ICLR 2026 论文列表

International Conference on Learning Representations

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5,358篇论文

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  • Oral
    2244.2%
  • Poster
    5,13495.8%

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Adaptive Debiasing Tsallis Entropy for Test-Time Adaptation

Xiangyu Wu, Dongming Jiang, Feng Yu, Yueying Tian, Jiaqi Tang, Qing-Guo Chen, Yang Yang, Jianfeng Lu

展开摘要

Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shannon Entropy (SE) at test time to measure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably results in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), a generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q^l derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE, even without hyperparameter tuning required by TE, to accurately select high-confidence views and seamlessly integrate with label adjustment strategy to enhance adaptation. Besides, our investigation reveals that both TE and ADTE can serve as direct, advanced alternatives to SE in TTA, without any other modifications. Experimental results show that ADTE outperforms state-of-the-art methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture or text prompts used. Our code is available at https://anonymous.4open.science/r/TTA-Entropy.

Poster
Text2Arch: A Dataset for Generating Scientific Architecture Diagrams from Natural Language Descriptions

Shivank Garg, Sankalp Mittal, Manish Gupta

展开摘要

Communicating complex system designs or scientific processes through text alone is inefficient and prone to ambiguity. A system that automatically generates scientific architecture diagrams from text with high semantic fidelity can be useful in multiple applications like enterprise architecture visualization, AI-driven software design, and educational content creation. Hence, in this paper, we focus on leveraging language models to perform semantic understanding of the input text description to generate intermediate code that can be processed to generate high-fidelity architecture diagrams. Unfortunately, no clean large-scale open-access dataset exists, implying lack of any effective open models for this task. Hence, we contribute a comprehensive dataset, \system, comprising scientific architecture images, their corresponding textual descriptions, and associated DOT code representations. Leveraging this resource, we fine-tune a suite of small language models, and also perform in-context learning using GPT-4o. Through extensive experimentation, we show that \system{} models significantly outperform existing baseline models like DiagramAgent and perform at par with in-context learning based generations from GPT-4o. We have added code and data as Supplementary material, and will make them (and models) publicly available on acceptance.

Poster
PoinnCARE: Hyperbolic Multi-Modal Learning for Enzyme Classification

Kun Xie, Peng Zhou, Xingyi Zhang, Wei Liu, Peilin Zhao, Sibo Wang, Biaobin Jiang

展开摘要

Enzyme Commission (EC) number prediction is vital for elucidating enzyme functions and advancing biotechnology applications. However, current methods struggle to capture the hierarchical relationships among enzymes and often overlook critical structural and active site features. To bridge this gap, we introduce PoinnCARE, a novel framework that jointly encodes and aligns multi-modal data from enzyme sequences, structures, and active sites in hyperbolic space. By integrating graph diffusion and alignment techniques, PoinnCARE mitigates data sparsity and enriches functional representations, while hyperbolic embedding preserves the intrinsic hierarchy of the EC system with theoretical guarantees in low-dimensional spaces. Extensive experiments on four datasets from the CARE benchmark demonstrate that PoinnCARE consistently and significantly outperforms state-of-the-art methods in EC number prediction.

Poster
Can Speech LLMs Think while Listening?

Yi-Jen Shih, Desh Raj, Chunyang Wu, Wei Zhou, SK Bong, Yashesh Gaur, Jay Mahadeokar, Ozlem Kalinli, Mike Seltzer

展开摘要

Recent advances in speech large language models (speech LLMs) have enabled seamless spoken interactions, but these systems still struggle with complex reasoning tasks. Previously, chain-of-thought (CoT) prompting or fine-tuning has been shown to significantly improve the reasoning abilities of text-based LLMs. In this work, we investigate the effect of CoT fine-tuning for multi-stream speech LLMs, demonstrating that reasoning in text space improves the accuracy of speech LLMs by 2.4x, on average, over a suite of spoken reasoning tasks. Beyond accuracy, the latency of the spoken response is a crucial factor for interacting with voice-based agents. Inspired by the human behavior of "thinking while listening," we propose methods to reduce the additional latency from reasoning by allowing the model to start reasoning before the user query has ended. To achieve this, we introduce an entropy-based metric, "question completeness," which acts as an indicator to guide the model on the optimal time to start reasoning. This method provides greater control over the accuracy-latency trade-off compared with heuristic-based approaches and, under equivalent latency conditions, yields a 4% accuracy gain on ARC-Easy. Finally, we use Direct Preference Optimization (DPO) on preference data created using rejection sampling to push the accuracy-latency pareto frontier further, resulting in a 70% reduction in latency without loss in accuracy.

