtual humans and robotics. The core challenges are twofold. First, achieving realistic whole-body motion requires tight coordination between the hands and the rest of the body, as their movements are interdependent during manipulation. Second, articulated object manipulation typically involves high degrees of freedom and demands higher precision, often requiring the fingers to be placed at specific regions to actuate movable parts. To address these challenges, we propose a novel coordinated diffusion noise optimization framework. Specifically, we perform noise-space optimization over three specialized diffusion models for the body, left hand, and right hand, each trained on its own motion dataset to improve generalization. Coordination naturally emerges through gradient flow along the human kinematic chain, allowing the global body posture to adapt in response to hand motion objectives with high fidelity. To further enhance precision in hand-object interaction, we adopt a unified representation based on basis point sets (BPS), where end-effector positions are encoded as distances to the same BPS used for object geometry. This unified representation captures fine-grained spatial relationships between the hand and articulated object parts, and the resulting trajectories serve as targets to guide the optimization of diffusion noise, producing highly accurate interaction motion. We conduct extensive experiments demonstrating that our method outperforms existing approaches in motion quality and physical plausibility, and enables various capabilities such as object pose control, simultaneous walking and manipulation, and whole-body generation from hand-only data. The code will be released for reproducibility.

Poster
Is This Tracker On? A Benchmark Protocol for Dynamic Tracking

Ilona Demler, Saumya Chauhan, Georgia Gkioxari

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We introduce ITTO, a challenging new benchmark suite for evaluating and diagnosing the capabilities and limitations of point tracking methods. Our videos are sourced from existing datasets and egocentric real-world recordings, with high-quality human annotations collected through a multi-stage pipeline. ITTO captures the motion complexity, occlusion patterns, and object diversity characteristic of real-world scenes -- factors that are largely absent in current benchmarks. We conduct a rigorous analysis of state-of-the-art tracking methods on ITTO, breaking down performance along key axes of motion complexity. Our findings reveal that existing trackers struggle with these challenges, particularly in re-identifying points after occlusion, highlighting critical failure modes. These results point to the need for new modeling approaches tailored to real-world dynamics. We envision ITTO as a foundation testbed for advancing point tracking and guiding the development of more robust tracking algorithms.

Poster
Harnessing the Computation Redundancy in ViTs to Boost Adversarial Transferability

Jiani Liu, Zhiyuan Wang, Zeliang Zhang, Chao Huang, Susan Liang, Yunlong Tang, Chenliang Xu

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Vision Transformers (ViTs) have demonstrated impressive performance across a range of applications, including many safety-critical tasks. Many previous studies have observed that adversarial examples crafted on ViTs exhibit higher transferability than those crafted on CNNs, indicating that ViTs contain structural characteristics favorable for transferable attacks. In this work, we take a further step to deeply investigate the role of computational redundancy brought by its unique characteristics in ViTs and its impact on adversarial transferability. Specifically, we identify two forms of redundancy, including the data-level and model-level, that can be harnessed to amplify attack effectiveness. Building on this insight, we design a suite of techniques, including attention sparsity manipulation, attention head permutation, clean token regularization, ghost MoE diversification, and learn to robustify before the attack. A dynamic online learning strategy is also proposed to fully leverage these operations to enhance the adversarial transferability. Extensive experiments on the ImageNet-1k dataset validate the effectiveness of our approach, showing that our methods significantly outperform existing baselines in both transferability and generality across diverse model architectures, including different variants of ViTs and mainstream Vision Large Language Models (VLLMs).

