ICLR 2025 Papers

Graph neural networks (GNNs) have recently emerged as powerful tools for solving complex optimization problems, often being employed to approximate solution mappings. Empirical evidence shows that even shallow GNNs (with fewer than ten layers) can achieve strong performance in predicting optimal solutions to linear programming (LP) problems. This finding is somewhat counter-intuitive, as LPs are global optimization problems, while shallow GNNs predict based on local information. Although previous theoretical results suggest that GNNs have the expressive power to solve LPs, they require deep architectures whose depth grows at least polynomially with the problem size, and thus leave the underlying principle of this empirical phenomenon still unclear. In this paper, we examine this phenomenon through the lens of distributed computing and average-case analysis. We establish that the expressive power of GNNs for LPs is closely related to well-studied distributed algorithms for LPs. Specifically, we show that any $d$-round distributed LP algorithm can be simulated by a $d$-depth GNN, and vice versa. In particular, by designing a new distributed LP algorithm and then unrolling it, we prove that constant-depth, constant-width GNNs suffice to solve sparse binary LPs effectively. Here, in contrast with previous analyses focusing on worst-case scenarios, in which we show that GNN depth must increase with problem size by leveraging an impossibility result about distributed LP algorithms, our analysis shifts the focus to the average-case performance, and shows that constant GNN depth then becomes sufficient no matter how large the problem size is. Our theory is validated by numerical results.

In this work, we explore the mechanism of in-context learning (ICL) on out-of-distribution (OOD) tasks that were not encountered during training. To achieve this, we conduct synthetic experiments where the objective is to learn OOD mathematical functions through ICL using a GPT-2 model. We reveal that Transformers may struggle to learn OOD task functions through ICL. Specifically, ICL performance resembles implementing a function within the pretraining hypothesis space and optimizing it with gradient descent based on the in-context examples. Additionally, we investigate ICL's well-documented ability to learn unseen abstract labels in context. We demonstrate that such ability only manifests in the scenarios without distributional shifts and, therefore, may not serve as evidence of new-task-learning ability. Furthermore, we assess ICL's performance on OOD tasks when the model is pretrained on multiple tasks. Both empirical and theoretical analyses demonstrate the existence of the \textbf{low-test-error preference} of ICL, where it tends to implement the pretraining function that yields low test error in the testing context. We validate this through numerical experiments. This new theoretical result, combined with our empirical findings, elucidates the mechanism of ICL in addressing OOD tasks.

Text-rich visual understanding—the ability to interpret both textual content and visual elements within a scene—is crucial for multimodal large language models (MLLMs) to effectively interact with structured environments. We propose leveraging webpage UIs as a naturally structured and diverse data source to enhance MLLMs’ capabilities in this area. Existing approaches, such as rule-based extraction, multimodal model captioning, and rigid HTML parsing, are hindered by issues like noise, hallucinations, and limited generalization. To overcome these challenges, we introduce MultiUI, a dataset of 7.3 million samples spanning various UI types and tasks, structured using enhanced accessibility trees and task taxonomies. By scaling multimodal instructions from web UIs through LLMs, our dataset enhances generalization beyond web domains, significantly improving performance in document understanding, GUI comprehension, grounding, and advanced agent tasks. This demonstrates the potential of structured web data to elevate MLLMs’ proficiency in processing text-rich visual environments and generalizing across domains.

Recent advancements in Transformer-based large language models (LLMs) have set new standards in natural language processing. However, the classical softmax attention incurs significant computational costs, leading to a $O(T)$ complexity for per-token generation, where $T$ represents the context length. This work explores reducing LLMs' complexity while maintaining performance by introducing Rodimus and its enhanced version, Rodimus$+$. Rodimus employs an innovative data-dependent tempered selection (DDTS) mechanism within a linear attention-based, purely recurrent framework, achieving significant accuracy while drastically reducing the memory usage typically associated with recurrent models. This method exemplifies semantic compression by maintaining essential input information with fixed-size hidden states. Building on this, Rodimus$+$ combines Rodimus with the innovative Sliding Window Shared-Key Attention (SW-SKA) in a hybrid approach, effectively leveraging the complementary semantic, token, and head compression techniques. Our experiments demonstrate that Rodimus$+$-1.6B, trained on 1 trillion tokens, achieves superior downstream performance against models trained on more tokens, including Qwen2-1.5B and RWKV6-1.6B, underscoring its potential to redefine the accuracy-efficiency balance in LLMs. Model code and pre-trained checkpoints are open-sourced at https://github.com/codefuse-ai/rodimus.