Poster
SeeDNorm: Self-Rescaled Dynamic Normalization

Wenrui Cai, Defa Zhu, Siyuan Qiao, Qingjie Liu, Qiyang Min

展开摘要

Normalization layer constitutes an essential component in neural networks. In transformers, the predominantly used RMSNorm constrains vectors to a unit hypersphere, followed by dimension-wise rescaling through a learnable scaling coefficient $\gamma$ to maintain the representational capacity of the model. However, RMSNorm discards the input norm information in forward pass and a static scaling factor $\gamma$ may be insufficient to accommodate the wide variability of input data and distributional shifts, thereby limiting further performance improvements, particularly in zero-shot scenarios that large language models routinely encounter. To address this limitation, we propose SeeDNorm, which enhances the representational capability of the model by dynamically adjusting the scaling coefficient based on the current input, thereby preserving the input norm information and enabling data-dependent, self-rescaled dynamic normalization. During backpropagation, SeeDNorm retains the ability of RMSNorm to dynamically adjust gradient according to the input norm. We provide a detailed analysis of the training optimization for SeedNorm and proposed corresponding solutions to address potential instability issues that may arise when applying SeeDNorm. We validate the effectiveness of SeeDNorm across models of varying sizes in large language model pre-training as well as supervised and unsupervised computer vision tasks. By introducing a minimal number of parameters and with negligible impact on model efficiency, SeeDNorm achieves consistently superior performance compared to previously commonly used normalization layers such as RMSNorm and LayerNorm, as well as element-wise activation alternatives to normalization layers like DyT.

Poster
TIPO: Text to Image with Text Pre-sampling for Prompt Optimization

SHIH-YING YEH, Yi Li, SangHyun Park, Giyeong Oh, Xuehai Wang, Min Song, Youngjae Yu, Shang-Hong Lai

展开摘要

TIPO (Text-to-Image Prompt Optimization) introduces an efficient approach for automatic prompt refinement in text-to-image (T2I) generation. Starting from simple user prompts, TIPO leverages a lightweight pre-trained model to expand these prompts into richer, detailed versions. Conceptually, TIPO samples refined prompts from a targeted sub-distribution within the broader semantic space, preserving the original intent while significantly improving visual quality, coherence, and detail. Unlike resource-intensive methods based on large language models (LLMs) or reinforcement learning (RL), TIPO provides computational efficiency and scalability, opening new possibilities for effective, automated prompt engineering in T2I tasks. We provide visual results, human preference report to investigate TIPO's effectiveness. Experimental evaluations on benchmark datasets demonstrate substantial improvements in aesthetic quality, significant reduction of visual artifacts, and enhanced alignment with target distributions along with significant human preference proficiency. These results highlight the importance of targeted prompt engineering in text-to-image tasks and indicate broader opportunities for automated prompt refinement.

Poster
Closing the Gap Between Text and Speech Understanding in LLMs

Santiago Cuervo, Skyler Seto, Maureen de Seyssel, Richard He Bai, Zijin Gu, Tatiana Likhomanenko, Navdeep Jaitly, Zakaria Aldeneh