Poster
Cost-Sensitive Freeze-thaw Bayesian Optimization for Efficient Hyperparameter Tuning

Dong Bok Lee, Aoxuan Silvia Zhang, Byungjoo Kim, Junhyeon Park, Steven Adriaensen, Juho Lee, Sung Ju Hwang, Hae Beom Lee

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In this paper, we address the problem of cost-sensitive hyperparameter optimization (HPO) built upon freeze-thaw Bayesian optimization (BO). Specifically, we assume a scenario where users want to early-stop the HPO process when the expected performance improvement is not satisfactory with respect to the additional computational cost. Motivated by this scenario, we introduce \emph{utility} in the freeze-thaw framework, a function describing the trade-off between the cost and performance that can be estimated from the user's preference data. This utility function, combined with our novel acquisition function and stopping criterion, allows us to dynamically continue training the configuration that we expect to maximally improve the utility in the future, and also automatically stop the HPO process around the maximum utility. Further, we improve the sample efficiency of existing freeze-thaw methods with transfer learning to develop a specialized surrogate model for the cost-sensitive HPO problem. We validate our algorithm on established multi-fidelity HPO benchmarks and show that it outperforms all the previous freeze-thaw BO and transfer-BO baselines we consider, while achieving a significantly better trade-off between the cost and performance.

Poster
MRO: Enhancing Reasoning in Diffusion Language Models via Multi-Reward Optimization

Chenglong Wang, Yang Gan, Hang Zhou, Chi Hu, Yongyu Mu, Kai Song, MuRun Yang, Bei Li, Chunliang Zhang, Tongran Liu, Jingbo Zhu, Zhengtao Yu, Tong Xiao

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Recent advances in diffusion language models (DLMs) have presented a promising alternative to traditional autoregressive large language models (LLMs). However, DLMs still lag behind LLMs in reasoning performance, especially as the number of denoising steps decreases. Our analysis reveals that this shortcoming arises primarily from the independent generation of masked tokens across denoising steps, which fails to capture the token correlation. In this paper, we define two types of token correlation: intra-sequence correlation and inter-sequence correlation, and demonstrate that enhancing these correlations improves reasoning performance. To this end, we propose a Multi-Reward Optimization (MRO) approach, which encourages DLMs to consider the token correlation during the denoising process. More specifically, our MRO approach leverages test-time scaling, reject sampling, and reinforcement learning to directly optimize the token correlation with multiple elaborate rewards. Additionally, we introduce group step and importance sampling strategies to mitigate reward variance and enhance sampling efficiency. Through extensive experiments, we demonstrate that MRO not only improves reasoning performance but also achieves significant sampling speedups while maintaining high performance on reasoning benchmarks.

Poster
Seeing through Uncertainty: Robust Task-Oriented Optimization in Visual Navigation

Yiyuan Pan, Yunzhe Xu, Zhe Liu, Hesheng Wang

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Visual navigation is a fundamental problem in embodied AI, yet practical deployments demand long-horizon planning capabilities to address multi-objective tasks. A major bottleneck is data scarcity: policies learned from limited data often overfit and fail to generalize OOD. Existing neural network-based agents typically increase architectural complexity that paradoxically become counterproductive in the small-sample regime. This paper introduce NeuRO, a integrated learning-to-optimize framework that tightly couples perception networks with downstream task-level robust optimization. Specifically, NeuRO addresses core difficulties in this integration: (i) it transforms noisy visual predictions under data scarcity into convex uncertainty sets using Partially Input Convex Neural Networks (PICNNs) with conformal calibration, which directly parameterize the optimization constraints; and (ii) it reformulates planning under partial observability as a robust optimization problem, enabling uncertainty-aware policies that transfer across environments. Extensive experiments on both unordered and sequential multi-object navigation tasks demonstrate that NeuRO establishes SoTA performance, particularly in generalization to unseen environments. Our work thus presents a significant advancement for developing robust, generalizable autonomous agents.

