ICLR 2025 Papers

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schr\"{o}dinger Bridge (PalSB). This framework leverages a diffusion bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques. The source code can be found at https://github.com/lzy12301/PalSB.

Recent studies highlight the promise of LLM-based prompt optimization, especially with TextGrad, which automates ``differentiation'' via texts and backpropagates textual feedback provided by LLMs. This approach facilitates training in various real-world applications that do not support numerical gradient propagation or loss calculation. It opens new avenues for optimization in decentralized, resource-constrained environments, suggesting that users of black-box LLMs (e.g., ChatGPT) could enhance components of LLM agentic systems (such as prompt optimization) through collaborative paradigms like federated learning (FL). In this paper, we systematically explore the potential and challenges of incorporating textual gradient into FL. Our contributions are fourfold. **Firstly**, we introduce a novel FL paradigm, Federated Textual Gradient (FedTextGrad), that allows FL clients to upload their locally optimized prompts derived from textual gradients, while the FL server aggregates the received prompts through text summarization. Unlike traditional FL frameworks, which are designed for numerical aggregation, FedTextGrad is specifically tailored for handling textual data, expanding the applicability of FL to a broader range of problems that lack well-defined numerical loss functions. **Secondly**, building on this design, we conduct extensive experiments to explore the feasibility of federated textual gradients. Our findings highlight the importance of properly tuning key factors (e.g., local steps) in FL training to effectively integrate textual gradients. **Thirdly**, we highlight a major challenge in federated textual gradient aggregation: retaining essential information from distributed prompt updates. Concatenation often produces prompts that exceed the LLM API’s context window, while summarization can degrade performance by generating overly condensed or complex text that lacks key context. **Last but not least**, in response to this issue, we improve the vanilla variant of FedTextGrad by providing actionable guidance to the LLM when summarizing client prompts by leveraging the Uniform Information Density principle. Such a design reduces the complexity of the aggregated global prompt, thereby better incentivizing the LLM's reasoning ability. Through this principled study, we enable the adoption of textual gradients in FL for optimizing LLMs, identify important issues, and pinpoint future directions, thereby opening up a new research area that warrants further investigation.

Diffusion probabilistic models have achieved mainstream success in many generative modeling tasks, from image generation to inverse problem solving. A distinct feature of these models is that they correspond to deep hierarchical latent variable models optimizing a variational evidence lower bound (ELBO) on the data likelihood. Drawing on a basic connection between likelihood modeling and compression, we explore the potential of diffusion models for progressive coding, resulting in a sequence of bits that can be incrementally transmitted and decoded with progressively improving reconstruction quality. Unlike prior work based on Gaussian diffusion or conditional diffusion models, we propose a new form of diffusion model with uniform noise in the forward process, whose negative ELBO corresponds to the end-to-end compression cost using universal quantization. We obtain promising first results on image compression, achieving competitive rate-distortion-realism results on a wide range of bit-rates with a single model, bringing neural codecs a step closer to practical deployment. Our code can be found at https://github.com/mandt-lab/uqdm.

Probing learned concepts in large language models (LLMs) is crucial for understanding how semantic knowledge is encoded internally. Training linear classifiers on probing tasks is a principle approach to denote the vector of a certain concept in the representation space. However, the single vector identified for a concept varies with both data and training, making it less robust and weakening its effectiveness in real-world applications. To address this challenge, we propose an approach to approximate the subspace representing a specific concept. Built on linear probing classifiers, we extend the concept vectors into Gaussian Concept Subspace (GCS). We demonstrate GCS's effectiveness through measuring its faithfulness and plausibility across multiple LLMs with different sizes and architectures. Additionally, we use representation intervention tasks to showcase its efficacy in real-world applications such as emotion steering. Experimental results indicate that GCS concept vectors have the potential to balance steering performance and maintaining the fluency in natural language generation tasks.