展开摘要

Large Language Models (LLMs) can be adapted to extend their text capabilities to speech inputs. However, these speech-adapted LLMs consistently underperform their text-based counterparts—and even cascaded pipelines—on language understanding tasks. We term this shortfall the text–speech understanding gap: the performance drop observed when a speech-adapted LLM processes spoken inputs relative to when the original text-based LLM processes the equivalent text. Recent approaches to narrowing this gap either rely on large-scale speech synthesis of text corpora, which is costly and heavily dependent on synthetic data, or on large-scale proprietary speech datasets, which are not reproducible. As a result, there remains a need for more data-efficient alternatives for closing the text-speech understanding gap. In this work, we analyze the gap as driven by two factors: (i) forgetting of text capabilities during adaptation, and (ii) cross-modal misalignment between speech and text. Based on this analysis, we introduce SALAD—Sample-efficient Alignment with Learning through Active selection and cross-modal Distillation—which combines cross-modal distillation with targeted synthetic data to improve alignment while mitigating forgetting. Applied to 3B and 7B LLMs, SALAD achieves competitive performance with a strong open-weight model across broad-domain benchmarks in knowledge, language understanding, and reasoning, while training on over an order of magnitude less speech data from publicly available corpora.

Poster
On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting

Wenhao Zhang, Yuexiang Xie, Yuchang Sun, Yanxi Chen, Guoyin Wang, Yaliang Li, Bolin Ding, Jingren Zhou

展开摘要

Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) are two prominent post-training paradigms for refining the capabilities and aligning the behavior of Large Language Models (LLMs). Existing approaches that integrate SFT and RL often face the risk of disrupting established response patterns and inducing overfitting to expert data. To address this, we present a novel investigation into the unified view of SFT and RL through an off-policy versus on-policy lens. We propose CHORD, a framework for Controllable Harmonization of On- and Off-Policy Reinforcement Learning via Dynamic Weighting, which reframes SFT not as a separate stage but as a dynamically weighted auxiliary objective within the on-policy RL process. Based on an analysis of off-policy expert data's influence at both holistic and granular levels, we incorporate a dual-control mechanism in CHORD. Specifically, the framework first employs a global coefficient to holistically guide the transition from off-policy imitation to on-policy exploration, and then applies a token-wise weighting function that enables granular learning from the expert, which promotes on-policy exploration and mitigates disruption from off-policy data. We conduct extensive experiments on mathematical reasoning problems and practical tool-use tasks, providing empirical evidence that CHORD achieves a stable and efficient learning process. By effectively harmonizing off-policy expert data with on-policy exploration, CHORD demonstrates significant improvements over baselines. We will release the source code to inspire further research.

Poster
Stop Tracking Me! Proactive Defense Against Attribute Inference Attack in LLMs

Dong Yan, Jian Liang, Ran He, Tieniu Tan

展开摘要

Recent studies have shown that large language models (LLMs) can infer private user attributes (e.g., age, location, gender) from user-generated text shared online, enabling rapid and large-scale privacy breaches. Existing anonymization-based defenses are coarse-grained, lacking word-level precision in anonymizing privacy-leaking elements. Moreover, they are inherently limited as altering user text to hide sensitive cues still allows attribute inference to occur through models' reasoning capabilities. To address these limitations, we propose a unified defense framework that combines fine-grained anonymization (TRACE) with inference-preventing optimization (RPS). TRACE leverages attention mechanisms and inference chain generation to identify and anonymize privacy-leaking textual elements, while RPS employs a lightweight two-stage optimization strategy to induce model rejection behaviors, thereby preventing attribute inference. Evaluations across diverse LLMs show that TRACE-RPS reduces attribute inference accuracy from around 50\% to below 5\% on open-source models. In addition, our approach offers strong cross-model generalization, prompt-variation robustness, and utility-privacy tradeoffs.

Poster
Reinforcement Learning from Dynamic Critic Feedback for Free-Form Generations

Mian Wu, Gavin Zhang, Sewon Min, Sergey Levine, Aviral Kumar

展开摘要

Open-ended generation tasks require outputs to satisfy diverse and often implicit task-specific evaluation rubrics. The sheer number of relevant rubrics leads to prohibitively high verification costs and incomplete assessments of a response, making reinforcement learning (RL) post-training with rubric-based rewards difficult to scale. This problem is exacerbated by the fact that often the best way to combine these rubrics into one single reward is also highly prompt-specific. We propose Reinforcement Learning from Dynamic Critic Feedback (RLDCF), a post-training approach that addresses these challenges via dynamic rubric verification. Our approach employs a large language model (LLM) as a critic that dynamically identifies only the most likely failure modes (e.g., a factual error or unhandled edge case), which are then verified by an external validator to optimize both generator and critic jointly. By training both the generator and the critic, this game enhances the critic's error detection and the generator's output quality while reducing required verifications. Our experiments demonstrate that RLDCF improves factual accuracy in text generation and correctness in code generation, while also outperforming exhaustive verification and reward model methods. We show that dynamic critics are more effective than fixed critics, showcasing the potential of RLDCF for scaling RL post-training to free-form generation tasks.