Poster
SynBrain: Enhancing Visual-to-fMRI Synthesis via Probabilistic Representation Learning

Weijian Mai, Jiamin Wu, Yu Zhu, Zhouheng Yao, Dongzhan Zhou, Andrew Luo, Qihao Zheng, Wanli Ouyang, Chunfeng Song

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Deciphering how visual stimuli are transformed into cortical responses is a fundamental challenge in computational neuroscience. This visual-to-neural mapping is inherently a one-to-many relationship, as identical visual inputs reliably evoke variable hemodynamic responses across trials, contexts, and subjects. However, existing deterministic methods struggle to simultaneously model this biological variability while capturing the underlying functional consistency that encodes stimulus information. To address these limitations, we propose SynBrain, a generative framework that simulates the transformation from visual semantics to neural responses in a probabilistic and biologically interpretable manner. SynBrain introduces two key components: (i) BrainVAE models neural representations as continuous probability distributions via probabilistic learning while maintaining functional consistency through visual semantic constraints; (ii) A Semantic-to-Neural Mapper acts as a semantic transmission pathway, projecting visual semantics into the neural response manifold to facilitate high-fidelity fMRI synthesis. Experimental results demonstrate that SynBrain surpasses state-of-the-art methods in subject-specific visual-to-fMRI encoding performance. Furthermore, SynBrain adapts efficiently to new subjects with few-shot data and synthesizes high-quality fMRI signals that are effective in improving data-limited fMRI-to-image decoding performance. Beyond that, SynBrain reveals functional consistency across trials and subjects, with synthesized signals capturing interpretable patterns shaped by biological neural variability. Our code is available at https://github.com/MichaelMaiii/SynBrain.

Poster
BurstDeflicker: A Benchmark Dataset for Flicker Removal in Dynamic Scenes

Lishen Qu, Zhihao Liu, Shihao Zhou, LUO YAQI, Jie Liang, Hui Zeng, Lei Zhang, Jufeng Yang

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Flicker artifacts in short-exposure images are caused by the interplay between the row-wise exposure mechanism of rolling shutter cameras and the temporal intensity variations of alternating current (AC)-powered lighting. These artifacts typically appear as uneven brightness distribution across the image, forming noticeable dark bands. Beyond compromising image quality, this structured noise also affects high-level tasks, such as object detection and tracking, where reliable lighting is crucial. Despite the prevalence of flicker, the lack of a large-scale, realistic dataset has been a significant barrier to advancing research in flicker removal. To address this issue, we present BurstDeflicker, a scalable benchmark constructed using three complementary data acquisition strategies. First, we develop a Retinex-based synthesis pipeline that redefines the goal of flicker removal and enables controllable manipulation of key flicker-related attributes (e.g., intensity, area, and frequency), thereby facilitating the generation of diverse flicker patterns. Second, we capture 4,000 real-world flicker images from different scenes, which help the model better understand the spatial and temporal characteristics of real flicker artifacts and generalize more effectively to wild scenarios. Finally, due to the non-repeatable nature of dynamic scenes, we propose a green-screen method to incorporate motion into image pairs while preserving real flicker degradation. Comprehensive experiments demonstrate the effectiveness of our dataset and its potential to advance research in flicker removal.

Poster
PT-MoE: An Efficient Finetuning Framework for Integrating Mixture-of-Experts into Prompt Tuning

Zongqian Li, Yixuan Su, Nigel Collier

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Parameter-efficient fine-tuning (PEFT) methods have shown promise in adapting large language models, yet existing approaches exhibit counter-intuitive phenomena: integrating either matrix decomposition or mixture-of-experts (MoE) individually decreases performance across tasks, though decomposition improves results on specific domains despite reducing parameters, while MoE increases parameter count without corresponding decrease in training efficiency. Motivated by these observations and the modular nature of PT, we propose PT-MoE, a novel framework that integrates matrix decomposition with MoE routing for efficient PT. Evaluation results across 17 datasets demonstrate that PT-MoE achieves state-of-the-art performance in both question answering (QA) and mathematical problem solving tasks, improving F1 score by 1.49 points over PT and 2.13 points over LoRA in QA tasks, while improving mathematical accuracy by 10.75 points over PT and 0.44 points over LoRA, all while using 25% fewer parameters than LoRA. Our analysis reveals that while PT methods generally excel in QA tasks and LoRA-based methods in math datasets, the integration of matrix decomposition and MoE in PT-MoE yields complementary benefits: decomposition enables efficient parameter sharing across experts while MoE provides dynamic adaptation, collectively enabling PT-MoE to demonstrate cross-task consistency and generalization abilities. These findings, along with ablation studies on routing mechanisms and architectural components, provide insights for future PEFT methods.