Strength estimation and adjustment are crucial in designing human-AI interactions, particularly in games where AI surpasses human players. This paper introduces a novel strength system, including a *strength estimator* (SE) and an SE-based Monte Carlo tree search, denoted as *SE-MCTS*, which predicts strengths from games and offers different playing strengths with human styles. The strength estimator calculates strength scores and predicts ranks from games without direct human interaction. SE-MCTS utilizes the strength scores in a Monte Carlo tree search to adjust playing strength and style. We first conduct experiments in Go, a challenging board game with a wide range of ranks. Our strength estimator significantly achieves over 80% accuracy in predicting ranks by observing 15 games only, whereas the previous method reached 49% accuracy for 100 games. For strength adjustment, SE-MCTS successfully adjusts to designated ranks while achieving a 51.33% accuracy in aligning to human actions, outperforming a previous state-of-the-art, with only 42.56% accuracy. To demonstrate the generality of our strength system, we further apply SE and SE-MCTS to chess and obtain consistent results. These results show a promising approach to strength estimation and adjustment, enhancing human-AI interactions in games. Our code is available at https://rlg.iis.sinica.edu.tw/papers/strength-estimator.

We present CHASE-SQL, a novel framework addressing large language model (LLM) performance challenges for Text-to-SQL tasks by leveraging multi-agent modeling and test-time compute for improved candidate generation and selection. CHASE-SQL uses LLMs to generate diverse SQL candidates with: (1) a divide-and-conquer approach to break down complex queries, (2) chain-of-thought reasoning based on query execution plans, and (3) instance-aware synthetic example generation for tailored few-shot demonstrations. A selection agent ranks candidates via pairwise comparisons using a fine-tuned binary selection LLM, offering robust performance. This framework improves SQL query quality and diversity, achieving state-of-the-art execution accuracy of 73.0% on the BIRD Text-to-SQL benchmark test set, topping the leaderboard at the time of submission.

The goal of the AlgoPerf: Training Algorithms competition is to evaluate practical speed-ups in neural network training achieved solely by improving the underlying training algorithms. In the external tuning ruleset, submissions must provide workload-agnostic hyperparameter search spaces, while in the self-tuning ruleset they must be completely hyperparameter-free. In both rulesets, submissions are compared on time-to-result across multiple deep learning workloads, training on fixed hardware. This paper presents the inaugural AlgoPerf competition's results, which drew 18 diverse submissions from 10 teams. Our investigation reveals several key findings: (1) The winning submission in the external tuning ruleset, using Distributed Shampoo, demonstrates the effectiveness of non-diagonal preconditioning over popular methods like Adam, even when compared on wall-clock runtime. (2) The winning submission in the self-tuning ruleset, based on the Schedule Free AdamW algorithm, demonstrates a new level of effectiveness for completely hyperparameter-free training algorithms. (3) The top-scoring submissions were surprisingly robust to workload changes. We also discuss the engineering challenges encountered in ensuring a fair comparison between different training algorithms. These results highlight both the significant progress so far, and the considerable room for further improvements.

To accelerate biochemical research, e.g., drug and protein discovery, molecular representation learning (MRL) has attracted much attention. However, most existing methods follow the closed-set assumption that training and testing data share identical distribution, which limits their generalization abilities in out-of-distribution (OOD) cases. In this paper, we explore designing a new disentangled mechanism for learning generalized molecular representation that exhibits robustness against distribution shifts. And an approach of Concept-Enhanced Feedback Disentanglement (CFD) is proposed, whose goal is to exploit the feedback mechanism to learn distribution-agnostic representation. Specifically, we first propose two dedicated variational encoders to separately decompose distribution-agnostic and spurious features. Then, a set of molecule-aware concepts are tapped to focus on invariant substructure characteristics. By fusing these concepts into the disentangled distribution-agnostic features, the generalization ability of the learned molecular representation could be further enhanced. Next, we execute iteratively the disentangled operations based on a feedback received from the previous output. Finally, based on the outputs of multiple feedback iterations, we construct a self-supervised objective to promote the variational encoders to possess the disentangled capability. In the experiments, our method is verified on multiple real-world molecular datasets. The significant performance gains over state-of-the-art baselines demonstrate that our method can effectively disentangle generalized molecular representation in the presence of various distribution shifts. The source code will be released at https://github.com/AmingWu/MoleculeCFD.