Poster
Zero-Shot Adaptation of Behavioral Foundation Models to Unseen Dynamics

Maksim Bobrin, Ilya Zisman, Alexander Nikulin, Vladislav Kurenkov, Dmitry V. Dylov

展开摘要

Behavioral Foundation Models (BFMs) proved successful in producing near-optimal policies for arbitrary tasks in a zero-shot manner, requiring no test-time retraining or task-specific fine-tuning. Among the most promising BFMs are the ones that estimate the successor measure learned in an unsupervised way from task-agnostic offline data. However, these methods fail to react to changes in the dynamics, making them inefficient under partial observability or when the transition function changes. This hinders the applicability of BFMs in a real-world setting, e.g., in robotics, where the dynamics can unexpectedly change at test time. In this work, we demonstrate that Forward–Backward (FB) representation, one of the methods from the BFM family, cannot produce reasonable policies under distinct dynamics, leading to an interference among the latent policy representations. To address this, we propose an FB model with a transformer-based belief estimator, which greatly facilitates zero-shot adaptation. Additionally, we show that partitioning the policy encoding space into dynamics-specific clusters, aligned with the context-embedding directions, yields additional gain in performance. Those traits allow our method to respond to the dynamics mismatches observed during training and to generalize to unseen ones. Empirically, in the changing dynamics setting, our approach achieves up to a 2x higher zero-shot returns compared to the baselines for both discrete and continuous tasks.

Poster
AlphaBench: Benchmarking Large Language Models in Formulaic Alpha Factor Mining

Haochen Luo, Ho Tin Ko, Jiandong Chen, David Sun, Yuan Zhang, Chen Liu

展开摘要

Formulaic alpha factor mining (FAFM) is a central problem in quantitative investment, where interpretable formulas are designed to extract predictive signals from historical financial series. With the emergence of large language models (LLMs), recent studies have begun to explore their roles in FAFM, yet their capabilities across different tasks and configurations remain unclear. In this work, we introduce AlphaBench, the first systematic benchmark for evaluating LLMs in FAFM. AlphaBench covers three core tasks, including factor generation, factor evaluation, and factor searching, which are all popular tasks integrated in the workflow of quantitative researchers. Beyond task-level evaluation, we further analyze how different LLM settings, including model type, prompting paradigm, and reasoning strategy, influence performance. Our experiments on a range of open-source and closed-source models reveal that LLMs hold strong potential in automating factor mining, while also facing persistent challenges in robustness, search efficiency, and practical usability. The project is available at: https://alphabench.cc/

Poster
Revisiting Confidence Calibration for Misclassification Detection in VLMs

Jincheng Huang, Jie Xu, Xiaoshuang Shi, Ping Hu, Lei Feng, Xiaofeng Zhu

展开摘要

Confidence calibration has been widely studied to improve the trustworthiness of predictions in vision-language models (VLMs). However, we theoretically reveal that standard confidence calibration inherently _impairs_ the ability to distinguish between correct and incorrect predictions (i.e., Misclassification Detection, MisD), which is crucial for reliable deployment of VLMs in high-risk applications. In this paper, we investigate MisD in VLMs and propose confidence recalibration to enhance MisD. Specifically, we design a new confidence calibration objective to replace the standard one. This modification theoretically achieves higher precision in the MisD task and reduces the mixing of correct and incorrect predictions at every confidence level, thereby overcoming the limitations of standard calibration for MisD. As the calibration objective is not differentiable, we introduce a differentiable surrogate loss to enable better optimization. Moreover, to preserve the predictions and zero-shot ability of the original VLM, we develop a post-hoc framework, which employs a lightweight meta network to predict sample-specific temperature factors, trained with the surrogate loss. Extensive experiments across multiple metrics validate the effectiveness of our approach on MisD.