Poster
PointMapPolicy: Structured Point Cloud Processing for Multi-Modal Imitation Learning

Xiaogang Jia, Qian Wang, Anrui Wang, Han A. Wang, Balázs Gyenes, Emiliyan Gospodinov, Xinkai Jiang, Ge Li, Hongyi Zhou, Weiran Liao, Xi Huang, Maximilian Beck, Moritz Reuss, Rudolf Lioutikov, Gerhard Neumann

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Robotic manipulation systems benefit from complementary sensing modalities, where each provides unique environmental information. Point clouds capture detailed geometric structure, while RGB images provide rich semantic context. Current point cloud methods struggle to capture fine-grained detail, especially for complex tasks, which RGB methods lack geometric awareness, which hinders their precision and generalization. We introduce PointMapPolicy, a novel approach that conditions diffusion policies on structured grids of points without downsampling. The resulting data type makes it easier to extract shape and spatial relationships from observations, and can be transformed between reference frames. Yet due to their structure in a regular grid, we enable the use of established computer vision techniques directly to 3D data. Using xLSTM as a backbone, our model efficiently fuses the point maps with RGB data for enhanced multi-modal perception. Through extensive experiments on the RoboCasa and CALVIN benchmarks and real robot evaluations, we demonstrate that our method achieves state-of-the-art performance across diverse manipulation tasks. The overview and demos are available on our project page: https://point-map.github.io/Point-Map/

Poster
How to Learn a Star: Binary Classification with Starshaped Polyhedral Sets

Marie-Charlotte Brandenburg, Katharina Jochemko

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We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate the expressivity of these function classes and describe the combinatorial and geometric structure of the loss landscape, most prominently the sublevel sets, for two loss-functions: the 0/1-loss (discrete loss) and a log-likelihood loss function. In particular, we give explicit bounds on the VC dimension of this model, and concretely describe the sublevel sets of the discrete loss as chambers in a hyperplane arrangement. For the log-likelihood loss, we give sufficient conditions for the optimum to be unique, and describe the geometry of the optimum when varying the rate parameter of the underlying exponential probability distribution.

Poster
SMMILE: An expert-driven benchmark for multimodal medical in-context learning

Melanie Rieff, Maya Varma, Ossian Rabow, Subathra Adithan, Julie Kim, Ken Chang, Hannah Lee, Nidhi Rohatgi, Christian Bluethgen, Mohamed S Muneer, Jean-Benoit Delbrouck, Michael Moor

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Multimodal in-context learning (ICL) remains underexplored despite significant potential for domains such as medicine. Clinicians routinely encounter diverse, specialized tasks requiring adaptation from limited examples, such as drawing insights from a few relevant prior cases or considering a constrained set of differential diagnoses. While multimodal large language models (MLLMs) have shown advances in medical visual question answering (VQA), their ability to learn multimodal tasks from context is largely unknown. We introduce SMMILE, the first expert-driven multimodal ICL benchmark for medical tasks. Eleven medical experts curated problems, each including a multimodal query and multimodal in-context examples as task demonstrations. SMMILE encompasses 111 problems (517 question-image-answer triplets) covering 6 medical specialties and 13 imaging modalities. We further introduce SMMILE++, an augmented variant with 1038 permuted problems. A comprehensive evaluation of 15 MLLMs demonstrates that most models exhibit moderate to poor multimodal ICL ability in medical tasks. In open-ended evaluations, ICL contributes only an 8% average improvement over zero-shot on SMMILE and 9.4% on SMMILE++. We observe a susceptibility for irrelevant in-context examples: even a single noisy or irrelevant example can degrade performance by up to 9.5%. Moreover, we observe that MLLMs are affected by a recency bias, where placing the most relevant example last can lead to substantial performance improvements of up to 71%. Our findings highlight critical limitations and biases in current MLLMs when learning multimodal medical tasks from context. SMMILE is available at https://smmile-benchmark.github.io.