Disaggregating the prefill and decoding phases represents an effective new paradigm for generative inference of large language models (LLM). This approach offers some significant system advantages, such as eliminating prefill-decoding interference and optimizing resource allocation. However, it is still an challenging open problem about how to deploy the disaggregated inference paradigm across a group of heterogeneous GPUs, which can be an economic alternative of the deployment over the homogeneous high performance GPUs. Towards this end, we introduce HexGen-2, a distributed system for high throughput and cost-efficient LLM serving on heterogeneous GPUs following the disaggragated paradigm. Built on top of HexGen, the core component of HexGen-2 is a sophisticated scheduling algorithm that formalizes the allocation of disaggregated LLM inference computations and communications over heterogeneous GPUs and network connections as a constraint optimization problem. We leverage the graph partitioning and max-flow algorithm to co-optimize resource allocation, parallel strategies for distinct inference phases, and the efficiency of inter-phase key-value (KV) cache communications. We conduct extensive experiments to evaluate HexGen-2, i.e., on OPT (30B) and Llama-2 (70B) models in various real-world settings, the results reveal that HexGen-2 delivers up to a 2.0$\times$ and on average a 1.3$\times$ improvement in serving throughput, reduces the average inference latency by 1.5$\times$ compared with state-of-the-art systems given the same price budget, and achieves comparable inference performance with a 30% lower price budget.

Offline meta reinforcement learning (OMRL) has emerged as a promising approach for interaction avoidance and strong generalization performance by leveraging pre-collected data and meta-learning techniques. Previous context-based approaches predominantly rely on the intuition that alternating optimization between the context encoder and the policy can lead to performance improvements, as long as the context encoder follows the principle of maximizing the mutual information between the task variable $M$ and its latent representation $Z$ ($I(Z;M)$) while the policy adopts the standard offline reinforcement learning (RL) algorithms conditioning on the learned task representation. Despite promising results, the theoretical justification of performance improvements for such intuition remains underexplored. Inspired by the return discrepancy scheme in the model-based RL field, we find that the previous optimization framework can be linked with the general RL objective of maximizing the expected return, thereby explaining performance improvements. Furthermore, after scrutinizing this optimization framework, we observe that the condition for monotonic performance improvements does not consider the variation of the task representation. When these variations are considered, the previously established condition may no longer be sufficient to ensure monotonicity, thereby impairing the optimization process. We name this issue \underline{task representation shift} and theoretically prove that the monotonic performance improvements can be guaranteed with appropriate context encoder updates. We use different settings to rein in the task representation shift on three widely adopted training objectives concerning maximizing $I(Z;M)$ across different data qualities. Empirical results show that reining in the task representation shift can indeed improve performance. Our work opens up a new avenue for OMRL, leading to a better understanding between the task representation and performance improvements.

Second-order methods for convex optimization outperform first-order methods in terms of theoretical iteration convergence, achieving rates up to $O(k^{-5})$ for highly-smooth functions. However, their practical performance and applications are limited due to their multi-level structure and implementation complexity. In this paper, we present new results on high-order optimization methods, supported by their practical performance. First, we show that the basic high-order methods, such as the Cubic Regularized Newton Method, exhibit global superlinear convergence for $\mu$-strongly star-convex functions, a class that includes $\mu$-strongly convex functions and some non-convex functions. Theoretical convergence results are both inspired and supported by the practical performance of these methods. Secondly, we propose a practical version of the Nesterov Accelerated Tensor method, called NATA. It significantly outperforms the classical variant and other high-order acceleration techniques in practice. The convergence of NATA is also supported by theoretical results. Finally, we introduce an open-source computational library for high-order methods, called OPTAMI. This library includes various methods, acceleration techniques, and subproblem solvers, all implemented as PyTorch optimizers, thereby facilitating the practical application of high-order methods to a wide range of optimization problems. We hope this library will simplify research and practical comparison of methods beyond first-order.

The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art. However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM. SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

Reward Models (RMs) are crucial for aligning language models with human preferences. Currently, the evaluation of RMs depends on measuring accuracy against a validation set of manually annotated preference data. Although this method is straightforward and widely adopted, the relationship between RM accuracy and downstream policy performance remains under-explored. In this work, we conduct experiments in a synthetic setting to investigate how differences in RM measured by accuracy translate into gaps in optimized policy performance. Our findings reveal that while there is a weak positive correlation between accuracy and downstream performance, policies optimized towards RMs with similar accuracy can exhibit quite different performance. Moreover, we discover that the way of measuring accuracy significantly impacts its ability to predict the final policy performance. Through the lens of the Regressional Goodhart effect, we recognize that accuracy, when used for measuring RM quality, can fail to fully capture the potential RM overoptimization. This underscores the inadequacy of relying solely on accuracy to reflect their impact on policy optimization.

