ICLR 2025 Papers

Recent advancements in dataset distillation have demonstrated the significant benefits of employing soft labels generated by pre-trained teacher models. In this paper, we introduce a novel perspective by emphasizing the full utilization of labels. We first conduct a comprehensive comparison of various loss functions for soft label utilization in dataset distillation, revealing that the model trained on the synthetic dataset exhibits high sensitivity to the choice of loss function for soft label utilization. This finding highlights the necessity of a universal loss function for training models on synthetic datasets. Building on these insights, we introduce an extremely simple yet surprisingly effective plug-and-play approach, GIFT, which encompasses soft label refinement and a cosine similarity-based loss function to efficiently leverage full label information. Extensive experiments indicate that GIFT consistently enhances state-of-the-art dataset distillation methods across various dataset scales without incurring additional computational costs. Importantly, GIFT significantly enhances cross-optimizer generalization, an area previously overlooked. For instance, on ImageNet-1K with IPC = 10, GIFT enhances the state-of-the-art method RDED by 30.8% in cross-optimizer generalization. Our code is available at https://github.com/LINs-lab/GIFT.

Out-of-Domain (OOD) generalization is the ability of a model trained on one or more domains to generalize to unseen domains. In the ImageNet era of computer vision, evaluation sets for measuring a model's OOD performance were designed to be strictly OOD with respect to style. However, the emergence of foundation models and expansive web-scale datasets has obfuscated this evaluation process, as datasets cover a broad range of domains and risk test domain contamination. In search of the forgotten domain generalization, we create large-scale datasets subsampled from LAION---LAION-Natural and LAION-Rendition---that are strictly OOD to corresponding ImageNet and DomainNet test sets in terms of style. Training CLIP models on these datasets reveals that a significant portion of their performance is explained by in-domain examples. This indicates that the OOD generalization challenges from the ImageNet era still prevail and that training on web-scale data merely creates the illusion of OOD generalization. Furthermore, through a systematic exploration of combining natural and rendition datasets in varying proportions, we identify optimal mixing ratios for model generalization across these domains. Our datasets and results re-enable meaningful assessment of OOD robustness at scale---a crucial prerequisite for improving model robustness.

Latent space matching, which consists of matching distributions of features in latent space, is a crucial component for tasks such as adversarial attacks and defenses, domain adaptation, and generative modelling. Metrics for probability measures, such as Wasserstein and maximum mean discrepancy, are commonly used to quantify the differences between such distributions. However, these are often costly to compute, or do not appropriately take the geometric and topological features of the distributions into consideration. Persistent homology is a tool from topological data analysis which quantifies the multi-scale topological structure of point clouds, and has recently been used as a topological regularizer in learning tasks. However, computation costs preclude larger scale computations, and discontinuities in the gradient lead to unstable training behavior such as in adversarial tasks. We propose the use of principal persistence measures, based on computing the persistent homology of a large number of small subsamples, as a topological regularizer. We provide a parallelized GPU implementation of this regularizer, and prove that gradients are continuous for smooth densities. Furthermore, we demonstrate the efficacy of this regularizer on shape matching, image generation, and semi-supervised learning tasks, opening the door towards a scalable regularizer for topological features.

Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly measure their true understanding of geometric structures, as LLMs can arrive at correct answers by coincidence. To fill this gap, we introduce the GeomRel dataset, designed to evaluate LLMs’ understanding of geometric structures by isolating the core step of geometric relationship identification in problem-solving. Using this benchmark, we conduct thorough evaluations of diverse LLMs and identify key limitations in understanding geometric structures. We further propose the Geometry Chain-of-Thought (GeoCoT) method, which enhances LLMs’ ability to identify geometric relationships, resulting in significant performance improvements.

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data for formal proofs is limited, posing a significant challenge to LLM-based tactic generation. To address this, we introduce a neuro-symbolic tactic generator that synergizes the mathematical intuition learned by LLMs with domain-specific insights encoded by symbolic methods. The key aspect of this integration is identifying which parts of mathematical reasoning are best suited to LLMs and which to symbolic methods. While the high-level idea of neuro-symbolic integration is broadly applicable to various mathematical problems, in this paper, we focus specifically on Olympiad inequalities (Figure~1). We analyze how humans solve these problems and distill the techniques into two types of tactics: (1) scaling, handled by symbolic methods, and (2) rewriting, handled by LLMs. In addition, we combine symbolic tools with LLMs to prune and rank the proof goals for efficient proof search. We evaluate our framework on 161 challenging inequalities from multiple mathematics competitions, achieving state-of-the-art performance and significantly outperforming existing LLM and symbolic approaches without requiring additional training data.