Poster
GLSim: Detecting Object Hallucinations in LVLMs via Global-Local Similarity

Seongheon Park, Sharon Li

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Object hallucination in large vision-language models presents a significant challenge to their safe deployment in real-world applications. Recent works have proposed object-level hallucination scores to estimate the likelihood of object hallucination; however, these methods typically adopt either a global or local perspective in isolation, which may limit detection reliability. In this paper, we introduce GLSim, a novel training-free object hallucination detection framework that leverages complementary global and local embedding similarity signals between image and text modalities, enabling more accurate and reliable hallucination detection in diverse scenarios. We comprehensively benchmark existing object hallucination detection methods and demonstrate that GLSim achieves superior detection performance, outperforming competitive baselines by a significant margin.

Poster
Uncertainty Quantification for Deep Regression using Contextualised Normalizing Flows

Adriel Sosa Marco, John D. Kirwan, Alexia Toumpa, Simos Gerasimou

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Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional information, neglecting the effect of multimodal or asymmetric distributions on decision-making. Similarly, full or approximated Bayesian methods, while yielding the predictive posterior density, demand major modifications to the model architecture and retraining. We introduce MCNF, a novel post hoc uncertainty quantification method that produces both prediction intervals and the full conditioned predictive distribution. MCNF operates on top of the underlying trained predictive model; thus, no predictive model retraining is needed. We provide experimental evidence that the MCNF-based uncertainty estimate is well calibrated, is competitive with state-of-the-art uncertainty quantification methods, and provides richer information for downstream decision-making tasks

Poster
ThinkBench: Dynamic Out-of-Distribution Evaluation for Robust LLM Reasoning

Shulin Huang, Linyi Yang, Yan Song, Shuang Chen, Leyang Cui, Ziyu Wan, Qingcheng Zeng, Ying Wen, Kun Shao, Weinan Zhang, Jun Wang, Yue Zhang

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Evaluating large language models (LLMs) poses significant challenges, particularly due to issues of data contamination and the leakage of correct answers. To address these challenges, we introduce ThinkBench, a novel evaluation framework designed to robustly evaluate the reasoning capability of LLMs. ThinkBench proposes a dynamic data generation method for constructing out-of-distribution (OOD) datasets and offers an OOD dataset that contains 2,912 samples drawn from reasoning tasks. ThinkBench unifies the evaluation of reasoning models and non-reasoning models. We evaluate 16 LLMs and 4 PRMs under identical experimental conditions and show that most of the LLMs' performance are far from robust and they face a certain level of data leakage. By dynamically generating OOD datasets, ThinkBench effectively provides a reliable evaluation of LLMs and reduces data contamination impact. Our data and codes are available at https://github.com/huangshulin123/ThinkBench.

Poster
Optimality and NP-Hardness of Transformers in Learning Markovian Dynamical Functions

Yanna Ding, Songtao Lu, Yingdong Lu, Tomasz J Nowicki, Jianxi Gao

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Transformer architectures can solve unseen tasks based on input-output pairs in a given prompt due to in-context learning (ICL). Existing theoretical studies on ICL have mainly focused on linear regression tasks, often with i.i.d. inputs. To understand how transformers express in-context learning when modeling dynamics-driven functions, we investigate Markovian function learning through a structured ICL setup, where we characterize the loss landscape to reveal underlying optimization behaviors. Specifically, we (1) provide the closed-form expression of the global minimizer (in an enlarged parameter space) for a single-layer linear self-attention (LSA) model; (2) prove that recovering transformer parameters that realize the optimal solution is NP-hard in general, revealing a fundamental limitation of one-layer LSA in representing structured dynamical functions; and (3) supply a novel interpretation of a multilayer LSA as performing preconditioned gradient descent to optimize multiple objectives beyond the square loss. These theoretical results are numerically validated using simplified transformers.

Poster