As large language models (LLMs) become increasingly prevalent across various applications, it is critical to establish safety guardrails to moderate input/output content of LLMs and ensure compliance with safety policies. Existing guardrail models, such as OpenAI Mod and LlamaGuard, treat various safety categories (e.g., self-harm, self-harm/instructions) independently and fail to explicitly capture the intercorrelations among them. This has led to limitations such as ineffectiveness due to inadequate training on long-tail data from correlated safety categories, susceptibility to jailbreaking attacks, and inflexibility regarding new safety categories. To address these limitations, we propose $R^2$-Guard, a robust reasoning enabled LLM guardrail via knowledge-enhanced logical reasoning. Specifically, $R^2$-Guard comprises two parts: data-driven guardrail models and reasoning components. The data-driven guardrail models provide unsafety probabilities of moderated content on different safety categories. We then encode safety knowledge among different categories as first-order logical rules and embed them into a probabilistic graphic model (PGM) based reasoning component. The unsafety probabilities of different categories from data-driven guardrail models are sent to the reasoning component for final inference. We employ two types of PGMs: Markov logic networks (MLNs) and probabilistic circuits (PCs), and optimize PCs to achieve precision-efficiency balance via improved graph structure. We also propose different methods to optimize the weights of knowledge. To further perform stress tests for guardrail models, we employ a pairwise construction method to construct a new safety benchmark TwinSafety, which features principled categories and presents new challenges for moderation. We show that $R^2$-Guard is effective even given unrepresentative categories or challenging jailbreaking prompts. We demonstrate the effectiveness of $R^2$-Guard by comparisons with eight strong guardrail models on six standard moderation datasets, and demonstrate the robustness of $R^2$-Guard against four SOTA jailbreaking attacks. $R^2$-Guard significantly surpasses SOTA method LlamaGuard by 12.6% on standard moderation datasets and by 59.9% against jailbreaking attacks. We further reveal that $R^2$-Guard can effectively adapt to safety category updates by simply editing the PGM reasoning graph.

The infinite width limit of random neural networks is known to result in Neural Networks as Gaussian Process (NNGP) (Lee et al. (2018)), characterized by task-independent kernels. It is widely accepted that larger network widths contribute to improved generalization (Park et al. (2019)). However, this work challenges this notion by investigating the narrow width limit of the Bayesian Parallel Branching Neural Network (BPB-NN), an architecture that resembles neural networks with residual blocks. We demonstrate that when the width of a BPB-NN is significantly smaller compared to the number of training examples, each branch exhibits more robust learning due to a symmetry breaking of branches in kernel renormalization. Surprisingly, the performance of a BPB-NN in the narrow width limit is generally superior to or comparable to that achieved in the wide width limit in bias-limited scenarios. Furthermore, the readout norms of each branch in the narrow width limit are mostly independent of the architectural hyperparameters but generally reflective of the nature of the data. We demonstrate such phenomenon primarily in the branching graph neural networks, where each branch represents a different order of convolutions of the graph; we also extend the results to other more general architectures such as the residual-MLP and demonstrate that the narrow width effect is a general feature of the branching networks. Our results characterize a newly defined narrow-width regime for parallel branching networks in general.

Benchmarking the capabilities and limitations of large language models (LLMs) in graph-related tasks is becoming an increasingly popular and crucial area of research. Recent studies have shown that LLMs exhibit a preliminary ability to understand graph structures and node features. However, the potential of LLMs in graph pattern mining remains largely unexplored. This is a key component in fields such as computational chemistry, biology, and social network analysis. To bridge this gap, this work introduces a comprehensive benchmark to assess LLMs' capabilities in graph pattern tasks. We have developed a benchmark that evaluates whether LLMs can understand graph patterns based on either terminological or topological descriptions. Additionally, our benchmark tests the LLMs' capacity to autonomously discover graph patterns from data. The benchmark encompasses both synthetic and real datasets, and a variety of models, with a total of 11 tasks and 7 models. Our experimental framework is designed for easy expansion to accommodate new models and datasets. Our findings reveal that: (1) LLMs have preliminary abilities to understand graph patterns, with O1-mini outperforming in the majority of tasks; (2) Formatting input graph data to align with the knowledge acquired during pretraining can enhance performance; (3) LLMs employ diverse potential algorithms to solve one task, with performance varying based on their execution capabilities.