The dominant paradigm for RLHF is *online* and *on-policy* RL: synchronously generating from the large language model (LLM) policy, labelling with a reward model, and learning using feedback on the LLM's own outputs. While performant, this paradigm is computationally inefficient. Inspired by classical deep RL literature, we propose separating generation and learning in RLHF. This enables asynchronous generation of new samples while simultaneously training on old samples, leading to faster training and more compute-optimal scaling. However, asynchronous training relies on an underexplored regime, online but *off-policy* RLHF: learning on samples from previous iterations of our model which give a worse training signal. We tackle the fundamental challenge in this regime: how much off-policyness can we tolerate for asynchronous training to speed up learning but maintain performance? Among several RLHF algorithms we test, online DPO is found to be most robust to off-policy data, and robustness increases with the scale of the policy model. We study further compute optimizations for asynchronous RLHF but find that they come at a performance cost, giving rise to a trade-off. We verify the scalability of asynchronous RLHF by training a general-purpose chatbot from LLaMA 3.1 8B on an instruction-following task $\sim$40\% faster than a synchronous run while matching final performance. Finally, we extend our results to math and reasoning to demonstrate asynchronous RL can finetune Rho 1B on GSM8k $\sim$70\% faster while matching synchronous accuracy.

The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy, limited scalability, or dependence on costly reference data. To address these issues, we introduce Equivariant Graph Exchange Correlation (EG-XC), a novel non-local XC functional based on equivariant graph neural networks (GNNs). Where previous works relied on semi-local functionals or fixed-size descriptors of the density, we compress the electron density into an SO(3)-equivariant nuclei-centered point cloud for efficient non-local atomic-range interactions. By applying an equivariant GNN on this point cloud, we capture molecular-range interactions in a scalable and accurate manner. To train EG-XC, we differentiate through a self-consistent field solver requiring only energy targets. In our empirical evaluation, we find EG-XC to accurately reconstruct `gold-standard' CCSD(T) energies on MD17. On out-of-distribution conformations of 3BPA, EG-XC reduces the relative MAE by 35% to 50%. Remarkably, EG-XC excels in data efficiency and molecular size extrapolation on QM9, matching force fields trained on 5 times more and larger molecules. On identical training sets, EG-XC yields on average 51% lower MAEs.

Vision-Language Models (VLMs) have shown broad effectiveness due to extensive training that aligns visual inputs with corresponding language responses. However, this conclusive alignment training causes models to overlook essential visual reasoning, leading to failures in handling detailed visual tasks and producing unfaithful responses. Drawing inspiration from human cognition in solving visual problems (e.g., marking, zoom in), this paper introduces Chain of Manipulations, a mechanism that enables VLMs to tackle problems step-by-step with evidence. After training, models can solve various visual problems by eliciting intrinsic manipulations (e.g., grounding, zoom in) with results (e.g., boxes, image) actively without relying external tools, while also allowing users to trace error causes. In this paper, we study the comprehensive methodology that includes: (1) a flexible design of manipulations based on extensive analysis, (2) an efficient automated data generation pipeline, (3) a compatible VLM architecture capable of multi-turn, multi-image, and (4) a model training process for versatile capabilities. With the design, we also manually annotate **6K** high-quality samples for challenging graphical mathematical problems. Our trained model, CogCoM, equipped with this mechanism and 17B parameters, achieves SOTA performance across **9** benchmarks in **4** categories, demonstrating its effectiveness while maintaining interpretability. Code, model, and data are available at https://github.com/THUDM/CogCoM.

Multimodal Large Language Models (MLLMs) have demonstrated impressive performance in general visual understanding tasks. However, their potential for high-level, fine-grained comprehension, such as anomaly understanding, remains unexplored. Focusing on traffic accidents, a critical and practical scenario within anomaly understanding, we investigate the advanced capabilities of MLLMs and propose TABot, a multimodal MLLM specialized for accident-related tasks. To facilitate this, we first construct TAU-106K, a large-scale multimodal dataset containing 106K traffic accident videos and images collected from academic benchmarks and public platforms. The dataset is meticulously annotated through a video-to-image annotation pipeline to ensure comprehensive and high-quality labels. Building upon TAU-106K, we train TABot using a two-step approach designed to integrate multi-granularity tasks, including accident recognition, spatial-temporal grounding, and an auxiliary description task to enhance the model's understanding of accident elements. Extensive experiments demonstrate TABot's superior performance in traffic accident understanding, highlighting not only its capabilities in high-level anomaly comprehension but also the robustness of the TAU-106K benchmark. Our code and data will be available at https://github.com/cool-xuan/TABot.