Real-world data distributions are often highly skewed. This has spurred a growing body of research on long-tailed recognition, aimed at addressing the imbalance in training classification models. Among the methods studied, multiplicative logit adjustment (MLA) stands out as a simple and effective method. What theoretical foundation explains the effectiveness of this heuristic method? We provide a justification for the effectiveness of MLA with the following two-step process. First, we develop a theory that adjusts optimal decision boundaries by estimating feature spread on the basis of neural collapse. Second, we demonstrate that MLA approximates this optimal method. Additionally, through experiments on long-tailed datasets, we illustrate the practical usefulness of MLA under more realistic conditions. We also offer experimental insights to guide the tuning of MLA hyperparameters.

Large language models (LLMs) could be valuable personal AI agents across various domains, provided they can precisely follow user instructions. However, recent studies have shown significant limitations in LLMs' instruction-following capabilities, raising concerns about their reliability in high-stakes applications. Accurately estimating LLMs' uncertainty in adhering to instructions is critical to mitigating deployment risks. We present, to our knowledge, the first systematic evaluation of the uncertainty estimation abilities of LLMs in the context of instruction-following. Our study identifies key challenges with existing instruction-following benchmarks, where multiple factors are entangled with uncertainty stems from instruction-following, complicating the isolation and comparison across methods and models. To address these issues, we introduce a controlled evaluation setup with two benchmark versions of data, enabling a comprehensive comparison of uncertainty estimation methods under various conditions. Our findings show that existing uncertainty methods struggle, particularly when models make subtle errors in instruction following. While internal model states provide some improvement, they remain inadequate in more complex scenarios. The insights from our controlled evaluation setups provide a crucial understanding of LLMs' limitations and potential for uncertainty estimation in instruction-following tasks, paving the way for more trustworthy AI agents.

Text-to-motion generation has significant potential in a wide range of applications including animation, robotics, and AR/VR. While recent works on masked motion models are promising, the task remains challenging due to the inherent ambiguity in text and the complexity of human motion dynamics. To overcome the issues, we propose a novel text-to-motion generation framework that integrates two key components: Hard Token Mining (HTM) and a Hierarchical Generative Masked Motion Model (HGM³). Our HTM identifies and masks challenging regions in motion sequences and directs the model to focus on hard-to-learn components for efficacy. Concurrently, the hierarchical model uses a semantic graph to represent sentences at different granularity, allowing the model to learn contextually feasible motions. By leveraging a shared-weight masked motion model, it reconstructs the same sequence under different conditioning levels and facilitates comprehensive learning of complex motion patterns. During inference, the model progressively generates motions by incrementally building up coarse-to-fine details. Extensive experiments on benchmark datasets, including HumanML3D and KIT-ML, demonstrate that our method outperforms existing methods in both qualitative and quantitative measures for generating context-aware motions.

Recent advancements have exploited diffusion models for the synthesis of either LiDAR point clouds or camera image data in driving scenarios. Despite their success in modeling single-modality data marginal distribution, there is an under- exploration in the mutual reliance between different modalities to describe com- plex driving scenes. To fill in this gap, we propose a novel framework, X-DRIVE, to model the joint distribution of point clouds and multi-view images via a dual- branch latent diffusion model architecture. Considering the distinct geometrical spaces of the two modalities, X-DRIVE conditions the synthesis of each modality on the corresponding local regions from the other modality, ensuring better alignment and realism. To further handle the spatial ambiguity during denoising, we design the cross-modality condition module based on epipolar lines to adaptively learn the cross-modality local correspondence. Besides, X-DRIVE allows for controllable generation through multi-level input conditions, including text, bounding box, image, and point clouds. Extensive results demonstrate the high-fidelity synthetic results of X-DRIVE for both point clouds and multi-view images, adhering to input conditions while ensuring reliable cross-modality consistency. Our code will be made publicly available at https://github.com/yichen928/X-Drive.