Poster
Measure Twice, Cut Once: A Semantic-Oriented Approach to Video Temporal Localization with Video LLMs

Zongshang Pang, Mayu Otani, Yuta Nakashima

展开摘要

Temporally localizing user-queried events through natural language is a crucial capability for video models. Recent methods predominantly adapt video LLMs to generate event boundary timestamps for temporal localization tasks, which struggle to leverage LLMs' pre-trained semantic understanding capabilities due to the uninformative nature of timestamp outputs. In this work, we explore a timestamp-free, semantic-oriented framework that fine-tunes video LLMs using two generative learning tasks and one discriminative learning task. We first introduce a structural token generation task that enables the video LLM to recognize the temporal structure of input videos based on the input query. Through this task, the video LLM generates a sequence of special tokens, called structural tokens, which partition the video into consecutive segments and categorize them as either target events or background transitions. To enhance precise recognition of event segments, we further propose a query-focused captioning task that enables the video LLM to extract fine-grained event semantics that can be effectively utilized by the structural tokens. Finally, we introduce a structural token grounding module driven by contrastive learning to associate each structural token with its corresponding video segment, achieving holistic temporal segmentation of the input video and readily yielding the target event segments for localization. Extensive experiments across diverse temporal localization tasks demonstrate that our proposed framework, MeCo, consistently outperforms methods relying on boundary timestamp generation, highlighting the potential of a semantic-driven approach for temporal localization with video LLMs.

Poster
HierLoc: Hyperbolic Entity Embeddings for Hierarchical Visual Geolocation

Hari Krishna Gadi, Daniel Matos, Hongyi Luo, Lu Liu, Yongliang Wang, Yanfeng Zhang, Liqiu Meng

展开摘要

Visual geolocalization, the task of predicting where an image was taken, remains challenging due to global scale, visual ambiguity, and the inherently hierarchical structure of geography. Existing paradigms rely on either large-scale retrieval, which requires storing a large number of image embeddings, grid-based classifiers that ignore geographic continuity, or generative models that diffuse over space but struggle with fine detail. We introduce an entity-centric formulation of geolocation that replaces image-to-image retrieval with a compact hierarchy of geographic entities embedded in Hyperbolic space. Images are aligned directly to country, region, subregion, and city entities through Geo-Weighted Hyperbolic contrastive learning by directly incorporating haversine distance into the contrastive objective. This hierarchical design enables interpretable predictions and efficient inference with 240k entity embeddings instead of over 5 million image embeddings on the OSV5M benchmark, on which our method establishes a new state-of-the-art performance. Compared to the current methods in the literature, it reduces mean geodesic error by 19.5\%, while improving the fine-grained subregion accuracy by 43\%. These results demonstrate that geometry-aware hierarchical embeddings provide a scalable and conceptually new alternative for global image geolocation.

Poster
CPQS-Tuning: A Model Self-Perception-Based Data Filtering Algorithm for Efficient Instruction Fine-Tuning

Yi Ren, Yanhui Li, Tianyi Zhang, Diandong Liu

展开摘要

Instruction fine-tuning is a key technique for enhancing the performance of large language models (LLMs), but low-quality and redundant data often hinder its effectiveness. Recent studies suggest that filtering a small amount of high-quality data for instruction fine-tuning can achieve faster and more efficient training performance. However, existing data filtering approaches predominantly depend on predefined evaluation models or manually designed metrics, without leveraging information from the target LLM itself. This limitation may result in a mismatch between the filtering criteria and the actual requirements of the LLM being fine-tuned, thereby reducing the effectiveness of the fine-tuning process. To address these issues, we propose a novel perspective: the hidden states of LLMs implicitly reflect the quality of the training data. Based on this insight, we propose a novel data filtering method that extracts the hidden states that reflect the target LLM’s perception of the data as representative features, and builds a data classification model upon them, which outputs the Contrastive Perception Quality Score (CPQS) for dataset filtering. Our experiments are conducted in both general and downstream domains. (1) In the general domain, our experiments show that training on under 10\% of the data from both the Alpaca\_GPT4 and DeepSeek-R1 synthesized reasoning datasets enables our method to outperform models trained on the complete datasets. Moreover, it surpasses the performance of current state-of-the-art data-selection techniques. (2) In downstream tasks, our approach delivers an average performance gain exceeding 3.6\% over leading data-selection algorithms across multiple benchmarks, including GSM8K, HumanEval, and HumanEval-Plus.