Weather nowcasting is an essential task that involves predicting future radar echo sequences based on current observations, offering significant benefits for disaster management, transportation, and urban planning. Current prediction methods are limited by training and storage efficiency, mainly focusing on 2D spatial predictions at specific altitudes. Meanwhile, 3D volumetric predictions at each timestamp remain largely unexplored. To address such a challenge, we introduce a comprehensive framework for 3D radar sequence prediction in weather nowcasting, using the newly proposed SpatioTemporal Coherent Gaussian Splatting (STC-GS) for dynamic radar representation and GauMamba for efficient and accurate forecasting. Specifically, rather than relying on a 4D Gaussian for dynamic scene reconstruction, STC-GS optimizes 3D scenes at each frame by employing a group of Gaussians while effectively capturing their movements across consecutive frames. It ensures consistent tracking of each Gaussian over time, making it particularly effective for prediction tasks. With the temporally correlated Gaussian groups established, we utilize them to train GauMamba, which integrates a memory mechanism into the Mamba framework. This allows the model to learn the temporal evolution of Gaussian groups while efficiently handling a large volume of Gaussian tokens. As a result, it achieves both efficiency and accuracy in forecasting a wide range of dynamic meteorological radar signals. The experimental results demonstrate that our STC-GS can efficiently represent 3D radar sequences with over $16\times$ higher spatial resolution compared with the existing 3D representation methods, while GauMamba outperforms state-of-the-art methods in forecasting a broad spectrum of high-dynamic weather conditions.

Self-correction is a highly desirable capability of large language models (LLMs), yet it has consistently been found to be largely ineffective in modern LLMs. Current methods for training self-correction typically depend on either multiple models, a more advanced model, or additional forms of supervision. To address these shortcomings, we develop a multi-turn online reinforcement learning (RL) approach, SCoRe, that significantly improves an LLM's self-correction ability using entirely self-generated data. To build SCoRe, we first show that variants of supervised fine-tuning (SFT) on offline model-generated correction traces are insufficient for instilling self-correction behavior. In particular, we observe that training via SFT either suffers from a distribution mismatch between the training data and the model's own responses or implicitly prefers only a certain mode of correction behavior that is often not effective at test time. SCoRe addresses these challenges by training under the model's own distribution of self-generated correction traces and using appropriate regularization to steer the learning process into learning a self-correction strategy that is effective at test time as opposed to simply fitting high-reward responses for a given prompt. This regularization prescribes running a first phase of RL on a base model to generate a policy initialization that is less susceptible to collapse and then using a reward bonus to amplify self-correction during training. When applied to Gemini 1.0 Pro and 1.5 Flash models, we find that SCoRe achieves state-of-the-art self-correction performance, improving the base models' self-correction by 15.6% and 9.1% respectively on the MATH and HumanEval benchmarks.

While a number of existing approaches for building foundation model agents rely on prompting or fine-tuning with human demonstrations, it is not sufficient in dynamic environments (e.g., mobile device control). On-policy reinforcement learning (RL) should address these limitations, but collecting actual rollouts in an environment is often undesirable in truly open-ended agentic problems such as mobile device control or interacting with humans, where each unit of interaction is associated with a cost. In such scenarios, a method for policy learning that can utilize off-policy experience by learning a trained action-value function is much more effective. In this paper, we develop an approach, called Digi-Q, to train VLM-based action-value Q-functions which are then used to extract the agent policy. We study our approach in the mobile device control setting. Digi-Q trains the Q-function using offline temporal-difference (TD) learning, on top of frozen, intermediate-layer features of a VLM. Compared to fine-tuning the whole VLM, this approach saves us compute and enhances scalability. To make the VLM features amenable for representing the Q-function, we need to employ an initial phase of fine-tuning to amplify coverage over actionable information needed for value function. Once trained, we use this Q-function via a Best-of-N policy extraction operator that imitates the best action out of multiple candidate actions from the current policy as ranked by the value function, enabling policy improvement without environment interaction. Digi-Q outperforms several prior methods on user-scale device control tasks in Android-in-the-Wild, attaining 21.2% improvement over prior best-performing method. In some cases, our Digi-Q ap- proach already matches state-of-the-art RL methods that require interaction. The project is open-sourced at https://github.com/DigiRL-agent/digiq