There is growing evidence of the effectiveness of Shampoo, a higher-order preconditioning method, over Adam in deep learning optimization tasks. However, Shampoo's drawbacks include additional hyperparameters and computational overhead when compared to Adam, which only updates running averages of first- and second-moment quantities. This work establishes a formal connection between Shampoo (implemented with the 1/2 power) and Adafactor --- a memory-efficient approximation of Adam --- showing that Shampoo is equivalent to running Adafactor in the eigenbasis of Shampoo's preconditioner. This insight leads to the design of a simpler and computationally efficient algorithm: **S**hampo**O** with **A**dam in the **P**reconditioner's eigenbasis (SOAP). With regards to improving Shampoo's computational efficiency, the most straightforward approach would be to simply compute Shampoo's eigendecomposition less frequently. Unfortunately, as our empirical results show, this leads to performance degradation that worsens with this frequency. SOAP mitigates this degradation by continually updating the running average of the second moment, just as Adam does, but in the current (slowly changing) coordinate basis. Furthermore, since SOAP is equivalent to running Adam in a rotated space, it introduces only one additional hyperparameter (the preconditioning frequency) compared to Adam. We empirically evaluate SOAP on language model pre-training with 360m and 660m sized models. In the large batch regime, SOAP reduces the number of iterations by over 40\% and wall clock time by over 35\% compared to AdamW, with approximately 20\% improvements in both metrics compared to Shampoo. An implementation of SOAP is available at https://github.com/nikhilvyas/SOAP.

We present Self-MoE, an approach that transforms a monolithic LLM into a compositional, modular system of self-specialized experts, named MiXSE (MiXture of Self-specialized Experts). Our approach leverages self-specialization, which constructs expert modules using self-generated synthetic data, each equipping a shared base LLM with distinct domain-specific capabilities, activated via self-optimized routing. This allows for dynamic and capability-specific handling of various target tasks, enhancing overall capabilities, without extensive human-labeled data and added parameters. Our empirical results reveal that specializing LLMs may exhibit potential trade-offs in performances on non-specialized tasks. On the other hand, our Self-MoE demonstrates substantial improvements (6.5%p on average) over the base LLM across diverse benchmarks such as knowledge, reasoning, math, and coding. It also consistently outperforms other methods, including instance merging and weight merging, while offering better flexibility and interpretability by design with semantic experts and routing. Our findings highlight the critical role of modularity, the applicability of Self-MoE to multiple base LLMs, and the potential of self-improvement in achieving efficient, scalable, and adaptable systems.

Graph Neural Networks (GNNs) have demonstrated strong capabilities in processing structured data. While traditional GNNs typically treat each feature dimension equally important during graph convolution, we raise an important question: **Is the graph convolution operation equally beneficial for each feature?** If not, the convolution operation on certain feature dimensions can possibly lead to harmful effects, even worse than convolution-free models. Therefore, it is required to distinguish convolution-favored and convolution-disfavored features. Traditional feature selection methods mainly focus on identifying informative features or reducing redundancy, but they are not suitable for structured data as they overlook graph structures. In graph community, some studies have investigated the performance of GNN with respect to node features using feature homophily metrics, which assess feature consistency across graph topology. Unfortunately, these metrics do not effectively align with GNN performance and cannot be reliably used for feature selection in GNNs. To address these limitations, we introduce a novel metric, Topological Feature Informativeness (TFI), to distinguish GNN-favored and GNN-disfavored features, where its effectiveness is validated through both theoretical analysis and empirical observations. Based on TFI, we propose a simple yet effective Graph Feature Selection (GFS) method, which processes GNN-favored and GNN-disfavored features with GNNs and non-GNN models separately. Compared to original GNNs, GFS significantly improves the extraction of useful topological information from each feature with comparable computational costs. Extensive experiments show that after applying GFS to $\textbf{8}$ baseline and state-of-the-art (SOTA) GNN architectures across $\textbf{10}$ datasets, $\textbf{90\%}$ of the GFS-augmented cases show significant performance boosts. Furthermore, our proposed TFI metric outperforms other feature selection methods for GFS. These results verify the effectiveness of both GFS and TFI. Additionally, we demonstrate that GFS's improvements are robust to hyperparameter tuning, highlighting its potential as a universally valid method for enhancing various GNN architectures. To facilitate reproducibility and further research, we have made our code publicly available at https://github.com/KTTRCDL/graph-feature-selection.