Poster
A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling

Jacob Helwig, Sai Sreeharsha Adavi, Xuan Zhang, Yuchao Lin, Felix S. Chim, Luke Takeshi Vizzini, Haiyang Yu, Muhammad Hasnain, Saykat Kumar Biswas, John J. Holloway, Narendra Singh, N. K. Anand, Swagnik Guhathakurta, Shuiwang Ji

展开摘要

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. We evaluate our methods by generating three supersonic flow datasets.

Poster
Mitigating Privacy Risk via Forget Set-Free Unlearning

Aviraj Newatia, Michael Cooper, Viet Nguyen, Rahul G. Krishnan

展开摘要

Training machine learning models requires the storage of large datasets, which often contain sensitive or private data. Storing data is associated with a number of potential risks which increase over time, such as database breaches and malicious adversaries. Machine unlearning is the study of methods to efficiently remove the influence of training data subsets from previously-trained models. Existing unlearning methods typically require direct access to the "forget set"---the data to be forgotten-and organisations must retain this data for unlearning rather than deleting it immediately upon request, increasing risks associated with the forget set. We introduce partially-blind unlearning---utilizing auxiliary information to unlearn without explicit access to the forget set. We introduce a practical framework Reload, a partially-blind method based on gradient optimization and structured weight sparsification to operationalize partially-blind unlearning. We show that Reload efficiently unlearns, approximating models retrained from scratch, and outperforms several forget set-dependent approaches. On language models, Reload unlearns entities using <0.025\% of the retain set and <7\% of model weights in <8 minutes on Llama2-7B. In the corrective case, Reload achieves unlearning even when only 10\% of corrupted data is identified.

Poster
From Utterance to Vividity: Training Expressive Subtitle Translation LLM via Adaptive Local Preference Optimization

Chaoqun Cui, Shijing Wang, Liangbin Huang, Qingqing Gu, Zhaolong Huang, Xiao Zeng, Wenji Mao

展开摘要

The rapid development of Large Language Models (LLMs) has significantly enhanced the general capabilities of machine translation. However, as application scenarios become more complex, the limitations of LLMs in vertical domain translations are gradually becoming apparent. In this study, we focus on how to construct translation LLMs that meet the needs of domain customization. We take visual media subtitle translation as our topic and explore how to train expressive and vivid translation LLMs. We investigated the situations of subtitle translation and other domains of literal and liberal translation, verifying the reliability of LLM as reward model and evaluator for translation. Additionally, to train an expressive translation LLM, we constructed and released a multidirectional subtitle parallel corpus dataset and proposed the Adaptive Local Preference Optimization (ALPO) method to address fine-grained preference alignment. Experimental results demonstrate that ALPO achieves outstanding performance in multidimensional evaluation of translation quality.

Poster
Physics-Informed Inference Time Scaling for Solving High-Dimensional Partial Differential Equations

Zexi Fan, Yan Sun, Shihao Yang, Yiping Lu

展开摘要

Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning (SCaSML), a framework that systematically improves pre-trained PDE solvers at inference time without any retraining. Our core idea is to derive a new PDE, which we term the Law of Defect, that precisely governs the error of a given surrogate model. Because this defect PDE retains the structure of the original problem, we can solve it efficiently with traditional stochastic simulators, yielding a targeted correction to the initial machine-learned solution. We prove that SCaSML achieves a faster convergence rate, with a final error bounded by the product of the surrogate and simulation errors. On challenging PDEs up to 160 dimensions, SCaSML reduces the error of various surrogate models, including PINNs and Gaussian Processes, by 20-80%. SCaSML provides a principled method to fuse the speed of machine learning with the rigor of numerical simulation, enhancing the trustworthiness of Al for scientific discovery.

Poster