A short clip of video may contain progression of multiple events and an interesting story line. A human need to capture both the event in every shot and associate them together to understand the story behind it. In this work, we present a new multi-shot video understanding benchmark \dataset with detailed shot-level captions, comprehensive video summaries and question-answering pairs. To facilitate better semantic understanding of videos, we provide captions for both visual signals and human narrations. We design several distinct tasks including single-shot video captioning, multi-shot video summarization, and multi-shot video question answering. Preliminary experiments show some challenges to generate a long and comprehensive video summary for multi-shot videos. Nevertheless, the generated imperfect summaries can already achieve competitive performance on existing video understanding tasks such as video question-answering, promoting an under-explored setting of video understanding with detailed summaries.

Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just a few denoising steps, modern discrete diffusion models still require hundreds or even thousands of denoising steps to perform well. In this paper, we identify a fundamental limitation that prevents discrete diffusion models from achieving strong performance with fewer steps -- they fail to capture dependencies between output variables at each denoising step. To address this issue, we provide a formal explanation and introduce a general approach to supplement the missing dependency information by incorporating another deep generative model, termed the copula model. Our method does not require fine-tuning either the diffusion model or the copula model, yet it enables high-quality sample generation with significantly fewer denoising steps. When we apply this approach to autoregressive copula models, the combined model outperforms both models individually in unconditional and conditional text generation. Specifically, the hybrid model achieves better (un)conditional text generation using 8 to 32 times fewer denoising steps than the diffusion model alone. In addition to presenting an effective discrete diffusion generation algorithm, this paper emphasizes the importance of modeling inter-variable dependencies in discrete diffusion.

We present a self-supervised framework that learns population-level codes for arbitrary ensembles of neural recordings at scale. We address key challenges in scaling models with neural time-series data, namely, sparse and variable electrode distribution across subjects and datasets. The Population Transformer (PopT) stacks on top of pretrained temporal embeddings and enhances downstream decoding by enabling learned aggregation of multiple spatially-sparse data channels. The pretrained PopT lowers the amount of data required for downstream decoding experiments, while increasing accuracy, even on held-out subjects and tasks. Compared to end-to-end methods, this approach is computationally lightweight, while achieving similar or better decoding performance. We further show how our framework is generalizable to multiple time-series embeddings and neural data modalities. Beyond decoding, we interpret the pretrained and fine-tuned PopT models to show how they can be used to extract neuroscience insights from large amounts of data. We release our code as well as a pretrained PopT to enable off-the-shelf improvements in multi-channel intracranial data decoding and interpretability. Code is available at https://github.com/czlwang/PopulationTransformer.

Gaussian processes (GPs) are widely recognized for their robustness and flexibility across various domains, including machine learning, time series, spatial statistics, and biomedicine. In addition to their common usage in regression tasks, GP kernel parameters are frequently interpreted in various applications. For example, in spatial transcriptomics, estimated kernel parameters are used to identify spatial variable genes, which exhibit significant expression patterns across different tissue locations. However, before these parameters can be meaningfully interpreted, it is essential to establish their identifiability. Existing studies of GP parameter identifiability have focused primarily on Mat\'ern-type kernels, as their spectral densities allow for more established mathematical tools. In many real-world applications, particuarly in time series analysis, other kernels such as the squared exponential, periodic, and rational quadratic kernels, as well as their combinations, are also widely used. These kernels share the property of being holomorphic around zero, and their parameter identifiability remains underexplored. In this paper, we bridge this gap by developing a novel theoretical framework for determining kernel parameter identifiability for kernels holomorphic near zero. Our findings enable practitioners to determine which parameters are identifiable in both existing and newly constructed kernels, supporting application-specific interpretation of the identifiable parameters, and highlighting non-identifiable parameters that require careful interpretation.

The scaling of inference computation has unlocked the potential of long-context large language models (LLMs) across diverse settings. For knowledge-intensive tasks, the increased compute is often allocated to incorporate more external knowledge. However, without effectively utilizing such knowledge, solely expanding context does not always enhance performance. In this work, we investigate inference scaling for retrieval augmented generation (RAG), exploring the combination of multiple strategies beyond simply increasing the quantity of knowledge, including in-context learning and iterative prompting. These strategies provide additional flexibility to scale test-time computation (e.g., by increasing retrieved documents or generation steps), thereby enhancing LLMs’ ability to effectively acquire and utilize contextual information. We address two key questions: (1) How does RAG performance benefit from the scaling of inference computation when optimally configured? (2) Can we predict the optimal test-time compute allocation for a given budget by modeling the relationship between RAG performance and inference parameters? Our observations reveal that increasing inference computation leads to nearly linear gains in RAG performance when optimally allocated, a relationship we describe as the inference scaling laws for RAG. Building on this, we further develop the computation allocation model to estimate RAG performance across different inference configurations. The model predicts optimal inference parameters under various computation constraints, which align closely with the experimental results. By applying these optimal configurations, we demonstrate that scaling inference compute on long-context LLMs achieves up to 58.9% gains on benchmark datasets compared to standard RAG.