Multimodal Large Language Models (MLLMs) are rapidly evolving, demonstrating impressive capabilities as multimodal assistants that interact with both humans and their environments. However, this increased sophistication introduces significant safety concerns. In this paper, we present the first evaluation and analysis of a novel safety challenge termed Multimodal Situational Safety, which explores how safety considerations vary based on the specific situation in which the user or agent is engaged. We argue that for an MLLM to respond safely—whether through language or action—it often needs to assess the safety implications of a language query within its corresponding visual context. To evaluate this capability, we develop the Multimodal Situational Safety benchmark (MSSBench) to assess the situational safety performance of current MLLMs. The dataset comprises 1,960 language query-image pairs, half of which the image context is safe, and the other half is unsafe. We also develop an evaluation framework that analyzes key safety aspects, including explicit safety reasoning, visual understanding, and, crucially, situational safety reasoning. Our findings reveal that current MLLMs struggle with this nuanced safety problem in the instruction-following setting and struggle to tackle these situational safety challenges all at once, highlighting a key area for future research. Furthermore, we develop multi-agent pipelines to coordinately solve safety challenges, which shows consistent improvement in safety over the original MLLM response.

Synthetic data has gained attention for training large language models, but poor-quality data can harm performance (see, e.g., Shumailov et al. (2023); Seddik et al. (2024)). A potential solution is data pruning, which retains only high-quality data based on a score function (human or machine feedback). Previous work Feng et al. (2024) analyzed models trained on synthetic data as sample size increases. We extend this by using random matrix theory to derive the performance of a binary classifier trained on a mix of real and pruned synthetic data in a high dimensional setting. Our findings identify conditions where synthetic data could improve performance, focusing on the quality of the generative model and verification strategy. We also show a smooth phase transition in synthetic label noise, contrasting with prior sharp behavior in infinite sample limits. Experiments with toy models and large language models validate our theoretical results.

Aligning AI systems with human preferences typically suffers from the infamous *reward hacking* problem, where optimization of an imperfect reward model leads to undesired behaviors. In this paper, we investigate reward hacking in offline preference optimization, which aims to improve an initial model using a preference dataset. We identify two types of reward hacking stemming from statistical fluctuations in the dataset: Type I Reward Hacking due to subpar choices appearing more favorable, and Type II Reward Hacking due to decent choices appearing less desirable. We prove that many (mainstream or theoretical) preference optimization methods suffer from both types of reward hacking. To mitigate Type I Reward Hacking, we propose POWER, a new preference optimization method that combines Guiasu's weighted entropy with a robust reward maximization objective. POWER enjoys finite-sample guarantees under general function approximation, competing with the best covered policy in the data. To mitigate Type II Reward Hacking, we analyze the learning dynamics of preference optimization and develop a novel technique that dynamically updates preference labels toward certain "stationary labels", resulting in diminishing gradients for untrustworthy samples. Empirically, POWER with dynamic labels (DL) consistently outperforms state-of-the-art methods on alignment benchmarks, achieving improvements of up to **13.0** points on AlpacaEval 2 and **11.5** points on Arena-Hard over DPO, while also improving or maintaining performance on downstream tasks such as mathematical reasoning. Strong theoretical guarantees and empirical results demonstrate the promise of POWER-DL in mitigating reward hacking.

Exploration in sparse reward environments remains a significant challenge in reinforcement learning, particularly in Contextual Markov Decision Processes (CMDPs), where environments differ across episodes. Existing episodic intrinsic motivation methods for CMDPs primarily rely on count-based approaches, which are ineffective in large state spaces, or on similarity-based methods that lack appropriate metrics for state comparison. To address these shortcomings, we propose Episodic Novelty Through Temporal Distance (ETD), a novel approach that introduces temporal distance as a robust metric for state similarity and intrinsic reward computation. By employing contrastive learning, ETD accurately estimates temporal distances and derives intrinsic rewards based on the novelty of states within the current episode. Extensive experiments on various benchmark tasks demonstrate that ETD significantly outperforms state-of-the-art methods, highlighting its effectiveness in enhancing exploration in sparse reward CMDPs.

Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior sample paths, especially in higher dimensions. We introduce an efficient global optimization strategy for posterior samples based on global rootfinding. It provides gradient-based optimizers with two sets of judiciously selected starting points, designed to combine exploration and exploitation. The number of starting points can be kept small without sacrificing optimization quality. Remarkably, even with just one point from each set, the global optimum is discovered most of the time. The algorithm scales practically linearly to high dimensions, breaking the curse of dimensionality. For Gaussian process Thompson sampling (GP-TS), we demonstrate remarkable improvement in both inner- and outer-loop optimization, surprisingly outperforming alternatives like EI and GP-UCB in most cases. Our approach also improves the performance of other posterior sample-based acquisition functions, such as variants of entropy search. Furthermore, we propose a sample-average formulation of GP-TS, which has a parameter to explicitly control exploitation and can be computed at the cost of one posterior sample.

The growing use of 3D point cloud data in autonomous vehicles (AVs) has raised serious privacy concerns, particularly due to the sensitive information that can be extracted from 3D data. While model inversion attacks have been widely studied in the context of 2D data, their application to 3D point clouds remains largely unexplored. To fill this gap, we present the first in-depth study of model inversion attacks aimed at restoring 3D point cloud scenes. Our analysis reveals the unique challenges, the inherent sparsity of 3D point clouds and the ambiguity between empty and non-empty voxels after voxelization, which are further exacerbated by the dispersion of non-empty voxels across feature extractor layers. To address these challenges, we introduce ConcreTizer, a simple yet effective model inversion attack designed specifically for voxel-based 3D point cloud data. ConcreTizer incorporates Voxel Occupancy Classification to distinguish between empty and non-empty voxels and Dispersion-Controlled Supervision to mitigate non-empty voxel dispersion. Extensive experiments on widely used 3D feature extractors and benchmark datasets, such as KITTI and Waymo, demonstrate that ConcreTizer concretely restores the original 3D point cloud scene from disrupted 3D feature data. Our findings highlight both the vulnerability of 3D data to inversion attacks and the urgent need for robust defense strategies.

Lean is an advanced proof assistant designed to facilitate formal theorem proving by providing a variety of interactive feedback. In this paper, we explore methodologies to leverage proof assistant feedback to augment the capabilities of large language models in constructing formal proofs. First, we deploy online reinforcement learning using Lean verification outcomes as the reward signal to improve the proof completion policy. This straightforward approach shows great promise in enhancing the model's alignment with the formal verification system. In addition, we propose RMaxTS, a variant of Monte-Carlo tree search that employs an intrinsic-reward-driven exploration strategy to generate diverse proof paths. The tree structure is organized to represent the transitions of intermediate tactic states, extracted from the compilation messages given by Lean's tactic mode. The intrinsic reward is constructed to incentivize the discovery of novel tactic states, which helps to to mitigate the sparse-reward problem inherent in proof search. These techniques lead to a more efficient planning scheme for formal proof generation, achieving new state-of-the-art results on both miniF2F and ProofNet benchmarks.

High-quality data plays an indispensable role in the era of large models, but the use of unauthorized data for model training greatly damages the interests of data owners. To overcome this threat, several unlearnable methods have been proposed, which generate unlearnable examples (UEs) by compromising the training availability of data. Clearly, due to unknown training purposes and the powerful representation learning capabilities of existing models, these data are expected to be unlearnable for models across multiple tasks, i.e., they will not help improve the model's performance. However, unexpectedly, we find that on the multi-task dataset Taskonomy, UEs still perform well in tasks such as semantic segmentation, failing to exhibit $\textit{cross-task unlearnability}$. This phenomenon leads us to question: $\textit{How far are we from attaining truly unlearnable examples?}$ We attempt to answer this question from the perspective of model optimization. To this end, we observe the difference in the convergence process between clean and poisoned models using a simple model architecture. Subsequently, from the loss landscape we find that only a part of the critical parameter optimization paths show significant differences, implying a close relationship between the loss landscape and unlearnability. Consequently, we employ the loss landscape to explain the underlying reasons for UEs and propose Sharpness-Aware Learnability (SAL) to quantify the unlearnability of parameters based on this explanation. Furthermore, we propose an Unlearnable Distance (UD) to measure the unlearnability of data based on the SAL distribution of parameters in clean and poisoned models. Finally, we conduct benchmark tests on mainstream unlearnable methods using the proposed UD, aiming to promote community awareness of the capability boundaries of existing unlearnable methods.