Prompting Large Language Models (LLMs), or providing context on the expected model of operation, is an effective way to steer the outputs of such models to satisfy human desiderata after they have been trained. But in rapidly evolving domains, there is often need to fine-tune LLMs to improve either the kind of knowledge in their memory or their abilities to perform open ended reasoning in new domains. When human's learn new concepts, we often do so by linking the new material that we are studying to concepts we have already learned before. To that end, we ask, "can prompting help us teach LLMs how to learn". In this work, we study a novel generalization of instruction tuning, called contextual fine-tuning, to fine-tune LLMs. Our method leverages instructional prompts designed to mimic human cognitive strategies in learning and problem-solving to guide the learning process during training, aiming to improve the model’s interpretation and understanding of domain-specific knowledge. We empirically demonstrate that this simple yet effective modification improves the ability of LLMs to be fine-tuned rapidly on new datasets both within the medical and financial domains.

The widespread deployment of sensing devices leads to a surge in data for spatio-temporal forecasting applications such as traffic flow, air quality, and wind energy. Although spatio-temporal graph neural networks (STGNNs) have achieved success in modeling various static spatio-temporal forecasting scenarios, real-world spatio-temporal data are typically received in a streaming manner, and the network continuously expands with the installation of new sensors. Thus, spatio-temporal forecasting in streaming scenarios faces dual challenges: the inefficiency of retraining models over newly-arrived data and the detrimental effects of catastrophic forgetting over long-term history. To address these challenges, we propose a novel prompt tuning-based continuous forecasting method, **_EAC_**, following two fundamental tuning principles guided by empirical and theoretical analysis: _**e**xpand **a**nd **c**ompress_, which effectively resolve the aforementioned problems with lightweight tuning parameters. Specifically, we integrate the base STGNN with a continuous prompt pool, utilizing stored prompts (\ie, few learnable parameters) in memory, and jointly optimize them with the base STGNN. This method ensures that the model sequentially learns from the spatio-temporal data stream to accomplish tasks for corresponding periods. Extensive experimental results on multiple real-world datasets demonstrate the multi-faceted superiority of **_EAC_** over the state-of-the-art baselines, including effectiveness, efficiency, universality, etc.

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

Machine learning (ML) techniques have shown great potential in generating high-quality solutions for integer linear programs (ILPs). However, existing methods typically rely on a *supervised learning* paradigm, leading to (1) *expensive training cost* due to repeated invocations of traditional solvers to generate training labels, and (2) *plausible yet infeasible solutions* due to the misalignment between the training objective (minimizing prediction loss) and the inference objective (generating high-quality solutions). To tackle this challenge, we propose **DiffILO** (**Diff**erentiable **I**nteger **L**inear Programming **O**ptimization), an *unsupervised learning paradigm for learning to solve ILPs*. Specifically, through a novel probabilistic modeling, DiffILO reformulates ILPs---discrete and constrained optimization problems---into continuous, differentiable (almost everywhere), and unconstrained optimization problems. This reformulation enables DiffILO to simultaneously solve ILPs and train the model via straightforward gradient descent, providing two major advantages. First, it significantly reduces the training cost, as the training process does not need the aid of traditional solvers at all. Second, it facilitates the generation of feasible and high-quality solutions, as the model *learns to solve ILPs* in an end-to-end manner, thus aligning the training and inference objectives. Experiments on commonly used ILP datasets demonstrate that DiffILO not only achieves an average training speedup of $13.2$ times compared to supervised methods, but also outperforms them by generating heuristic solutions with significantly higher feasibility ratios and much better solution qualities.

Sliced Optimal Transport (OT) simplifies the OT problem in high-dimensional spaces by projecting supports of input measures onto one-dimensional lines, then exploiting the closed-form expression of the univariate OT to reduce the computational burden of OT. Recently, the Tree-Sliced method has been introduced to replace these lines with more intricate structures, known as tree systems. This approach enhances the ability to capture topological information of integration domains in Sliced OT while maintaining low computational cost. Inspired by this approach, in this paper, we present an adaptation of tree systems on OT problem for measures supported on a sphere. As counterpart to the Radon transform variant on tree systems, we propose a novel spherical Radon transform, with a new integration domain called spherical trees. By leveraging this transform and exploiting the spherical tree structures, we derive closed-form expressions for OT problems on the sphere. Consequently, we obtain an efficient metric for measures on the sphere, named Spherical Tree-Sliced Wasserstein (STSW) distance. We provide an extensive theoretical analysis to demonstrate the topology of spherical trees, the well-definedness and injectivity of our Radon transform variant, which leads to an orthogonally invariant distance between spherical measures. Finally, we conduct a wide range of numerical experiments, including gradient flows and self-supervised learning, to assess the performance of our proposed metric, comparing it to recent benchmarks.